Quantum hydrodynamic equations of fermions at nonzero temperatures

L. S. Kuz’menkov, Сергей Геннадьевич Максимов, Владислав Владимирович Федосеев

Maciej Lewkowicz, Mirosław Brewczyk, Mariusz Gajda +1 more

Using numerical methods, we study the formation of self-bound quantum Bose-Fermi droplets at nonzero temperatures. We describe an attractive atomic Bose-Fermi mixture using quantum hydrodynamics enriched by beyond-mean-field corrections and thermal fluctuations, together with a simplified self-consistent Hartree-Fock model. With these models, we determine that low-temperature droplets with finite lifetimes can exist in free space when the attraction between bosons and fermions is sufficiently strong. Additionally, Bose-Fermi droplets at nonzero temperatures can exist in a box potential in equilibrium with bosonic and fermionic vapor. We discuss the properties of Bose-Fermi droplets at nonzero temperatures in terms of the initial condensate fraction, total atom number, and interspecies attraction strength.

Serguei Maximov, L. S. Kuz’menkov, J.L. Guardado

Abstract The quantum distribution function is derived to reach an accordance with quantum hydrodynamics and to conserve quantum properties of the system. This distribution function, when calculating statistical averages, leads to correct local values of the fundamental physical quantities; and the local conservation laws of the microscopic quantum hydrodynamics can be obtained from such statistics by passing to mathematical expectatives. The equation for the one‐particle distribution function generates the many‐particle distribution functions. Then, the BBGKY hierarchy equations are obtained. The one‐particle statistical operator of a system of fermions in the local equilibrium at arbitrary temperatures is calculated. The dynamics of local hydrodynamic functions (chemical potential, hydrodynamic velocity, and temperature) completely determine the dynamics of the one‐particle statistical operator. The quantum hydrodynamic equations for the proton‐neutron system at low temperatures are obtained from the equation for one‐particle distribution function. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Oleg Yu. Dinariev

Pavel A. Andreev

We present a derivation of the quantum hydrodynamic (QHD) equations for neutral bosons. We consider the short-range interaction between particles. This interaction consist of a binary interaction U( ri, rj) and a three-particle interaction (TPI) U( ri, rj, rk) and the last one does not include binary interaction between particles. From QHD equations for Bose–Einstein condensate we derive a nonlinear Schrödinger equation. This equation was derived for zero temperature and contains the nonlinearities of the third and the fifth degree. Explicit form of the constant of the TPI is obtained. First of all, developed method we used for studying of dispersion of the linear waves. Dispersion characteristics of the linear waves are compared for different particular cases. We make comparison of the two-particle interaction in the third order by the interaction radius (TOIR) and TPI at the zero temperature. We consider influence of the temperature on the dispersion of the elementary excitations. For this aim we derive a system of the QHD equations at nonzero temperature. Obtained system of equation is an analog of the well-known two-fluid hydrodynamics. Moreover, it is generalization of the two-fluid hydrodynamics equations due to TPI. Explicit expressions of the velocities for the first and the second sound via the concentration of superfluid and noncondensate components is calculated.

Imran Siddique