Related papers: The semi-classical limit of large fermionic system…
A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…
We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
We consider the dynamical system consisting of a quantum degree of freedom $A$ interacting with $N$ quantum oscillators described by the Lagrangian \bq L = {1\over 2}\dot{A}^2 + \sum_{i=1}^{N} \left\{{1\over 2}\dot{x}_i^2 - {1\over 2}( m^2…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…
Quasi-one-dimensional (quasi-1d) two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated…
We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with…
We use all-optical methods to produce a highly-degenerate Fermi gas of spin-1/2 $^6$Li atoms. A magnetic field tunes the gas near a collisional (Feshbach) resonance, producing strong interactions between spin-up and spin-down atoms. This…
The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different…
We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…
We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low…
We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between Landau levels set to the same order as that of potential…
Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally…
Models with range-free frustrated Ising spin- and Hubbard interaction are treated exactly by means of the discrete time slicing method. Critical and tricritical points, correlations, and the fermion propagator, are derived as a function of…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
We use first-order perturbation theory near the fermionic limit of the delta-function Bose gas in one dimension (i.e., a system of weakly interacting fermions) to study three situations of physical interest. The calculation is done using a…