Related papers: Wigner function of noninteracting trapped fermions
A one dimensional experiment in granular dynamics is carried out to test the thermodynamic theory of weakly excited granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78, 2764(1997)] where granular particles are treated as spinless…
We present one-dimensional simulation results for the cold atom tunneling experiments by the Heidelberg group [G. Z\"urn {\em{et al.}}, Phys. Rev. Lett. {\bf{108}}, 075303 (2012) and G. Z\"urn {\em{et al.}}, Phys. Rev. Lett. {\bf{111}},…
We discuss the confining features of the Schwinger model on the Poincare half plane. We show that despite the fact that the expectation value of the large Wilson loop of massless Schwinger model displays the perimeter behavior, the system…
In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…
We study by non perturbative techniques a vector, axial--vector theory characterized by a parameter which interpolates between pure vector and chiral Schwinger models. Main results are two windows in the space of parameters which exhibit…
We study a system of $N$ interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$…
The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having $N_x$ sites, the universal Casimir scaling function, which characterises the leading…
Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof…
We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface.…
We consider possible dynamical models for a light fermion confined by a potential field. With the Dirac equation only Lorentz scalar confinement yields normalizable wavefunctions, while with the ``no pair'' variant of the Dirac equation…
We study the ground state of $N \gg 1$ noninteracting fermions in a two-dimensional harmonic trap rotating at angular frequency $\Omega>0$. The support of the density of the Fermi gas is a disk of radius $R_e$. We calculate the variance of…
We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f(W)$. Going beyond the well studied tracial mode, $\mathrm{Tr}[f(W)]$, which is equivalent to the customary linear statistics of…
We assess the performance of nonempirical, truly nonlocal and semi-local functionals with regard to structural and thermal properties of $3d$, $4d$, and $5d$ non-magnetic transition metals. We focus on constraint-based functionals and…
The scaling property of the thermodynamic free energy ($\Phi$) of a system at global equilibrium has been examined using a real-time method known as the virial theorem. We demonstrate these scaling properties through a derived relation…
A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related…
Combining the Bethe Ansatz with a functional deviation expansion and using an asymptotic expansion of the Bethe Ansatz equations, we compute the curvature of levels D_n at any filling for the one-dimensional lattice spinless fermion model.…
The aim of the article is to discuss the S-matrix interpretation of perturbation theory for the Wigner functions generating functional at a finite temperature. For sake of definiteness, fruitful from pedagogical point of view, the concrete…
The Wigner function of a dynamical infinite dimensional lattice is studied. A closed differential equation without diffusion terms for this function is obtained and solved. We map atom-photon interaction systems, such as the Jaynes-Cummings…
In this paper, we show that the ground-state of many-body Schr\"odinger operators for electrons in one dimension is non-degenerate. More precisely, we consider Schr\"odinger operators of the form $H_N(v,w) = -\Delta + \sum_{i\neq j}^N…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…