We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its applicability to the late-time dynamics of a specific bosonic quantum system by developing a microscopic non-equilibrium quantum field theory. Employing a self-consistent $1/N$ approximation in the number of field components, we extract all entries of a generalized diffusion matrix and determine their dependence on microscopic model parameters. We discuss the relation of our results to experiments in ultracold atom quantum simulators.
Kosterlitz--Thouless Criticality in a Dipole-Conserving XY Model
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, and School of Physics, Sun Yat-sen University（中山大学物理学院）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University（西湖大学理学院）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究中心）
We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally …
Dipole oscillation is studied in a normal phase of a trapped Bose--Fermi-mixture gas composed of single-species bosons and single-species fermions. Applying the moment method to the linearized Boltzmann equation, we derive a closed set of equations of motion for the center-of-mass position and momentum of both components. By solving the coupled equations, we reveal the behavior of dipole modes in the transition between the collisionless regime and the hydrodynamic regime. We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime: one collisio…
We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at low temperatures is described. Despite the fact that we consider the neutral particles we account the short-range interaction between particles. We consider the particles in the Bose-Einstein condensate (BEC) state. This method is called the method of quantum hydrodynamics, because natural for of the quantum mechanics rewritten in terms of material fields o…
A recent time-of-flight (TOF) expansion experiment with polarized fermionic erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid due to dipole-dipole interaction, thus confirming previous theoretical predictions. Here we perform a systematic study of the ground-state properties and TOF dynamics for trapped dipolar Fermi gases from the collisionless to the hydrodynamic regime at zero temperature. To this end we solve analytically the underlying Boltzmann-Vlasov equation within the relaxation-time approximation in the vicinity of equilibrium by using a suitable rescali…
We introduce equations of motion for spin dynamics in a ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction, written using a vector expressing the superfluid velocity and a complex scalar describing the magnetization. This simple hydrodynamical description extracts the dynamics of spin wave and affords a straightforward approach by which to investigate the spin dynamics of the condensate. To demonstrate the advantages of the description, we illustrate dynamical instability and magnetic fluctuation preference, which are expressed in analytical forms.
Recently, a seminal STIRAP experiment allowed the creation of 40K-87Rb molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. In order to describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system as, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release fro…
By using a sum rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a 1D harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized, in the high temperature collisionless regime, by a beating signal of two different frequencies ($ω_z$ and $3ω_z$) while, in the high temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}ω_z$). This behaviour differs from the case …
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time…
We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is estimated. Quantum equations for the evolution of medium polarization are constructed for the first time. The mathematical method we developed allows studying the effects of interactions on the evolution of polarization. The developed method may be applied to various physical systems in which dynamics is affected by DDI. A problem of elementary excitations i…
