Related papers: General relations for quantum gases in two and thr…
We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise…
We derive exact general relations between various observables for N bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for…
We present universal relations for a two-dimensional Fermi gas with pairwise contact interactions. The derivation of these relations is made possible by obtaining the explicit form of a generalized function -- selector -- in the momentum…
We derive the full set of universal relations for spin-polarized Fermi gases with $p$-wave interaction in two dimensions, simply using the short-range asymptotic behavior of fermion-pair wave functions. For $p$-wave interactions, an…
We derive exact relations that connect the universal $C/k^4$-decay of the momentum distribution at large $k$ with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact…
We present a comprehensive derivation of a set of universal relations for spin-orbit-coupled Fermi gases in three or two dimension, which follow from the short-range behavior of the two-body physics. Besides the adiabatic energy relations,…
We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to…
A dilute homogeneous 3D Fermi gas in the ground state is considered for the case of a repulsive pairwise interaction. The low-density (dilution) expansions for the kinetic and interaction energies of the system in question are calculated up…
The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: $$E_\text{internal}=\hbar^2\Omega C/4\pi am+\sum_{\vect k\sigma}(\hbar^2 k^2/2m)(n_{\vect…
The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point…
The spectral function of a spin-balanced two-dimensional Fermi gas with short-range interactions is calculated by means of a quantum cluster expansion. Good qualitative agreement is found with a recent experiment by Feld $\textit{et al.}$…
The synthetic spin-orbit coupled quantum gases is widely studied both experimentally and theoretically in recent years. As previous studies show, this modification of single-body dispersion will in general couple different partial waves and…
Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently…
The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing pheomena in solid materials, such as high-$T_{c}$ superconductivity and the fractional quantum Hall effect.…
We study the system of trapped two-component Fermi gases with zero-range interaction in two dimensions (2D) or one dimension (1D). We calculate the one-particle density matrices of these systems at small displacements, from which we show…
We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tan's contact of an unpolarized system of short-range, attractively interacting spin-1/2 fermions in one spatial…
We theoretically investigate equal-mass spin-balanced two-component Fermi gases in which pairs of atoms with opposite spins interact via a short-range isotropic model potential. We probe the distinction between two-dimensional and…
Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a…
One-dimensional spinless Bose and Fermi gases with contact interactions have the close interrelation via Girardeau's Bose-Fermi mapping, leading to the correspondences in their energy spectra and thermodynamics. However, correlation…
We present the results of the computation of the third order corrections to the ground state energy of the diluted polarized gas of nonrelativistic spin $1/2$ fermions interacting through a spin-independent repulsive two-body potential. The…