TL;DR
This review discusses fundamental theoretical issues in Bose-Einstein condensates, addressing symmetry breaking, conservation laws, disorder effects, fluctuations, and nonequilibrium states with detailed solutions and examples.
Contribution
It provides comprehensive insights into key theoretical problems of Bose-Einstein condensates, offering solutions and clarifications for longstanding issues.
Findings
Clarified the relation between BEC and gauge symmetry breaking
Resolved the Hohenberg-Martin dilemma for conserving and gapless theories
Described nonequilibrium condensates like turbulent superfluids
Abstract
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-state condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and…
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