Patterns of Symmetry Breaking

by Arodz, Henryk; Dziarmaga, Jocek; Zurek, Wojciech Hubert

• ISBN13: 9781402017452
• ISBN10: 1402017456
• Format: Paperback
• Copyright: 2003-12-01
• Publisher: Kluwer Academic Pub

Summary

The concept of spontaneous symmetry breaking plays a fundamental role in contemporary physics. It is essential to descriptions of such phenomena as the presence of degenerate ground states, massless modes, and topological defects. Examples are abundant in condensed matter physics, atomic and particle physics, as well as in astrophysics and cosmology. The book contains comprehensive, instructive reviews of significant aspects of the physics of spontaneous symmetry breaking. The emphasis is on topological defects: their appearance after phase transitions and the consequences of their presence. The most attractive feature of the book is that it embraces phenomena belonging to traditionally distinct branches of physics, such as the low temperature physics, liquid crystals, particle physics and cosmology. Both experimental and theoretical physics are represented. The unity and coherence of the underlying concepts is illustrated by an enormous variety of physical phenomena. As such, the book will interest any professional physicist working in modern physics.

Table of Contents

Preface	1	(3)
Symmetry Breaking and Defects	3	(34)
T.W.B. Kibble
Acknowledgments	33	(1)
References	34	(3)
Liquid 4He and Its Superfluidity	37	(46)
O.J. Griffiths
P.C. Hendry
P.V.E. McClintock
H.A. Nichol
Acknowledgments	76	(1)
References	76	(7)
The Role of Topological Defects in Cosmology	83	(28)
M. Sakellariadou
References	107	(4)
Cosmic Defects and Partical Physics Constraints	111	(28)
A.C. Davis
Theory-F	125	(1)
Theory-D	125	(4)
Scaling Cosmic Strings	129	(1)
Friction Dominated Strings	130	(1)
Vortons	130	(4)
Constraints	134	(3)
References	137	(2)
Introduction to the Modern Theory of Phase Transitions	139	(22)
Jozef Sznajd
Phase Transitions: From Early Universe to Ice Cube	139	(2)
Spontaneous Symmetry Breaking	141	(1)
Symmetry and Phase Transitions. Order Parameter	142	(2)
Landau theory	143	(1)
Fluctuations	144	(2)
Power laws - Saint Graal of the complex system science	146	(2)
Company size distribution	146	(1)
Mortality evolution	146	(1)
Lifespan	147	(1)
Goal distribution	147	(1)
Family name distribution	147	(1)
Opinion evolution	147	(1)
Scaling	148	(2)
Renormalization Group	150	(7)
Renormalization group transformation	150	(1)
Fixed points	151	(1)
Critical index	152	(1)
Renormalization group techniques	152	(1)
Real-space renormalization	153	(2)
Upper critical dimension	155	(1)
Momentum-space renormalization	156	(1)
Final remarks	157	(4)
References	158	(3)
Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects	161	(36)
O.D. Lavrentovich
Introduction	161	(2)
Experimental observations of LC structures	163	(4)
Polarizing Microscopy of Liquid Crystals	163	(4)
Defects in nematics	167	(13)
Topological classification	167	(4)
Disclination textures	171	(1)
Elasticity	172	(4)
Surface anchoring phenomena; Equilibrium point defects in nematic droplets	176	(4)
Defects in SmA and other Lamellar Systems	180	(13)
Elasticity	180	(3)
Dislocations	183	(6)
Focal Conic Domains: Surface facetting and Grain boundaries	189	(4)
Summary	193	(4)
Acknowledgments	193	(1)
References	193	(4)
Scaling Laws for Fluxon Formation in Annular Josephson Tunnel Junctions	197	(12)
R. Monaco
R.J. Rivers
Scaling Laws for Fluxon Production	197	(2)
Background	197	(1)
The Scaling Predictions For Fluxons	198	(1)
The Experiment	199	(6)
Measuring Fluxons	199	(1)
The experimental setup	200	(3)
The measurements	203	(2)
The results	205	(1)
Comments, Future Experiments and Conclusions	206	(3)
Acknowledgments	207	(1)
References	207	(2)
Nonholonomic Field Theory of Vortices and Defect and their Physe Transitions	209	(64)
H. Kleinert
Summary	209	(2)
Phase Transitions in Nambu-Goldstone Systems	211	(3)
Superfluid 4He and Superconductors	214	(22)
Gradient Energy	214	(2)
Vortex Density	216	(1)
The Partition Function	217	(1)
Interaction Energy between Vortices	218	(1)
