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arXiv:2210.04540 · Chinese Physics Letters

Hydrodynamics of a Multi-Component Bosonic Superfluid

Fan Zhang, Lan Yin

Published May 1, 2023• 7 citations
arXivHTMLPDF

Abstract

We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the nonuniform case. Our approach can be extended to systems with long-range interactions such as dipole-dipole interactions by treating the Hartree energy properly. For a highly symmetric superfluid, we obtain the excitation spectrum and show that except for the density phonon, all other excitations are all degenerate. The implication of our results is discussed.

DOI
10.1088/0256-307x/40/6/066701

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We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the nonuniform case. Our approach can be extended to systems with long-range interactions such as dipole-dipole interactions by treating the Hartree energy properly. For a highly symmetric superfluid, we obtain the excitation spectrum and show that except for the density phonon, all other excitations are all degenerate. The implication of our results is discussed.
Properties of solutions to superfluid hydrodynamic equations as applied to the degenerate Bose gas are considered. The equations are split into two independent pairs of equations. One pair is written for the normal component implies the instability of solutions, which manifests itself in the majorant catastrophe with respect to the total density. The case when the thermodynamic functions depend on the difference of the normal and superfluid velocities is also considered. In that case, the system is not split; however, the instability and the majorant catastrophe occur when the initial temperature tends to absolute zero.
The equations of motion for the reduced density matrices of an interacting Bose system are treated using the concept of off-diagonal long-range order. The equations are decoupled on the one-particle level. With this approximation, the hydrodynamic equations for the densities and the velocities of the condensate and the depletion are derived. The interaction between the two fluid components depends on density variations and on the relative velocity. The latter interaction terms appear as kinetic pressure terms and a Magnus force term. Via the equation for the total momentum, a connection between the velocities of the condensate and the depletion, and the velocities in Landau's two-fluid model is derived. The excitation spectrum of the system is investigated in the phonon region. A comparison of the resulting velocities for the first and second sound with the experimentally determined ones shows that the functional dependence of the condensate density on temperature is similar to that of the superfluid component.
Abstract Chapter 2 describes the basic knowledge of Bose-condensed systems in order to study the quantum hydrodynamics for both the superfluid helium and the atomic-gas BECs in the following sections. Starting from the field theoretical formulation, we will first give a self-contained explanation of the derivation of the most fundamental GP equation for weakly interacting Bose gases at zero temperature. We will also highlight the theoretical treatment for incorporating the concept of elementary excitations to describe low-energy excitations of Bose systems, the definition of normal and superfluid components, and eventually the celebrated model of two-fluid hydrodynamics. Finally, the microscopic structure and dynamics of topological excitations obtained from the GP equation are discussed by exemplifying solitons, vortex lines, and vortex rings.
We rigorously analyze the low-temperature properties of homogeneous three-dimensional two-component Bose mixture with dipole-dipole interaction. For such a system the effective hydrodynamic action that governs the behavior of low-energy excitations is derived. The infrared structure of the exact single-particle Green's functions is obtained in terms of macroscopic parameters, namely the inverse compressibility and the superfluid density matrices. Within the one-loop approximation we calculate some of the most relevant observable quantities and give the beyond mean-field stability condition for the binary dipolar Bose gas in the dilute limit. A brief variational derivation of the coupled equations that describe macroscopic hydrodynamics of the system in the external nonuniform potential at zero temperature is presented.
Abstract Ultracold Bose atoms is the physical system existing at the small finite temperatures, where the quantum and nonlinear phenomena play crucial role. Bosons are considered to be composed of two different fluids: the Bose–Einstein condensate and the normal fluid (the thermal component). The extended hydrodynamic models are obtained for each fluids, where the pressure evolution equations and the pressure flux third rank tensor evolution equations are obtained along with the continuity and Euler equations. It is found that the pressure evolution equation contains zero contribution of the short-range interaction. The pressure flux evolution equation contains the interaction which simplifies to the quantum fluctuations in the zero temperature limit. The structure of the third rank tensor describing this interaction is obtained in the regime of small temperature and weak interaction. The model is derived via the straightforward calculation of evolution of macroscopic functions using the microscopic many-particle Schrodinger equation in the coordinate representation. Finally, the two-fluid hydrodynamics is constructed in form of four equations for each fluid in order to give model describing the quantum fluctuations in BEC and the thermal effects in the normal fluid.
In this work we studied two sistems of bosonic superfluids at zero temperature, ultra-cold Bose gases and superfluid helium, within a simple classical field formalism and we underlined differences and similarities between them. We also analyzed how the presence of strong interactions, as in the case of helium, modifies the quasiparticle excitation spectrum and subsequently the vortex line density profile. After a general review about these bosonic systems properties we started in general from the Hartree equation of a bosonic system and, with different hypotesis on the interaction potential between bosons, we obtained the equations describing the two above mentioned systems, mainly focusing on elementary quasiparticle excitations and quantized vortices. Furthermore throughout this work the results were compared with experimental data and aftermaths of the main theories in literature.