Related papers: The quantum drift-diffusion model: existence and e…
This work is devoted to the analysis of the quantum Liouville-BGK equation. This equation arises in the work of Degond and Ringhofer on the derivation of quantum hydrodynamical models from first principles. Their theory consists in…
We introduce in this work an efficient numerical method for the simulation of the quantum Liouville-BGK equation, which models the diffusive transport of quantum particles. The corner stone to the model is the BGK collision operator,…
We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, M\`{e}hats and Ringhofer in one space dimension. With our approach, that uses consistently matrices on ${\mathbb C}^N$ instead…
The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $\epsilon$, evolution equations are…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to the quantum drift-diffusion equation is performed in the framework of finite energy weak solutions. No assumptions on the limiting solution are made. The proof…
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact,…
We consider the problem of quantum and stochastic confinement for drift-diffusion equations on domains $ \Omega \subset \mathbb R^d$. We obtain various sufficient conditions on the behavior of the coefficients near the boundary of $\Omega$…
We present a model for decoherence in time-dependent transport. It boils down into a form of wave function that undergoes a smooth stochastic drift of the phase in a local basis, the Quantum Drift (QD) model. This drift is nothing else but…
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the rate of convergence to equilibrium is maximized. We solve…
We discuss the unitary quantum dynamics of the Dicke model (spin and oscillator coupled). A suitable quasiprobabilty representing the quantum state turns out to obey a Fokker-Planck equation, with drift terms representing the underlying…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in non-divergence form. Specifically, in these equations, the diffusion coefficient…
A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time towards a thermal equilibrium limit, is derived from nonequilibrium-statistical considerations: Adapting an…
In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the…
We are interested in this work in the numerical resolution of the Quantum Liouville-BGK equation, which arises in the derivation of quantum hydrodynamical models from first principles. Such models are often obtained in some asymptotic…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog…
We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…