arXiv:cond-mat/0105588 · Journal of Physics A Mathematical and General

Correlations in a confined magnetized free-electron gas

M M Kettenis, L.G. Suttorp

Published Sep 21, 2001• 2 citations

Abstract

Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation, the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.

DOI: 10.1088/0305-4470/34/39/306

Related papers

Time correlations in a confined magnetized free-electron gas

L.G. Suttorp

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.

arXiv:cond-mat/0306172Journal of Physics A Mathematical and GeneralJul 17, 20030 citations

Short-ranged correlations and the ferromagnetic electron gas

A. K. Rajagopal, John C. Kimball, Mahadev Banerjee

A discussion of the various properties of pair correlation functions of a magnetic electron gas is presented. The cusp conditions obeyed by the many-electron wave functions for a pair of electrons with parallel and antiparallel spins in close proximity are expressed as derivative conditions on the corresponding parallel-and antiparallel-spin pair correlation functions. In particular, it is shown that in a fully ferromagnetic gas the parallel spin correlations determine the correlation energy whereas in the paramagnetic case, this function is of less importance in comparison to the antiparallel-spin correlation function. In the high-momentum limit, it is found that the momentum distribution of electrons is dominated by antiparallel-spin correlations in the partially magnetic case whereas in the fully ferromagnetic case, it is dominated by parallel-spin correlations but is smaller by a factor of ${q}^{\ensuremath{-}2}$. A calculation of the parallel-spin correlation function for the ferromagnetic gas in perturbation theory is presented. A model for the exchange correlation energy of the system which takes into account the exact conditions given here is proposed. Corresponding results for the two-dimensional electron gas are also stated.

Physical review. B, Condensed matterSep 1, 1978117 citations

Correlation function algebra for inhomogeneous fluids

Andrew O. Parry, Peter S. Swain

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z = 0 and z = L respectively) and focus on the structure of the pair correlation function . We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform and the zeroth moment at different positions and . These relations form an algebra which severely restricts the possible form of the function . For the common situations in which the equilibrium one-body (magnetization/number density) profile exhibits an odd or even reflection symmetry in the plane, the algebra simplifies considerably, and is used to relate the correlation function to the finite-size excess free energy . We rederive non-trivial scaling expressions for the finite-size contribution to the free energy at bulk criticality and for systems where large-scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered.

arXiv:cond-mat/9701092Journal of Physics Condensed MatterMar 17, 19974 citations

One-dimensional non-interacting fermions in harmonic confinement: equilibrium and dynamical properties

Patrizia Vignolo, Anna Minguzzi

We consider a system of one-dimensional non-interacting fermions in external harmonic confinement. Using an efficient Green's function method we evaluate the exact profiles and the pair correlation function, showing a direct signature of the Fermi statistics and of the single quantum-level occupancy. We also study the dynamical properties of the gas, obtaining the spectrum both in the collisionless and in the collisional regime. Our results apply as well to describe a one-dimensional Bose gas with point-like hard-core interactions.

arXiv:cond-mat/0202086Journal of Physics B Atomic Molecular and Optical PhysicsNov 23, 200117 citations

Interaction quench in a trapped 1D Bose gas

Paolo P. Mazza, Mario Collura, Márton Kormos +1 more

We studied the non-equilibrium quench dynamics from free to hard-core 1D bosons in the presence of a hard-wall confining potential. The density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution was characterised. It was found that for long times the system relaxes to a uniform density profile, but the correlation function memorises the initial state with a stationary algebraic long-distance decay, which is opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which was found to decay exponentially for large distances. A two-step mechanism was shown to govern the time evolution; a quick approach to an almost stationary value was followed by a slow algebraic relaxation to the true stationary state.

arXiv:1407.1037Journal of Statistical Mechanics Theory and ExperimentNov 10, 201449 citations

Time and Temperature Dependent Correlation Functions of the One-Dimensional Impenetrable Electron Gas

Frank Göhmann, Anatoli G. Izergin, V. E. Korepin +1 more

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.

arXiv:cond-mat/9805192International Journal of Modern Physics BSep 20, 199826 citations