Confined harmonically interacting spin-polarized fermions (original) (raw)

Confined harmonically interacting spin-polarized fermions in a magnetic field: Thermodynamics

Physical Review E, 1999

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin polarized fermions in a confiment potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three dimensional model of N harmonically interacting spin polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied. 03.75.Fi, 32.80.Pj.

Correlations in a confined gas of harmonically interacting spin-polarized fermions

Physical Review E, 1998

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220 and filling the Fermi level completely.

The polarization function of a finite number of confined spin polarized fermions

Solid State Communications, 2001

The Fourier transform of an inhomogeneous two-point correlation function, in space and Euclidean time, is derived for a limited number of spin polarized fermions in an external potential. The formulation is based on the many-body generalization of the Feynman±Kac functional. Special attention is given to the ®nite number aspects and the implications thereof for the fugacity. An analysis of the correlation function in terms of single-particle propagators is obtained, leading to an occupation function representation. For the harmonic model, the temporal Fourier components of the two-point correlation matrix are worked out in the low-temperature limit. q

SPIN 1/2 FERMIONS IN THE UNITARY REGIME AT FINITE TEMPERATURE

International Journal of Modern Physics B, 2006

We have performed a fully non-perturbative calculation of the thermal properties of a system of spin 1/2 fermions in 3D in the unitary regime. We have determined the critical temperature for the superfluid-normal phase transition. The thermodynamic behavior of this system presents a number of unexpected features, and we conclude that spin 1/2 fermions in the BCS-BEC crossover should be classified as a new type of superfluid.

Thermodynamic properties of correlated fermions in lattices with spin-dependent disorder

New Journal of Physics, 2013

Motivated by the rapidly growing possibilities for experiments with ultracold atoms in optical lattices, we investigate the thermodynamic properties of correlated lattice fermions in the presence of an external spindependent random potential. The corresponding model, a Hubbard model with spin-dependent local random potentials, is solved within dynamical mean-field theory. This allows us to present a comprehensive picture of the thermodynamic properties of this system. In particular, we show that for a fixed total number of fermions spin-dependent disorder induces a magnetic polarization. The magnetic response of the polarized system differs from that of a system with conventional disorder.

Energy Spectrum Analysis of 1D Spin-3/2 Fermionic Chains

Journal of Superconductivity and Novel Magnetism, 2015

We study an ultracold atomic gas of repulsively interacting spin-3/2 fermions loaded into one-dimensional optical lattices. The physics of the lowest band can be described by a Hubbard Hamiltonian that becomes a generalized Heisenberg model for strong enough interactions since the system undergoes into a Mott insulator phase. For few lattice sites (up-to 6 sites), we solve numerically this model by means of the exact diagonalization technique. For larger systems (up-to 9 sites), we use the Lanczos algorithm in order to infer the physics expected in the thermodynamic limit. We present the numerical calculation of the energy spectrum and the energy gap as a function of the lattice sizes, and performing finite-size scaling we show that such small systems are able to recover the main thermodynamiclimit properties of the two distinguished magnetic phases present in this system namely spin liquid and spin Peierls.

Thermodynamics of a statistically interacting quantum gas in D dimensions

Physical Review E, 2007

We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear Schroedinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase transition occurs at T>0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D.

Density of a gas of spin-polarized fermions in a magnetic field

Physical Review E, 2000

For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.

Thermodynamic Properties of Strongly Degenerate Interacting Fermi Systems

A numerical approach is presented which allows to calculate the equilibrium properties of Fermi systems which are both, strongly coupled and strongly degenerate. Based on a novel path integral representation of the many-particle density operator, quantum and spin effects are included. As an illustration, results for the pressure and energy of an electronproton plasma are presented.

Use of the chemical potential for a limited number of fermions with a degenerate groundstate

The European Physical Journal B - Condensed Matter, 2003

For fermions with degenerate single-particle energy levels, the usual relation between the total number of particles and the chemical potential µ is only satisfied for a specific number of particles, i.e. those leading to closed shells. The treatment of an arbitrary number of fermions requires a modification of the chemical potential, similar to the one proposed by Landsberg for Bose-condensed systems. We study the implications of the required modification for fermions in a potential, by calculating the ground state energy, the free energy, the density, the partition function and the dynamic two-point correlation function. It turns out that the modified relation between the fugacity and the number of particles leads to the correct ground state energy and density. But for other quantities like the entropy and the two-point correlation functions, an additional correction is required and derived. These calculations indicate that many-body perturbation theories based on H − µN with Lagrange multiplier µ, are not applicable in unmodified form for a fixed number of fermions at low temperature.