arXiv subjects

Frédéric Hébert

Publications and source records attributed to Frédéric Hébert.

3 recordsLinked to original sources

arXiv2023

Critical velocity of a two-dimensional superflow past a potential barrier of arbitrary penetrability

We theoretically investigate the critical velocity for dissipationless motion of a two-dimensional superfluid past a static potential barrier of large width. The circular-shaped barrier provides a comprehensive analytical framework for the critical speed, for which we derive closed-form expressions using the hydraulic approximation, the hodograph method, and Janzen-Rayleigh expansions of the velocity potential. These analytical estimates are shown to be in good agreement with the numerical results of an imaginary-time integration of the full wave equation. In contrast to most of the state of the art, our study is not restricted to an impenetrable potential barrier nor to a quartic interaction Hamiltonian, which enables realistic modeling of recent experiments with atomic Bose-Einstein condensates and paraxial superfluids of light in two dimensions.

cond-mat.quant-gas↗

arXiv2023

Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle

We consider in this work the different possible stationary flows of a one dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.

cond-mat.quant-gas↗

arXiv2022

Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions

We study the equilibrium properties of a one-dimensional mixture of two Tonks-Girardeau gases on a ring geometry in the limit of strongly-repulsive inter-species interactions. We derive the exact many-body wavefunction and compare it to the $SU(2)$ solution where intra- and inter-species interactions are also diverging but equal. We focus on the role of the $SU(2)$-symmetry breaking on the behaviour of the large- and short-distance correlations by studying the zero-momentum occupation number and the Tan's contact from the asymptotic behavior of the momentum distribution. Although the symmetry is only weakly broken, it has important consequences on spin correlations in the system as the reduction by a factor of two of the zero-momentum occupation number with respect to the $SU(2)$ case in the thermodynamic limit and the decrease of the Tan's contact.

cond-mat.quant-gas↗