# Preprints - Theory

The information that appears here has been provided by the different authors. The rather arbitrary ordering of the papers corresponds to the order in which the authors have informed the network. In principle the scope of the list is restricted to those papers written in the realm of Defect Formation and Non-equilibrium Field Theory, with support from the ESF. The links to abstract, source, other formats, and authors' list of papers are to the Spanish mirror of the xxx archives. After each entry, however, links have been set up to the postscript files located at the Los Alamos server and to the European mirrors. It is not unlikely (actually, it is very likely) that errors in the links will have escaped my attention. If so, please let me know.

### astro-ph/9703005 [abs, src, ps, other] :

Title: Primordial magnetic fields, righthanded electrons, and the abelian anomaly

Authors: M. Joyce, M. Shaposhnikov.
Journal-ref.: Phys.Rev.Lett. 79 (1997) 1193-1196

In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the GUT scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ($\sim 10^{22}$ gauss at $T\sim 100$ GeV with typical inhomogeneity scale $\sim \frac{ 10^6}{T}$) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms. Previously derived bounds on exotic $B-L$ violating operators may also be evaded.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9708303 [abs, src, ps, other] :

Title: Primordial magnetic fields, anomalous isocurvature fluctuations and Big Bang nucleosynthesis

Authors: M. Giovannini, M. Shaposhnikov.

We show that the presence of primordial stochastic (hypercharge) magnetic fields before the electroweak (EW) phase transition induces isocurvature fluctuations (baryon number inhomogeneities). Depending on the details of the magnetic field spectrum and on the particle physics parameters (such as the strength of the EW phase transition and electron Yukawa couplings) these fluctuations may survive until the Big Bang nucleosynthesis (BBN). Their lenghtscale may exceed the neutron diffusion length at that time, while their magnitude can be so large that sizable antimatter domains are present. This provides the possibility of a new type of initial conditions for non-homogeneous BBN or, from a more conservative point of view, stringent bounds on primordial magnetic fields.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9710234 [abs, src, ps, other] :

Title: Primordial Hypermagnetic Fields and Triangle Anomaly

Authors: M. Giovannini, M. Shaposhnikov.

The high-temperature plasma above the electroweak scale $\sim 100$ GeV may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number. In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case. We show that a not completely homogeneous hypermagnetic background induces fermion number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration. We argue that, depending upon the various particle physics parameters involved in our estimate (electron Yukawa coupling, strength of the electroweak phase transition) and upon the hypermagnetic energy spectrum, sizeable matter-antimatter fluctuations can be generated in the plasma. These fluctuations may modify the predictions of the standard Big Bang nucleosynthesis (BBN). We derive constraints on the magnetic fields from the requirement that the homogeneous BBN is not changed. We analyse the influence of primordial magnetic fields on the electroweak phase transition and show that some specific configurations of the magnetic field may be converted into net baryon number at the electroweak scale.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9711031 [abs, src, ps, other] :

Title: Superfluid 3He, Particle Physics and Cosmology

Authors: G.E. Volovik.

Superfluid 3He-A and high-temperature superconductors both have gapless fermionic quasiparticles with the "relativistic" spectrum close to the gap nodes. The interaction of these "relaitivistic" fermions with bosonic collective modes of the order parameter is described by the quantum field theory, which results in a close connection with particle physics. Many phenomena in high-energy physics and cosmology can thus be simulated in superfluid phases of 3He and in unconventional superconductors. This includes axial anomaly, vacuum polarization, zero-charge effect, fermionic charge of the vacuum, baryogenesis, event horizon, vacuum instability, Hawking radiation, etc. Analogs of some of these phenomena, which are related to the axial anomaly, have been experimentally simulated in superfluid 3He. This includes the baryogenesis by textures (Manchester), the baryogenesis by cosmic strings (Manchester) and the generation of the primordial magnetic field via the axial anomaly (Helsinki).

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9709159 [abs, src, ps, other] :

Title: Fermions in the vortex core as edge states

Authors: G.E. Volovik.