Physical Jumping Surfaces	218	(1)
Gauge Field of Superflow	219	(3)
Disorder Field Theory	222	(3)
Disorder Theory of Superconductor	225	(3)
Order versus Disorder	228	(4)
Order of Superconducting Phase Transition---Tricritical Point	232	(1)
Vortex Lattices	233	(3)
Abelian Quark Confinement	236	(8)
References	239	(5)
Superfluid 4He	244	(16)
Gradient Energy	244	(1)
Vortex Density	245	(1)
The Partition Function	246	(1)
Interaction Energy between Vortices	247	(1)
Physical Jumping Surfaces	247	(1)
Gauge Field of Superflow	248	(2)
Disorder Field Theory	250	(3)
Disorder Theory of Ginzburg-Superconductor	253	(2)
Order versus Disorder	255	(4)
Order of Superconducting Phase Transition---Tricritical Point	259	(1)
Vortex Lattices	260	(1)
Crystals	260	(8)
Abelian Quark Confinement	268	(5)
Acknowledgments	272	(1)
References	272	(1)
Vortices and Flat Directions: the Uses of Bogomolnyi Bounds	273	(14)
A. Achucarro
Introduction	273	(1)
Energy bounds for topological defects	274	(2)
Bogomolnyi bounds for Abrikosov--Nielsen--Olesen vortices	276	(2)
Semilocal strings	278	(1)
D--term supersymmetric QED	279	(2)
Bogomolnyi bounds, supersymmetry and fermion zero modes	281	(3)
Summary	284	(3)
References	284	(3)
Evolution of Local Vortices and Interfaces	287	(26)
Henryk Arodz
Introduction	287	(1)
Simple example - kink in one spatial dimension	288	(4)
Vortex in the Abelian Higgs model	292	(9)
Evolution of interface in a dissipative system	301	(8)
Remarks	309	(4)
References	311	(2)
Non-Equilibrium Mott Transition in a lattice of Bose-Einstein condensates	313	(22)
J. Dziarmaga
A. Smerzi
W.H. Zurek
A.R. Bishop
Introduction	313	(2)
Josephson junction arrays	315	(2)
The quantum phase model	317	(1)
Linear Quench	318	(3)
Adiabatic transition: τQ → ∞	319	(1)
Instanteneous transition: τQ → O	319	(1)
Diabatic transition	319	(2)
The gaussian regime	321	(4)
Soft modes	323	(2)
Commensurate versus non-commensurate	325	(1)
The critical regime	325	(2)
From superfluid to insulating phase	327	(3)
Conclusion	330	(5)
Acknowledgments	331	(1)
Appendix	331	(1)
References	332	(3)
Spontaneous Breakdown of chiral symmetry in QCD	335	(32)
Maciej A. Nowak
Introduction	335	(2)
QCD in a nut-shell	337	(4)
Diffusion and QCD Vacuum	341	(6)
Instantons - defects of the vacuum	347	(3)
Spectral universal fluctuations in the QCD	350	(3)
Lattice as a quantum dot	353	(4)
Prospects	357	(10)
Acknowledgments	360	(4)
References	364	(3)
Domain Wall Solutions	367	(14)
Tanmay Vachaspati
Introduction	367	(1)
The kink	368	(1)
SU (5) x Z2 walls	369	(12)
Domain wall lattice	374	(2)
Formation of domain walls	376	(2)
Importance in cosmology	378	(1)
References	378	(3)
Phenomenology of Effective Gravity	381
G.E. Volvik
Introduction	381
Gravity as perturbation of quantum vacuum	382
Einstein theory in standard formulation	382
Cosmological constant as vacuum energy	383
Sakharov gravity as elasticity of quantum vacuum	384
Conservation of energy and momentum	384
Three components of `cosmic fluid'	385
Induced cosmological constant	385
Gibbs-Duhem relation and cosmological constant	386
Cosmological constant from vacuum perturbations	387
Robertson-Walker metric and its energy momentum tensor	388
Einstein action	388
Energy-momentum tensor for gravitational field	388
Einstein static Universe	389
Equation of state for gravitational field	389
Einstein solution from phenomenology	389
de Sitter solution as a thermodynamic equilibrium state	390
Phenomenology of Godel Universe	391
Rotating Universe	391
Spin susceptibility of the vacuum	392
Equation of state for the gravitational field and equilibrium state	393
Modification of Einstein equation and relaxation of the vacuum energy	394
Cosmological constant as evolving parameter	394
Dissipation in Einstein equation	395
Cosmological constant as integration constant	396
Flat Universe with two relaxation parameters	397
Relaxation after cosmological phase transition	397
Dark energy as dark matter	398
Analog of quintessence	399
On energy and momentum of gravitational waves	399
Discussion	402
Acknowledgments	403
References	403