F. Brosens

Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

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.

Canonical Bose-Einstein condensation in a parabolic well

Abstract The Bose-Einstein condensation is investigated for N particles in a parabolic confining potential. The partition function in the grand-canonical as well as in the canonical ensemble is obtained analytically, and the thermodynamical quantities are studied for the one-dimensional (1D) and for the three-dimensional (3D) version of the model. In 1D, a dramatic rise in the ground state occupancy with decreasing temperature is predicted. Both the grand-canonical and the canonical ensemble yield the same behavior of the specific heat as a function of the temperature and the number of particles. There is no indication of a critical phenomenon for a finite number of particles, neither in the ground state occupancy nor in the specific heat. Also in 3D, both ensembles give an identical contribution for the specific heat, but showing thereby a phase transition with a critical temperature which scales with the cube root of the number of particles, as predicted before by semi-classical continuum models.

Superconductivity in a wedge : Analytical variational results II

Abstract An analytical variational solution is found for the linearized Ginzburg–Landau equation describing the superconducting phase in a wedge. The nucleation magnetic field H c 3 is analyzed as a function of the wedge’s angle α for 0 α 2 π . For α / π ≥ 0.4411 plane-surface superconductivity is found to be predominant, leading to a lower bound H c 3 / H c 2 ≥ ( 1 − 2 / π ) − 1 / 2 for the nucleation field H c 3 , where H c 2 is the bulk upper critical field. For smaller α , corner-surface superconductivity–as described earlier–determines the nucleation field.

Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

Departement Natuurkunde, Universiteit Antwerpen (RUCA), Groenenborgerlaan171, B-2020 Antwerpen(March 11, 1998)For a fermion gas with equally spaced energy levels, the density and the pair correlation functionare obtained. The derivation is based on the path integral approach for identical particles and theinversion of the generating functions for both static responses. The density and the pair correlationfunction are evaluated explicitly in the ground state of a confined fermion system with a number ofparticles ranging from 1 to 220 and filling the Fermi level completely.05.30.-d, 03.75.Fi, 32.80.Pj.I. INTRODUCTION

DENSITY AND PAIR CORRELATION FUNCTION OF CONFINED IDENTICAL PARTICLES : THE BOSE-EINSTEIN CASE

Two basic correlation functions are calculated for a model of N harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case. The dependence of these static response properties on the complete range of the temperature and of the number of particles is obtained. The calculation technique is based on the path integral approach of symmetrized density matrices for identical particles in a parabolic confining well. {copyright} {ital 1997} {ital The American Physical Society}

Optical absorption of a many-polaron system confined in a quantum dot

Abstract The ground state energy and the optical absorption spectra are obtained for N electrons interacting with each other and with the longitudinal optical (LO) phonons at an arbitrary electron–phonon coupling strength in a parabolic confinement potential. In order to account for the fermion statistics, we use the path integral formalism for identical particles. The approach is at present limited to closed shells. In the case of strong electron–phonon interaction, a ferromagnetic-to-nonmagnetic transition is shown to occur between states with different total spin of the system. This transition is revealed through the optical absorption spectra and should be experimentally observable. When the confinement frequency parameter is in resonance with the LO phonon frequency, strong mixing between zero-phonon and one-phonon states is manifested in the absorption spectrum.

Variational path-integral treatment of a translation invariant many-polaron system

A translation invariant

The energy loss function of the polaron gas

N

Ground state and optical conductivity of interacting polarons in a quantum dot

-polaron system is investigated at arbitrary electron-phonon coupling strength, using a variational principle for path integrals for identical particles. An upper bound for the ground-state energy is found as a function of the number of spin up and spin down polarons, taking the electron-electron interaction and the Fermi statistics into account. The resulting addition energies and the criteria for multipolaron formation are discussed.

Wigner distribution functions for complex dynamical systems: A path integral approach

Abstract The energy loss function Im 1/ K (π, ω) of a gas of polarons is calculated in the RPA approximation. For typical densities of degenerate polar semiconductors, the energy loss function has pronounced structure. Up to three resonances appear. The coupled phonon-plasmon resonance, with frequency between ω TO and ω LO , leads to an extremely sharp peak in Im 1/ K (π, ω), for appropriate values of wavevector and densities.