The splitting of the spectrum of the electronic bound states in the vortex core with broken parity and axisymmetry is dicussed using (i) the phenomenological approach, and (ii) the simple model, in which the vortex core is represented by the vortex sheet of the radius R much larger than the coherence length. In this model the bound states are concentrated in the vortex sheet and represent the chiral edge states similar to that in Quantum Hall Effect. The fermions are 1D particles with the "relativistic" spectrum moving in the direction determined by the sign of the winding number. This motion is governed by the effective gauge and gravity fields simulated by the order parameter texture. For the vortex with winding number n=1 the effective "electric" charge of the fermion changes sign after the fermion trajectory encloses the vortex axis. This phenomenon is similar to that in the Alice cosmic string. The energy levels are obtained by quasiclassical quantization of the fermion motion on closed classical trajectories along the sheet. We found that the energy levels remain equidistant even in the presence of the broken symmetry fields. This conradicts to the Feigel'man and Skvortsov (Phys. Rev. Lett. 78 (1997) 2640) suggestion that the spectrum becomes chaotic in the presence of impurities. For the vortex with winding number n=1 we found that the symmetry violation leads to the splitting of the spectrum into two sub-branches. The levels on each sub-branch are equidistant, but the sub-branches are symmetrically shifted from each other. This is similar to what was found by Larkin and Ovchinnikov in a recent preprint cond-mat/9708202 for the case when the symmetry is violated by impurities.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9706172 [abs, src, ps, other] :

Title: Simulation of Quantum Field Theory and Gravity in Superfluid He-3

Authors: G.E. Volovik.
Journal-ref.: Low Temp. Phys. (Kharkov) 24 (1998) 127-129.

Superfluid phases of 3He are quantuim liquids with the interacting fermionic and bosonic fields. In many respects they can simulate the interacting quantum fields in the physcal vacuum. One can observe analogs of such phenomena as axial anomaly, vacuum polarization, zero-charge effect, fermionic charge of the vacuum, baryogenesis, ergoregion, vacuum instability, etc. We discuss some topics on example of several linear defects in 3He-A: (1) disgyration, which simulates the extremely massive cosmic string: (2) singular vortex, which is analogous to the spinning cosmic string; and (3) continuous vortex, which motion causes the "momentogenesis" which is the analog of baryogenesis in early Universe. The production of the fermionic momentum by the vortex motion (the counterpart of the electroweak baryogenesis) has been recently measured in Manchester experiments on rotating superfluid 3He-A and 3He-B. To simulate the other phenomena one needs rather low temperature and high homogeneity, which probably can be reached under microgravity conditions.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9706149 [abs, src, ps, other] :

Title: Baryon Asymmetry of Universe: View from Superfluid 3He

Authors: G.E. Volovik.
Journal-ref.: J. Low Temp. Phys. 110 (1998) 23-37.

The origin of the excess of matter over antimatter in our Universe remains one of the fundamental problems. The dynamical baryogenesis in the process of the broken symmetry electroweak transition in the expanding Universe is the widely discussed model where the baryonic asymmetry is induced by the quantum chiral anomaly. We discuss the modelling of this phenomenon in superfluid 3He and superconductors where the chiral anomaly is realized in the presence of quantized vortex, which introduces the nodes in the energy spectrum of the fermionic quasiparticles. The spectral flow of fermions through the nodes during the vortex motion leads to creation of the fermionic charge from the superfluid vacuum and to transfer of the superfluid linear momentum into the heat bath, thus producing an extra force on the vortex, which in some cases compensates the Magnus force. This spectral-flow force was calculated 20 years ago by Kopnin and Kravtsov for s-wave superconductors, but only recently it was measured in a broad temperature range in Manchester experiments on rotating superfluid 3He. The "momentogenesis" observed in 3He is analogous to the dynamical production of the baryons by cosmic strings. Some other possible scenaria of the baryogenesis related to superfluid 3He are discussed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9706082 [abs, src, ps, other] :

Title: Rotating vortex core: An instrument for detecting the core excitations

Authors: N.B. Kopnin, G.E. Volovik.
Journal-ref.: Phys. Rev. B 57 (1998) 8526-8531.

