Bose-Einstein condensation and gauge symmetry breaking

Abstract

The fundamental problem is analized, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement that, though gauge symmetry breaking helps for describing Bose-Einstein condensation, but the latter, in principle, does not require any symmetry breaking. This, however, is not correct. The analysis is based on the known mathematical theorems. But in order not to overcomplicate the presentation and to make it accessible to all readers, technical details are often omitted here. The emphasis is made on the following basic general facts: Spontaneous breaking of gauge symmetry is the necessary and sufficient condition for Bose-Einstein condensation. Condensate fluctuations, in thermodynamic limit, are negligible. Their catastrophic behavior can arise only as a result of incorrect calculations, when a Bose-condensed system is described without gauge symmetry breaking. It is crucially important to employ the representative statistical ensembles equipped with all conditions that are necessary for a unique and mathematically correct description of the given statistical system. Only then one is able to develop a self-consistent theory, free of paradoxes.

Latex file, 29 pages

References in corpus (10)

• Fragmentation of Bose-Einstein Condensates
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Fluctuations of composite observables and stability of statistical systems
• Gapless Hartree-Fock-Bogoliubov Approximation for Bose Gases
• Generalized canonical ensembles and ensemble equivalence
• Self-Consistent Theory of Bose-Condensed Systems
• Nonequivalent operator representations for Bose-condensed systems
• Bose-Einstein-condensed gases with arbitrary strong interactions
• Nonequilibrium Bose systems and nonground-state Bose-Einstein condensates
• Representative Ensembles in Statistical Mechanics

Cited by in corpus (47)

• Finite Temperature Models of Bose-Einstein Condensation
• Cold Bosons in Optical Lattices
• Basics of Bose-Einstein Condensation
• Effects of symmetry breaking in finite quantum systems
• The Stochastic Gross-Pitaevskii Equation and some Applications
• Dipolar and spinor bosonic systems
• Theory of Cold Atoms: Basics of Quantum Statistics
• Thermodynamics of ultracold trapped gases. Generalized mechanical variables, equation of state and heat capacity
• Turbulent superfluid as continuous vortex mixture
• Theory of cold atoms: Bose-Einstein statistics
• Bose-Einstein condensation temperature of weakly interacting atoms
• Adiabatic theorems for linear and nonlinear Hamiltonians
• Generation of nonground-state condensates and adiabatic paradox
• Formation of granular structures in trapped Bose-Einstein condensates under oscillatory excitations
• Cold atoms in double-well optical lattices
• Difference in Bose-Einstein condensation of conserved and unconserved particles
• On the order of BEC transition in weakly interacting gases predicted by mean-field theory
• Ground state of a homogeneous Bose gas of hard spheres
• Nonlinear dynamics of ultracold gases in double-well lattices
• Bose systems in spatially random or time-varying potentials
• Particle fluctuations in nonuniform and trapped Bose gases
• Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets
• Bose-Einstein condensation in self-consistent mean-field theory
• Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
• Mode interference in quantum joint probabilities for multimode Bose-condensed systems
• Dynamical Universal Behavior in Quantum Chaotic Systems
• Extended Bose-Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation
• Mesoscopic disorder in double-well optical lattices
• Fluctuation indices for atomic systems with Bose-Einstein condensate
• Generation of mesoscopic superpositions of a binary Bose-Einstein condensate in a slightly asymmetric double well
• Regulating atomic imbalance in double-well lattices
• Entanglement production with Bose atoms in optical lattices
• From Coherent Modes to Turbulence and Granulation of Trapped Gases
• Models of Mixed Matter
• Quantum entanglement and Hawking temperature
• Bose-Einstein Condensation and Symmetry Breaking of a Complex Charged Scalar Field
• Local condensate depletion at trap center under strong interactions
• Condensation of Fluctuations in the Ising Model: a Transition without Spontaneous Symmetry Breaking
• Self-consistent approach for Bose-condensed atoms in optical lattices
• Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
• Mid-range order in trapped quasi-condensates of bosonic atoms
• Stability of normal quantum-fluid mixtures
• Symmetry breaking and physical properties of the bosonic single-impurity Anderson model
• Unified theory of quantum crystals and optical lattices with Bose-Einstein condensate
• Fermionic condensation in ultracold atoms, nuclear matter and neutron stars
• Particle Fluctuations in Mesoscopic Bose Systems
• BEC phase diagram of a ${}^{87}$Rb trapped gas in terms of macroscopic thermodynamic parameters