We use Feynman's influence-functional theory to study the quantum dynamics of a heavy particle moving in a free Fermi gas with arbitrary average velocity. A semiclassical expansion yields a nonlinear Langevin equation with the exact friction coefficient as derived in an earlier publication. The fluctuations around a steady state far from equilibrium are due to a nonclassical state-dependent noise term and can be described by a diffusion constant. In the limit of zero average velocity, the Einstein relation is fulfilled for arbitrary temperatures. For finite velocities the diffusion around the steady state is different in longitudinal and transverse directions and can be expressed in terms of the transport cross section and a ``diffusion'' cross section. In the case where the frictional force exhibits a maximum as a function of velocity and thus an unstable branch for v> ${\mathit{v}}_{\mathit{c}}$ , the longitudinal diffusion constant diverges on approaching ${\mathit{v}}_{\mathit{c}}$ from below. Numerical results for the noise spectrum and the temperature and velocity dependence of the diffusion constants are presented for simple repulsive interaction potentials in one and three dimensions.We use Feynman's influence-functional theory to study the quantum dynamics of a heavy particle moving in a free Fermi gas with arbitrary average velocity. A semiclassical expansion yields a nonlinear Langevin equation with the exact friction coefficient as derived in an earlier publication. The fluctuations around a steady state far from equilibrium are due to a nonclassical state-dependent noise term and can be described by a diffusion constant. In the limit of zero average velocity, the Einstein relation is fulfilled for arbitrary temperatures. For finite velocities the diffusion around the steady state is different in longitudinal and transverse directions and can be expressed in terms of the transport cross section and a ``diffusion'' cross section. In the case where the frictional force exhibits a maximum as a function of velocity and thus an unstable branch for v>${\mathit{v}}_{\mathit{c}}$, the longitudinal diffusion constant diverges on approaching ${\mathit{v}}_{\mathit{c}}$ from below. Numerical results for the noise spectrum and the temperature and velocity dependence of the diffusion constants are presented for simple repulsive interaction potentials in one and three dimensions.

Physical review. B, Condensed matterJul 1, 199210 citations

Derivation of the diffusion coefficient of stochastic quantum mechanics

L. de la Peña-Auerbach, Ana Marı́a Cetto

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BAug 1, 19723 citations

Non-Markovian Quantum State Diffusion in a Fermionic Bath

Evgeny Polyakov, Alexey N. Rubtsov

We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these fluctuations in the basis of the particle-hole coherent states, then these fluctuations produce a classical particle-hole noise.The probability distribution of this noise is provided by the generalized particle-hole Husimi function of the vacuum. Then we define the dressed quantum trajectory as the evolution of the open system and the bath which is conditioned on a particular particle-hole noise sample. The resulting description resembles the non-Markovian quantum state diffusion for the bosonic bath. Therefore, we expect that our fermionic approach will share its favourable propeties like the possibility to carry out Monte-Carlo simulations of non-Markovian quantum dynamics on long times.We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these fluctuations in the basis of the particle-hole coherent states, then these fluctuations produce a classical particle-hole noise.The probability distribution of this noise is provided by the generalized particle-hole Husimi function of the vacuum. Then we define the dressed quantum trajectory as the evolution of the open system and the bath which is conditioned on a particular particle-hole noise sample. The resulting description resembles the non-Markovian quantum state diffusion for the bosonic bath. Therefore, we expect that our fermionic approach will share its favourable propeties like the possibility to carry out Monte-Carlo simulations of non-Markovian quantum dynamics on long times.

arXiv:1909.05760Sep 12, 20190 citations

Intermediate scattering function and quantum recoil in non-Markovian quantum diffusion