Effects of fermionic zero modes (bound states in a vortex core) on the rotational dynamics of vortices with sponaneously broken axisymmetry are considered. The results are compared with the Helsinki experiments where the vortex cores were driven to a fast rotation and torsional oscillations by an NMR r.f. field (Kondo et al, Phys. Rev. Lett. 67, 81 (1991)). We predict a resonance NMR absorption on localized states at the external frequency comparable with the interelevel distance, which is similar to the cyclotron Landau damping. The resonances can experimentally resolve the localized levels in vortex cores. For a pure rotation of the core, the effect depends on the relative signs of the vortex winding number and of the core rotation; thus it is sensitive to the direction of rotation of the container. The similarity with the fermionic zero modes on the fundamental strings, which simulate the thermodynamics of black holes, is discussed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9706327 [abs, src, ps, other] :

Title: Baryon Density in the Central Region of a Heavy-Ion Collision

Authors: Alasdair James Gill.

The O(4) linear sigma model of the chiral transition in QCD is similar to models of the superfluid transition in 4He and 3He. Observations of vortex formation in superfluid helium have recently improved the understanding of the dynamics of such transitions. This is exploited to estimate the baryon density in the central region of a heavy ion region and the result is consistent with the long held belief that this density is very small in comparison with the pion density.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### Defects and... [No archive source] :

Title: Defects and the Dynamics of Phase Transitions

Authors: Alasdair James Gill.
Journal-ref.: Accepted for publication in Contemporary Physics.

Phase transitions are one of the most common physical phenomena. Symmetry-breaking phase transitions where a system not only changes it's state but also changes its symmetry properties are a particularly interesting example of this phenomenon and the dynamics of how the phase transition occurs in this case is extremely generic. One particular generic feature is the formation of topological defects during many of these transitions. In this article we explore the physical reasons for such universal behaviour and then go on to describe how the researchers involved have exploited the formation of topological defects to improve our understanding of the dynamics of symmetry-breaking phase transitions.

### hep-ph/9708215 [abs, src, ps, other] :

Title: The Thermodynamics of Cosmic String densities in U(1) Scalar Field Theory

Authors: Luis M. A. Bettencourt, Nuno D. Antunes, Mark Hindmarsh.

We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both for the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are show to correspond to the infinite temperature limit of the theory.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9709232 [abs, src, ps, other] :

Title: Non-Perturbative Quantum Dynamics of a New Inflation Model

Authors: D. Boyanovsky, D. Cormier, H. J. de Vega, R. Holman, S. P. Kumar.

We consider an O(N) model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to new inflation' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. We show how this reinterpretation saves the standard picture of how metric perturbations are generated during inflation and that the spinodal growth of fluctuations dominates the time dependence of the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturbations and argue that in all models of this type the spinodal instabilities are responsible for a red' spectrum of primordial scalar density perturbations. A criterion for the validity of these models is provided and contact with the reconstruction program is established validating some of the results within a non-perturbative framework. The decoherence aspects and the quantum to classical transition through inflation are studied in detail by following the full evolution of the density matrix and relating the classicality of cosmological perturbations to that of long-wavelength matter fluctuations.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9801031 [abs, src, ps, other] :

Title: Thermo Field Dynamics and quantum algebras

Authors: E. Celeghini, S. De Martino, S. De Siena, A. Iorio, M. Rasetti, G. Vitiello.

The algebraic structure of Thermo Field Dynamics lies in the $q$-deformation of the algebra of creation and annihilation operators. Doubling of the degrees of freedom, tilde-conjugation rules, and Bogoliubov transformation for bosons and fermions are recognized as algebraic properties of $h_{q}(1)$ and of $h_{q}(1|1)$, respectively.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9802217 [abs, src, ps, other] :

Title: Images and nonlocal vortex pinning in thin superfluid films

Authors: H. H. Lee, J. M. F. Gunn.

For thin films of superfluid adsorbed on a disordered substrate, we derive the equation of motion for a vortex in the presence of a random potential within a mean field (Hartree) description of the condensate. The compressible nature of the condensate leads to an effective pinning potential experienced by the vortex which is nonlocal, with a long range tail that smoothes out the random potential coupling the condensate to the substrate. We interpret this nonlocality in terms of images, and relate the effective potential governing the dynamics to the pinning energy arising from the expectation value of the Hamiltonian with respect to the vortex wavefunction.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9802091 [abs, src, ps, other] :

Title: Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki

Authors: G. E. Volovik.
Journal-ref.: Physica B 255 (1998) 86-107.

