Effective action for Bose-Einstein condensates

Abstract

We clarify basic properties of an effective action (i.e., self-consistent perturbation expansion) for interacting Bose-Einstein condensates, where field $\psi$ itself acquires a finite thermodynamic average $⟨\psi ⟩$ besides two-point Green's function $\hat{G}$ to form an off-diagonal long-range order. It is shown that the action can be expressed concisely order by order in terms of the interaction vertex and a special combination of $⟨\psi ⟩$ and $\hat{G}$ so as to satisfy both Noether's theorem and Goldstone's theorem (I) corresponding to the first proof. The self-energy is predicted to have a one-particle-reducible structure due to $⟨\psi ⟩\ne 0$ to transform the Bogoliubov mode into a bubbling mode with a substantial decay rate.

9 pages, 10 figures

References in corpus (11)

• Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Introduction to Nonequilibrium Statistical Mechanics with Quantum Field
• Exact Conservation Laws of the Gradient Expanded Kadanoff-Baym Equations
• Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws
• Exact results on the two-particle Green's function of a Bose-Einstein condensate
• Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate
• Self-Consistent Approximations for Superconductivity beyond the Bardeen-Cooper-Schrieffer Theory
• Lifetime of Single-Particle Excitations in a Dilute Bose-Einstein Condensate at Zero Temperature
• Ground-State Energy and Condensate Density of a Dilute Bose Gas Revisited

Cited by in corpus (7)

• Are Quasiparticles and Phonons Identical in Bose--Einstein Condensates?
• 3/2-Body Correlations and Coherence in Bose-Einstein Condensates
• Strong connection between single-particle and density excitations in Bose-Einstein condensates
• Quantum Field Theory of Correlated Bose-Einstein condensates: I. Basic Formalism
• Hidden Bose-Einstein Singularities in Correlated Electron Systems
• Hidden Bose-Einstein Singularities in Correlated Electron Systems: II. Pseudogap Phase in the Weakly Attractive Hubbard Model
• Hidden Bose-Einstein Singularities in Correlated Electron Systems: III. Thermodynamic Signals