Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
arXiv:1410.8448 · doi:10.1103/PhysRevA.91.033627
Abstract
We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of novel terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (super-localized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.
23 pages, 5 figures
References in corpus (14)
- Anomalous transport in the crowded world of biological cells
- Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
- Attractive and repulsive Fermi polarons in two dimensions
- Quantum transport through a Tonks-Girardeau gas
- Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
- Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
- Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
- The equilibrium states of open quantum systems in the strong coupling regime
- Force measurement in the presence of Brownian noise: Equilibrium distribution method vs. Drift method
- The Accuracy of Perturbative Master Equations
- Bloch oscillations of bosonic lattice polarons
- Smoluchowski-Kramers approximation in the case of variable friction
- Thermophoresis of Brownian particles driven by coloured noise
- Dynamical Effects of Multiplicative Feedback on a Noisy System