The gapless fermionic excitations in superfluid 3He-A have "relativistic" spectrum close to the gap nodes. They are the counterpart of the chiral particles (left-handed and right-handed) in high energy physics above the electroweak transition. We discuss the effective gravity and the effective gauge fields, induced by these massless fermions in the low-energy corner. The interaction of the chiral fermions with the gauge field in 3He-A is discussed in detail. It gives rise to the effect of axial anomaly: conversion of the charge from the coherent motion of the condensate (vacuum) to the quasiparticles (matter). The charge of the quasiparticles is thus not conserved: in other words the matter can be created without creating antimatter. This effect is instrumental for the vortex dynamics, in which the vortex is the mediator of the conversion of the linear momentum from the condensate to the normal component via the spectral flow in the vortex core. The same effect leads to the instability of the counterflow in 3He-A, in which the flow of the normal component (incoherent degrees of freedom) is transformed to the order parameter texture (coherent degrees of freedom). We discuss the analogs of these phenomena in high energy physics. The conversion of the momentum from the vortex to the heat bath is equivalent to the nonconservation of baryon number in the presence of textures and cosmic strings. The counterflow instability is equivalent to the generation of the hypermagnetic field via the axial anomaly. We discuss also an analog of axions and different sources of the mass of the "hyperphoton" in 3He-A.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9803355 [abs, src, ps, other] :

Title: Core Phase Structure of Cosmic Strings and Monopoles

Authors: Axenides M., Perivolaropoulos L., Tomaras T. .

Global and local symmetries may or may not be restored inside topological defects depending upon the values of the parameters of the model. A detailed study of this parameter dependence of the core structure of strings and monopoles is presented in the context of simple models.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9801232 [abs, src, ps, other] :

Title: Phase Transitions in the Core of Global Embedded Defects

Authors: Minos Axenides, Leandros Perivolaropoulos, Mark Trodden.

We demonstrate the existence of global monopole and vortex configurations whose core exhibits a phase structure. We determine the critical values of parameters for which the transition from the symmetric to the non-symmetric phase occurs and discuss the novel dynamics implied by the non-symmetric cores for defect interactions. We model phase transitions in the core of global embedded topological defects by identifying the relevant parameters with the vacuum expectation value of a dynamical scalar field. Finally, we argue that superheavy defects that undergo a core phase transition in the very early universe provide a novel realization for topological inflation.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9803184 [abs, src, ps, other] :

Title: Regularization schemes and the multiplicative anomaly

Authors: T. S. Evans .

I study the regularization of the effective action of two free Euclidean scalar fields in flat space. Elizalde, Vanzo, and Zerbini have shown that in this case with zeta-function regularization one finds a multiplicative anomaly', which is related to the Wodzicki residue. I show that there is no anomaly when using a wide range of other regularization schemes. I then show that a similar anomaly exists when considering mass shifts of a single free scalar field but again only under zeta-function regularization. Thus the multiplicative anomaly is regularization dependent and can have no physical relevance. Some dangerous aspects of zeta-function regularization have thus been illustrated.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9803303 [abs, src, ps, other] :

Title: Cosmic Strings in Low Mass Higgs Cosmology

Authors: Warren B. Perkins, Anne-Christine Davis.

A class of grand unified theories with symmetry breaking scale of order $10^{16} GeV$ have a Higgs particle with mass in the $TeV$ scale. The cosmology of such theories is very different from usual. We study the cosmic strings obtained in such theories. These strings are much fatter than usual and their mass per unit length is reduced, resulting in a significant reduction in their cosmological effects. We also study the temperature evolution of such models.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9712125 [abs, src, ps, other] :

Title: Geometric Laws of Vortex Quantum Tunneling

Authors: Uwe R. Fischer.

In the semiclassical domain the exponent of vortex quantum tunneling is dominated by a volume which is associated with the path the vortex line traces out during its escape from the metastable well. We explicitly show the influence of geometrical quantities on this volume by describing point vortex motion in the presence of an ellipse. It is argued that for the semiclassical description to hold the introduction of an additional geometric constraint, the distance of closest approach, is required. This constraint implies that the semiclassical description of vortex nucleation by tunneling at a boundary is in general not possible. Geometry dependence of the tunneling volume provides a means to verify experimental observation of vortex quantum tunneling in the superfluid Helium II.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9802241 [abs, src, ps, other] :

