Related papers: Dynamics of the Bose-Hubbard Chain for Weak Intera…
We study, both analytically and numerically, the Boltzmann transport equation for the Hubbard chain with nearest neighbor hopping and spatially homogeneous initial condition. The time-dependent Wigner function is matrix-valued because of…
The standard Fermi-Hubbard chain becomes non-integrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the…
We investigate transport properties of one-dimensional fermionic tight binding models featuring nearest and next-nearest neighbor hopping, where the fermions are additionally subject to a weak short range mutual interaction. To this end we…
For the spin-$\{1}{2}$ Fermi-Hubbard model we derive the kinetic equation valid for weak interactions by using time-dependent perturbation expansion up to second order. In recent theoretical and numerical studies the kinetic equation has…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-Reservoir system, namely, the single-site Bose-Hubbard model coupled to two reservoirs at different…
The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…
We study the kinetic theory of a weakly interacting quantum field. Assuming a state that is close to homogeneous and stationary, we derive a closed kinetic equation for the rate of change of the occupation numbers, perturbatively in the…
A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach…
Deviations from diffusive heat transport in high thermal conductivity crystalline insulators are generally understood within the framework of the phonon Boltzmann Transport Equation. However, for low thermal conductivity materials with…
For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, $f$, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and,…
We study ballistic thermal transport in Heisenberg spin chain with nearest-neighbor ferromagnetic interactions at low temperatures. Explicit expressions for transmission coefficients are derived for thermal transport in a periodic spin…
To account for the anomalous/spin Hall conductivities and spin-orbit torque in the zeroth order of electron scattering time in strongly spin-orbit coupled systems, the Boltzmann transport theory in the case of weak disorder-potentials has…
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach…
The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which…
We consider $N$ interacting dipolar bosonic atoms at zero temperature in a double-well potential. This system is described by the two-space-mode extended Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH terms)…
We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the…
Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations…
We study Hilbert-space fragmentation and thermalization in a one-dimensional dipole-conserving Bose-Hubbard chain. By analyzing the structure of the Hamiltonian matrix in the Fock basis, we show that the system exhibits weak Hilbert-space…
Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling.…