We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short-and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures. At a fixed chemical potential, we map out the distributions of the superfluid order parameters and number densities with respect to the temperatures. For a charge density wave, we find that the global-range interaction enhances the charge order by increasing the transition temperature at which the charge order melts out, while for a supersolid phase, we find that the disappearance of the charge order and the superfluid order occurs at different temperature. At a fixed number-density filling factor, we extract the temperature dependence of the thermodynamic functions such as internal energy, specific heat and entropy. Across the superfluid phase transition, the specific heat has a discontinuous jump.
We develop a method to extract the dissipation for a heavy moving impurity immersed in superfluid Fermi gases. The drag force is derived analytically. As a reward, we are able to extract the dynamical structure factor, from which density excitations of the system is carefully examined. We show that dissipations through drag force is associated with two types of excitations, one being single-particle and the other being collective. We map out the critical velocity for dissipation across the BEC-BCS crossover, consistent with existing experiments. For a magnetic impurity, we show that the dissipation is immune to collective excitations. Our study clearly manifests that dissipation and associated excitations can be controlled by coupling superfluid Fermi gases with a moving impurity, and paves the way for further exploring intriguing realm of nonequilibrium phenomena and dissipation dynamics.
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