Title: Quantum Field Theory of Vortices in Superfluid Films

Authors: Joerg P. Kottmann, Adriaan M. J. Schakel

A quantum field theory, consisting of the effective action of sound waves linearly coupled to a Chern-Simons term, is proposed to describe the dynamics of vortices in a superfluid film at the absolute zero of temperature.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9805152 [abs, src, ps, other] :

Title: Boulevard of Broken Symmetries

Effective theories of quantum liquids (superconductors and superfluids of various types) are derived starting from microscopic models at the absolute zero of temperature. Special care is taken to assure Galilei invariance. The effective theories are employed to investigate the quantum numbers carried by the topological defects present in the phases with spontaneously broken symmetries. Due to topological terms induced by quantum fluctuations, these numbers are sometimes found to be fractional. The zero-temperature effective theories are further used to study the quantum critical behavior of the liquid-to-insulator transition which these systems undergo as the applied magnetic field, the amount of impurities, or the charge carrier density varies. The classical, finite-temperature phase transitions to the normal state are discussed from the point of view of dual theories, where the defects of the original formulation become the elementary excitations. A connection with bosonization is pointed out.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9806010 [abs, src, ps, other] :

Title: Induced Gravity in Superfluid 3He

Authors: G.E. Volovik
Journal-ref.: J. Low Temp. Phys. 113 (1998) 667-680.

The gapless fermionic excitations in superfluid 3He-A have the "relativistic" spectrum close to the gap nodes. This allowed us to model the modern cosmological scenaria of baryogenesis and magnetogenesis. The same massless fermions induce another low-energy property of the quantum vacuum -- the gravitation. The effective metric of the space, in which the free quasiparticles move along geodesics, is not generally flat. Different order parameter textures correspond to curved effective space and produce many different exotic metrics, which are theoretically discussed in quantum gravity and cosmology. This includes the condensed matter analog of the black hole and event horizon, which can be realized in the moving soliton. This will allow us to simulate and thus experimentally investigate such quantum phenomena as the Hawking radiation from the horizon, the Bekenstein entropy of the black hole, and the structure of the quantum vacuum behind the horizon. One can also simulate the conical singularities produced by cosmic strings and monopoles; inflation; temperature dependence of the cosmological and Newton constants, etc.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9804308 [abs, src, ps, other] :

Title: Vortex vs spinning string: Iordanskii force and gravitational Aharonov-Bohm effect

Authors: G.E. Volovik
Journal-ref.: JETP Lett. 67 (1998) 881 - 887.

We discuss the transverse force acting on the spinning cosmic string, moving in the background matter. It comes from the gravitational Aharonov-Bohm effect and corresponds to the Iordanskii force acting on the vortex in superfluids, when the vortex moves with respect to the normal component of the liquid.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9804078 [abs, src, ps, other] :

Title: Gravity of Monopole and String and Gravitational Constant in 3He-A

Authors: G.E. Volovik
Journal-ref.: JETP Lett. 67 (1998) 698 - 704.

We discuss the effective metric produced in superfluid 3He-A by such topological objects as radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole correspondingly. But in 3He-A they have the negative angle deficit, which corresponds to the negative mass of the topological objects. The effective gravitational constant G in superfluid 3He-A, derived from the comparison with relativistic theories, is inversely proportional to the square of the gap amplitude Delta, which plays the part of the Planck energy cut-off. G depends on temperature and increases with T, which corresponds to the vacuum screening of the Newton's constant.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### Cosmic strings and foams... [No archive source] :

Title: Formation of cosmic strings as a foaming transition

Authors: N. Pittet (GMCM, Université de Rennes 1, 35042 Rennes, France), N. Rivier (LDFC), S. Correia (LPT, Universit é Louis Pasteur, 67084 Strasbourg, France)

The formation of cosmic strings (which can be made in He3 [1]) is simulated by modelling the foaming transition [2]. The thermodynamics of foaming can be described as the nucleation of gas bubbles at random positions and times in a liquid matrix. Supercritical bubbles grow until they touch. A network of contacts between bubbles, a random graph, is built up progressively, through the growth of its vertices which stops when an edge (contact) is established [2]. Let the nucleated bubbles (each representing now a Higgs vacuum) have also a random phase. We model the formation of a graph as a graded structure. The dynamics on vertices stops when edges are established. At this point begins the dynamics of edges (phase equalization) which stops when non-trivial simplices are formed. These non-trivial simplices surround the cosmic strings. The number of cosmic strings increases as a power law with time. The density of cosmic strings is large (< 25% in 2D), much larger than that obtained in simulations on lattices, and close to the estimate of trapped flux in superconductors. This work is the result of a network supported by the European Science Foundation.

