Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions

We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been proven only in one or two dimensions, and give other interesting relations involving several densities or the particle density alone. We show that in the asymptotic limit of large particle numbers, the densities go over into the semi-classica...

We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e. the Fourier Law does not hold. Our conclusions are based on the analysis of the dependence of the heat current on the number of particles, of the internal temperature profile and on the Green-Kubo formalism.

We study the ground state properties of a quasi one dimensional electron gas, interacting via an effective potential with a harmonic transversal confinement and long range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows to sample t...

We consider a small and fixed number of fermions in an isolated one-dimensional trap (microcanonical ensemble). The ground state of the system is defined at T=0, with the lowest single-particle levels occupied. The number of particles in this ground state fluctuates as a function of excitation energy. By breaking up the energy spectrum into particle and hole sectors, and mapping the problem onto the classic number partitioning theory, we formulate a new method to calculate th...

We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the thermodynamic function considered, and on temperature, we find that the probability distributions are dominated either (i) by the local fluctuations of the single-particle spectrum on the scale of the mean level spacing, or (ii) by the long...

We consider the real time dynamics of $N$ noninteracting fermions in $d=1$. They evolve in a trapping potential $V(x)$, starting from the equilibrium state in a potential $V_0(x)$. We study the time evolution of the Wigner function $W(x,p,t)$ in the phase space $(x,p)$, and the associated kernel which encodes all correlation functions. At $t=0$ the Wigner function for large $N$ is uniform in phase space inside the Fermi volume, and vanishes at the Fermi surf over a scale $e_N...

We consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. We show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, we obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtelties ...

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose-Einstein condensation are discussed.

Number fluctuations in a one-dimensional Bose gas consist of contributions from many smaller independent localized fluctuations, the density grains. We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature that exactly determine all higher order moments of number fluctuations. These moments are closely related to the statistics of the localized (but not zero-range) density grains. We directly calculate the mean occupation of thes...

We investigate the particle and kinetic-energy densities for $N$ non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed non-periodic classical orbits. We derive universal relations between the oscillating parts of the densities for potentials with spherical symmetry in arbitrary dimensions, and a ``local virial theorem'' valid also for arbitrary non-integra...