Peter S. M. Townsend, Alex W. Chin

Exact expressions are derived for the intermediate scattering function (ISF) of a quantum particle diffusing in a harmonic potential and linearly coupled to a harmonic bath. The results are valid for arbitrary strength and spectral density of the coupling. The general, exact non-Markovian result is expressed in terms of the classical velocity autocorrelation function, which represents an accumulated phase during a scattering event. The imaginary part of the exponent of the ISF is proportional to the accumulated phase, which is an antisymmetric function of the correlation time $t$ . The expressions extend previous results given in the quantum Langevin framework where the classical response of the bath was taken as Markovian. For a special case of non-Markovian friction, where the friction kernel decays exponentially in time rather than instantaneously, we provide exact results relating to unconfined quantum diffusion, and identify general features that allow insight to be exported to more complex examples. The accumulated phase as a function of the $t$ has a universal gradient at the origin, depending only on the mass of the diffusing system particle. At large $t$ the accumulated phase reaches a constant limit that depends only on the classical diffusion coefficient and is therefore independent of the detailed memory properties of the friction kernel. Non-Markovian properties of the friction kernel are encoded in the details of how the accumulated phase switches from its $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ to its $t\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit, subject to the constraint of the universal gradient. When memory effects are significant, the transition from one limit to the other becomes nonmonotonic, owing to oscillations in the classical velocity autocorrelation. The result is interpreted in terms of a solvent caging effect, in which slowly fluctuating bath modes create transient wells for the system particle.Exact expressions are derived for the intermediate scattering function (ISF) of a quantum particle diffusing in a harmonic potential and linearly coupled to a harmonic bath. The results are valid for arbitrary strength and spectral density of the coupling. The general, exact non-Markovian result is expressed in terms of the classical velocity autocorrelation function, which represents an accumulated phase during a scattering event. The imaginary part of the exponent of the ISF is proportional to the accumulated phase, which is an antisymmetric function of the correlation time $t$. The expressions extend previous results given in the quantum Langevin framework where the classical response of the bath was taken as Markovian. For a special case of non-Markovian friction, where the friction kernel decays exponentially in time rather than instantaneously, we provide exact results relating to unconfined quantum diffusion, and identify general features that allow insight to be exported to more complex examples. The accumulated phase as a function of the $t$ has a universal gradient at the origin, depending only on the mass of the diffusing system particle. At large $t$ the accumulated phase reaches a constant limit that depends only on the classical diffusion coefficient and is therefore independent of the detailed memory properties of the friction kernel. Non-Markovian properties of the friction kernel are encoded in the details of how the accumulated phase switches from its $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ to its $t\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit, subject to the constraint of the universal gradient. When memory effects are significant, the transition from one limit to the other becomes nonmonotonic, owing to oscillations in the classical velocity autocorrelation. The result is interpreted in terms of a solvent caging effect, in which slowly fluctuating bath modes create transient wells for the system particle.

arXiv:1807.07990Physical Review AAug 3, 20182 citations

{\mathit{v}}_{\mathit{c}}

, the longitudinal diffusion constant diverges on approaching

{\mathit{v}}_{\mathit{c}}

from below. Numerical results for the noise spectrum and the temperature and velocity dependence of the diffusion constants are presented for simple repulsive interaction potentials in one and three dimensions.

t

. The expressions extend previous results given in the quantum Langevin framework where the classical response of the bath was taken as Markovian. For a special case of non-Markovian friction, where the friction kernel decays exponentially in time rather than instantaneously, we provide exact results relating to unconfined quantum diffusion, and identify general features that allow insight to be exported to more complex examples. The accumulated phase as a function of the

t

has a universal gradient at the origin, depending only on the mass of the diffusing system particle. At large

t

the accumulated phase reaches a constant limit that depends only on the classical diffusion coefficient and is therefore independent of the detailed memory properties of the friction kernel. Non-Markovian properties of the friction kernel are encoded in the details of how the accumulated phase switches from its $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ to its $t\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit, subject to the constraint of the universal gradient. When memory effects are significant, the transition from one limit to the other becomes nonmonotonic, owing to oscillations in the classical velocity autocorrelation. The result is interpreted in terms of a solvent caging effect, in which slowly fluctuating bath modes create transient wells for the system particle.