[1] Bäuerle, C. Bunkov Y.M., Fisher S.N., Godfrin H. and Pickett G.R., La Recherche 291 (1996) 26.

[2] Pittet, N., PhD Thesis, Strasbourg 1997. Chapters by N. Pittet and N. Rivier, in Foams and Emulsions, ed. by J.F Sadoc and N. Rivier, Kluwer 1998, p.563.

### hep-th/9811185 [abs, src, ps, other] :

Title: Vortex Line Nucleation of First-Order Transition U(1)-Symmetric Field Systems

Authors: H. Kleinert

We show that in field systems with U(1)-symmetry, first-order transitions are nucleated by vortex lines, not bubbles, thus calling for a reinvestigation of the Kibble mechanism for the phase transition of the early universe.

Comment: Author Information under this http URL. Latest update of paper also at this http URL.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### gr-qc/9811014 [abs, src, ps, other] :

Title: Effective spacetime and Hawking radiation from moving domain wall in thin film of 3He-A

Authors: T.A. Jacobson and G.E. Volovik
Journal-ref.: JETP Lett. 68 (1998) 874-880.

An event horizon for "relativistic" fermionic quasiparticles can be constructed in a thin film of superfluid 3He-A. The quasiparticles see an effective "gravitational" field which is induced by a topological soliton of the order parameter. Within the soliton the "speed of light" crosses zero and changes sign. When the soliton moves, two planar event horizons (black hole and white hole) appear, with a curvature singularity between them. Aside from the singularity, the effective spacetime is incomplete at future and past boundaries, but the quasiparticles cannot escape there because the nonrelativistic corrections become important as the blueshift grows, yielding "superluminal" trajectories. The question of Hawking radiation from the moving soliton is discussed but not resolved.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9705134 [abs, src, ps, other] :

Title: Double Universe

Authors: E. Alfinito, R. Manka, G. Vitiello

We discuss the canonical quantization of non-unitary time evolution in inflating Universe. We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics, thus exhibiting the link between inflationary evolution and thermal properties. In particular we discuss the entropy and the free energy of the system. The state space splits into many unitarily inequivalent representations of the canonical commutation relations parametrized by time $t$ and non-unitary time evolution is described as a trajectory in the space of the representations: the system evolves in time by running over unitarily inequivalent representations. The generator of time evolution is related to the entropy operator. A central ingredient in our discussion is the doubling of the degrees of freedom which turns out to be the bridge to the unified picture of non-unitary time evolution, squeezing and thermal properties in inflating metrics.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### gr-qc/9807002 [abs, src, ps, other] :

Title: Canonical Quantization and Expanding Metrics

Authors: E. Alfinito, G. Vitiello

The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical commutation relations. Thermal properties of inflating Universe are also discussed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9902124 [abs, src, ps, other] :

Title: Berry phase for oscillating neutrinos

Authors: Massimo Blasone, Peter A. Henning, G. Vitiello

We show the presence of a topological (Berry) phase in the time evolution of a mixed state. For the case of mixed neutrinos, the Berry phase is a function of the mixing angle only.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9905460 [abs, src, ps, other] :

Title: Macroscopic parity violating effects and 3He-A

Authors: G.E. Volovik, A. Vilenkin

We discuss the parity violating effects in relativistic quantum theory and their analogues in effective field theory of superfluid 3He-A. The mixed axial-gravitational Chern-Simons term in the effective actions of the two systems is responsible for the chiral fermion flux along the rotation axis of the heat bath in relativistic system and for the unusual \Omega-odd dependence of the zero-temperature density of the normal component on the rotation velocity in 3He-A.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9905320 [abs, src, ps, other] :

Title: Defect formation in inhomogeneous 2-nd order phase transition: theory and experiment

Authors: G.E. Volovik.

