arXiv subjects

P L Krapivsky

Publications and source records attributed to P L Krapivsky.

3 recordsLinked to original sources

arXiv2026

Expansion of a free Fermi gas released from an isotropic trapping potential

We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly released. Using semi-classical techniques, we derive the full late-time profile of the expanding cloud in the regime when the fermion number is large. We thus obtain explicit expressions for power-law potentials with arbitrary exponent $a$ and in all dimensions $d$. The momentum distribution and the spatial profile of the cloud exhibit a universal edge exponent $d/a$, thus generalizing the Wigner semi-circle law and the Thomas-Fermi distribution.

cond-mat.stat-mech↗

arXiv2019

Return probability of $N$ fermions released from a 1D confining potential

We consider $N$ non-interacting fermions prepared in the ground state of a 1D confining potential and submitted to an instantaneous quench consisting in releasing the trapping potential. We show that the quantum return probability of finding the fermions in their initial state at a later time falls off as a power law in the long-time regime, with a universal exponent depending only on $N$ and on whether the free fermions expand over the full line or over a half-line. In both geometries the amplitudes of this power-law decay are expressed in terms of finite determinants of moments of the one-body bound-state wavefunctions in the potential. These amplitudes are worked out explicitly for the harmonic and square-well potentials. At large fermion numbers they obey scaling laws involving the Fermi energy of the initial state. The use of the Selberg-Mehta integrals stemming from random matrix theory has been instrumental in the derivation of these results.

cond-mat.stat-mech↗

arXiv2018

Bulk diffusion in a kinetically constrained lattice gas

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas, viz. to the Kob-Andersen model on the square lattice.

cond-mat.stat-mech↗