Off-diagonal long-range order in a harmonically confined two-dimensional Bose gas

We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density martix provides an exact description of the spatial correlations known to be associated with the existence of a Bose-Einstein condensate below the transition temperature $T^{(0)}_c$. We treat the effects of repulsive interactions within the semiclassical Hartree-Fock-Bogliubov approximation and find that even though the system remains in the same {\em uncondensed phase} for all $T \geq 0$, there appears to be a revival of off-diagonal long-range order for temperatures $T < T^{(0)}_c$. We suggest that this reentrant order is related to a phase transition in the system which {\em is not} the BEC state.Comment: figures embedded in text, typos correcte

Local-energy density functionals for an N-dimensional electronic system in a magnetic field

We present a general approach for the construction of the exact local-energy-density functionals for a uniform N-dimensional electronic system in a magnetic field. For arbitrary dimension, we obtain explicit expressions for the matter, kinetic, and exchange density functionals. In the zero-field limit, we recover the usual N-dimensional Thomas-Fermi theory. As an application of our results, we develop a current-density-functional theory, in the spirit of the Thomas-Fermi-Dirac approximation, for an inhomogeneous many-electron system in a magnetic field.Comment: 9 pages, RevTeX, 1 eps figure included in the tex

Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics in dd-dimensions

Closed form, analytical results for the finite-temperature one-body density matrix, and Wigner function of a $d$-dimensional, harmonically trapped gas of particles obeying exclusion statistics are presented. As an application of our general expressions, we consider the intermediate particle statistics arising from the Gentile statistics, and compare its thermodynamic properties to the Haldane fractional exclusion statistics. At low temperatures, the thermodynamic quantities derived from both distributions are shown to be in excellent agreement. As the temperature is increased, the Gentile distribution continues to provide a good description of the system, with deviations only arising well outside of the degenerate regime. Our results illustrate that the exceedingly simple functional form of the Gentile distribution is an excellent alternative to the generally only implicit form of the Haldane distribution at low temperatures.Comment: 17 pages, 2 eps figure

Universality of the energy spectrum for two interacting harmonically trapped ultra-cold atoms in one and two dimensions

Motivated by the recent article of P. Shea {\it et al.} [Am. J. Phys. {\bf 77} (6), 2009] we examine the exactly solvable problem of two harmonically trapped ultra-cold bosonic atoms interacting {\it via} a short range potential in one and two dimensions. A straightforward application in one dimension shows that the energy spectrum is universal, provided that the range of the potential is much smaller than the oscillator length, in addition to clearly illustrating why regularization is not required in the limit of zero range. The two dimensional problem is less trivial, requiring a more careful treatment as compared to the one dimensional case. Our two dimensional analysis likewise reveals that the low-energy physics is also universal, in addition to providing a simple method for obtaining the appropriately regularized two dimensional pseudopotential.Comment: No figures. Accepted for publication in J. Phys. A: Math. Theo

Thomas-Fermi von Weizs\"acker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizs\"acker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions, and provide physical insight into why it can be represented as a local functional. Finally, a simple, and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.Comment: 6 figures. Accepted for publication in Phys. Rev. A. In productio

A Comprehensive Dynamical Study of Nucleation and Growth in a One--Dimensional Shear Martensitic Transition

We have constructed a complete hydrodynamic theory of nucleation and growth in a one--dimensional version of an elastic shear martensitic transformation with open boundary conditions where we have accounted for interfacial energies with strain--gradient contributions. We have studied the critical martensitic nuclei for this problem: Interestingly, the bulk critical nuclei are {\em twinned} structures, although we have determined that the dominant route for the formation of martensite is through {\em surface nucleation}. We have analytically solved for the surface nuclei and evaluated exact nucleation rates showing the strong preference for surface nucleation. We have also examined the growth of martensite: There are two possible martensitic growth fronts, {\em viz}., dynamical twinning and so-called two--kink solutions. These transformation fronts are separated by a {\em dynamical} phase transition. We analytically derive this phase diagram and determine expressions for the speeds of the martensitic growth fronts.Comment: 17 Postscript figures, to appear in Met. Trans

Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi von Weizs\"acker hydrodynamic theory. We focus on repulsive interactions, and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are {\em independent} of the interactions in the large particle limit. We argue quite generally that it is the {\em local} character of the two-dimensional energy density which is responsible for the insensitivity of surface excitations to the dipolar interaction strength, and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.Comment: 5 figure

A manifestly Hermitian semiclassical expansion for the one-particle density matrix of a two-dimensional Fermi gas

The semiclassical $\hbar$-expansion of the one-particle density matrix for a two-dimensional Fermi gas is calculated within the Wigner transform method of Grammaticos and Voros, originally developed in the context of nuclear physics. The method of Grammaticos and Voros has the virture of preserving both the Hermiticity and idempotency of the density matrix to all orders in the $\hbar$-expansion. As a topical application, we use our semiclassical expansion to go beyond the local-density approximation for the construction of the total dipole-dipole interaction energy functional of a two-dimensional, spin-polarized dipolar Fermi gas. We find a {\em finite}, second-order gradient correction to the Hartree-Fock energy, which takes the form $\varepsilon (\nabla \rho)^2/\sqrt{\rho}$, with $\varepsilon$ being small ($|\varepsilon| \ll1$) and negative. We test the quality of the corrected energy by comparing it with the exact results available for harmonic confinement. Even for small particle numbers, the gradient correction to the dipole-dipole energy provides a significant improvement over the local-density approximation.Comment: 1 figur

The Zel'dovich effect in harmonically trapped, ultra-cold quantum gases

We investigate the Zel'dovich effect in the context of ultra-cold, harmonically trapped quantum gases. We suggest that currently available experimental techniques in cold-atoms research offer an exciting opportunity for a direct observation of the Zel'dovich effect without the difficulties imposed by conventional condensed matter and nuclear physics studies. We also demonstrate an interesting scaling symmetry in the level rearragements which has heretofore gone unnoticed

Testing the nonlocal kinetic energy functional of an inhomogeneous, two-dimensional degenerate Fermi gas within the average density approximation

In a recent paper [Phys.~Rev.~A {\bf 89}, 022503 (2014)], the average density approximation (ADA) was implemented to develop a parameter-free, nonlocal kinetic energy functional to be used in the orbital-free density-functional theory of an inhomogenous, two-dimensional (2D), Fermi gas. In this work, we provide a detailed comparison of self-consistent calculations within the ADA with the exact results of the Kohn-Sham density-functional theory, and the elementary Thomas-Fermi (TF) approximation. We demonstrate that the ADA for the 2D kinetic energy functional works very well under a wide variety of confinement potentials, even for relatively small particle numbers. Remarkably, the TF approximation for the kinetic energy functional, {\em without any gradient corrections}, also yields good agreement with the exact kinetic energy for all confining potentials considered, although at the expense of the spatial and kinetic energy densities exhibiting poor point-wise agreement, particularly near the TF radius. Our findings illustrate that the ADA kinetic energy functional yields accurate results for {\em both} the local and global equilibrium properties of an inhomogeneous 2D Fermi gas, without the need for any fitting parameters.Comment: 6 figure