The status quo in our understanding of defect formation during a rapid transition into the broken symmetry state in condensed matter and cosmology is discussed. An observation of vortex nucleation in neutron absorption experiments in superfluid 3He-B is interpreted in terms of defect formation during inhomogeneous cooling through T_c. Due to the temperature gradient in the locally heated region the superfluid phase transition occurs as a propagating front. The theoretical considerations of vortex formation at the propagating front are based on work by Kibble-Volovik, Kopnin-Thuneberg, and Aranson-Kopnin-Vinokur.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9905008 [abs, src, ps, other] :

Title: On induced CPT-odd Chern-Simons terms in 3+1 effective action

Authors: G.E. Volovik.

This paper was originally designated as Comment to the paper by R. Jackiw and V. Alan Kostelecky (hep-ph/9901358). We provide an example of the fermionic system, the superfluid 3He-A, in which the CPT-odd Chern-Simons terms in the effective action are unambiguously induced by chiral fermions. In this system the Lorentz and gauge invariances both are violated at high energy, but the behavior of the system beyond the cut-off is known. This allows us to construct the CPT-odd action, which combines the conventional 3+1 Chern-Simons term and the mixed axial-gravitational Chern-Simons term discussed in hep-ph/9905460. The influence of Chern-Simons term on the dynamics of the effective gauge field has been experimentally observed in rotating 3He-A.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9902171 [abs, src, ps, other] :

Title: 3He and Universe parallelism

Authors: G.E. Volovik.
Comments: RevTex file, 18 pages, 6 figures, prepared for Proceedings of the NATO Advanced Study Institute "Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions", February 16 - 26, 1999, Les Houches. Corrections made, references added

We discuss topological properties of the ground state of spatially homogeneous ensemble of fermions. There are several classes of topologically different fermionic vacua; in each case the momentum space topology of the vacuum determines the low-energy (infrared) properties of the fermionic energy spectrum. Among them there is a class of the gapless systems which is characterized by the Fermi-hypersurface, which is the topologically stable singularity in momentum space. This class contains the conventional Landau Fermi-liquid and also the non-Landau Luttinger Fermi-liquid. Another important class of gapless systems is characterized by the topologically stable point nodes (Fermi points). Superfluid 3He-A and electroweak vacuum belong to this universality class. The fermionic quasiparticles (particles) in this class are chiral: close to the Fermi points they are left-handed or right-handed massless relativistic particles. Since the spectrum becomes relativistic at low energy, the symmetry of the system is enhanced in the low-energy edge. The low-energy dynamics acquires local invariance, Lorentz invariance and general covariance, which become better and better when the energy decreases. Interaction of the fermions near the Fermi point leads to collective bosonic modes, which look like effective gauge and gravitational fields. Since the vacuum of superfluid 3He-A and electroweak vacuum are topologically similar, we can use 3He-A for simulation of many phenomena in high energy physics, including axial anomaly. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. Possible simulation in 3He-A of event horizon, Hawking radiation, rotating vacuum and conical space are discussed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9901163 [abs, src, ps, other] :

Title: Rotational quantum friction in superfluids: Radiation from object rotating in superfluid vacuum

Authors: A. Calogeracos, G.E. Volovik.
Journal-ref: JETP Lett. 69 (1999) 281-287.

We discuss the friction experienced by the body rotating in superfluid liquid at T=0. The effect is analogous to the amplification of electromagnetic radiation and spontaneous emission by the body or black hole rotating in quantum vacuum, first discussed by Zel'dovich and Starobinsky. The friction is caused by the interaction of the part of the liquid, which is rigidly connected with the rotating body and thus represents the comoving detector, with the "Minkowski" vacuum outside the body. The emission process is the quantum tunneling of quasiparticles from the detector to the ergoregion, where the energy of quasiparticles is negative in the rotating frame. This quantum rotational friction caused by the emission of quasiparticles is estimated for phonons and rotons in superfluid 4He and for Bogoliubov fermions in superfluid 3He.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### gr-qc/9901077 [abs, src, ps, other] :

Title: Simulation of Panleve-Gullstrand black hole in thin 3He-A film

Authors: G.E. Volovik.
Journal-ref: Pisma Zh.Eksp.Teor.Fiz. 69 (1999) 662-668

The quasi-stationary superfluid state is constructed, which exhibits the event horizon and Hawking radiation.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### cond-mat/9812381 [abs, src, ps, other] :

Title: Field theory in superfluid 3He: What are the lessons for particle physics, gravity and high-temperature superconductivity?

Authors: G.E. Volovik.

