Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

Abstract

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions (repulsive or attractive) are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is payed to the thermodynamic properties of bosons and their condensation.

13 REVTEX pages + 9 postscript figures

Cited by in corpus (32)

• Froehlich Polaron and Bipolaron: Recent Developments
• Comparing and contrasting nuclei and cold atomic gases
• Non-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact One-Particle Properties at Zero Temperature
• Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble
• Bose-Einstein Condensation, Fluctuations, and Recurrence Relations in Statistical Mechanics
• Fröhlich Polarons from 0D to 3D: Concepts and Recent Developments
• Bose-Einstein condensation under external conditions
• Density and Pair Correlation Function of Confined Identical Particles: the Bose-Einstein Case
• Analytical theory of mesoscopic Bose-Einstein condensation in ideal gas
• Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions
• Partition functions and symmetric polynomials
• Analytic solutions of topologically disjoint systems
• Ground state and optical conductivity of interacting polarons in a quantum dot
• Virial expansion coefficients in the harmonic approximation
• Condensation and interaction range in harmonic boson traps: a variational approach
• Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations
• Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light
• Statistical mechanics and path integrals for a finite number of bosons
• Variational path-integral treatment of a translation invariant many-polaron system
• Self-similar analytical solution of the critical fluctuations problem for the Bose-Einstein condensation in an ideal gas
• The center-of-mass response of confined systems
• Confined Harmonically Interacting Spin-Polarized Fermions in a Magnetic Field: Thermodynamics
• Analytical framework for non-equilibrium phase transition to Bose--Einstein condensate
• Momentum distribution of confined bosons: temperature dependence
• Path-integral approach to the thermodynamics of bosons with memory: Partition function and specific heat
• The many-body diffusion algorithm, harmonic fermions
• The Partition Function of a Spinor Gas
• The Loop-Gas Approach to Bose-Einstein Condensation for Trapped Particles
• Characterization of shell filling of interacting polarons in a quantum dot through their optical absorption
• Density of a gas of spin polarized fermions in a magnetic field
• Collective excitation frequencies of Bosons in a parabolic potential with interparticle harmonic interactions
• Path-integral approach to the thermodynamics of bosons with memory: Density and correlation functions