There are several classes of homogeneous Fermi-systems which are characterized by the topology of the energy spectrum of fermionic quasiparticles: (1) Gapless systems with a Fermi-surface; (2) Systems with a gap in their spectrum; (3) Gapless systems with topologically stable point nodes (Fermi points); and (4) Gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality Class (3). The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of Class (3) are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to Class (4). They have gapless fermionic quasiparticles with a "relativistic" spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9701240 [abs, src, ps, other] :

Title: Non-Abelian String Conductivity

Authors: T. W. B. Kibble, G. Lozano, A. J. Yates.
Journal-ref: Phys.Rev. D56 (1997) 1204-1214

We examine current-carrying configurations of cosmic strings in non-Abelian gauge theories. We study the solutions numerically and point out that the currents will be at best dynamically stable and not subject to any topological quantisation or conservation, as in conventional models of string superconduction. We suggest that non-Abelian string loops may be unable to support persistent currents in the absence of external fields. This will have relevance to vorton stability.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9803414 [abs, src, ps, other] :

Title: The evolution of a network of cosmic string loops

Authors: E. J. Copeland, T. W. B. Kibble, D. A. Steer.
Journal-ref: Phys.Rev. D58 (1998) 043508

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9904177 [abs, src, ps, other] :

Title: Classifying Vortex Solutions to Gauge Theories

Authors: Nathan F. Lepora, T. W. B. Kibble
Journal-ref: Phys.Rev. D59 (1999) 125019

We classify the spectrum, family structure and stability of Nielsen-Olesen vortices embedded in a larger gauge group when the vacuum manifold is related to a symmetric space.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9904178 [abs, src, ps, other] :

Title: Electroweak Vacuum Geometry

Authors: Nathan F. Lepora, T. W. B. Kibble
Journal-ref: JHEP 9904 (1999) 027

We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-th/9902139 [abs, src, ps, other] :

Title: Defect Formation Through Boson Condensation in Quantum Field Theory

Authors: Giuseppe Vitiello.
Comments: Lectures given at Les-Houches Winter School "Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions", February 16 - 26, 1999

Kinks, vortices, monopoles are extended objects, or defects, of quantum origin with topologically non-trivial properties and macroscopic behavior. They are described in Quantum Field Theory in terms of non-homogeneous boson condensation. I will review the related QFT formalism, the spontaneous breakdown of symmetry framework in which the defects appear and discuss finite temperature effects, also in connection with phase transition problematics.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### gr-qc/9904027 [abs, src, ps, other] :

Title: Vacuum structure for expanding geometry

Authors: E. Alfinito, R. Manka, G. Vitiello.

We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the state space splits into many unitarily inequivalent representations of the canonical commutation relations. Non-unitary time evolution is described as a trajectory in the space of the representations. The generator of time evolution is related to the entropy operator. The thermodynamic arrow of time is shown to point in the same direction of the cosmological arrow of time. The vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics. The link between expanding geometry, squeezing and thermal properties is exhibited.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9907456 [abs, src, ps, other] :

Title: Momentum-Space Topology of Standard Model

Authors: G.E. Volovik.
Comments: talk prepared for CWS-99 - International Workshop on LT Physics in Microgravity Environment, ISSP, Chernogolovka (Moscow region), July 28 - Aug 2

The momentum-space topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentum-space invariants to chiral anomaly is also discussed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.

### hep-ph/9908398 [abs, src, ps, other] :

Title: Cosmological Consequences of Slow-Moving Bubbles in First-Order Phase Transition

Authors: A.C. Davis and M. Lilley.

In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. We examine the evolution and collision of slow-moving true-vacuum bubbles. Our lattice simulations indicate that phase oscillations, predicted and observed in systems with a local symmetry and with a global symmetry where the bubbles move at speeds less than the speed of light, do not occur inside collisions of slow-moving local-symmetry bubbles. We observe almost instantaneous phase equilibration which would lead to a decrease in the expected initial defect density, or possibly prevent defects from forming at all. We illustrate our findings with an example of defect formation suppressed in slow-moving bubbles. Slow-moving bubble walls also prevent the formation of `extra defects', and in the presence of plasma conductivity may lead to an increase in the magnitude of any primordial magnetic field formed.

Postscript from: Los Alamos, Zaragoza, Trieste, Paris, Augsburg, Southampton, Moscow.