Quantum transport in chains with noisy off-diagonal couplings
arXiv:cond-mat/0505346 · doi:10.1063/1.2148962
Abstract
We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.
6 pages, to appear in J. Chem. Phys
References in corpus (16)
- Thermal conduction in classical low-dimensional lattices
- Anomalous heat conduction in one dimensional momentum-conserving systems
- Heat conduction in one dimensional nonintegrable systems
- Granular Avalanches in Fluids
- Semiclassical Theory of Chaotic Quantum Transport
- Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
- Fermi-Pasta-Ulam lattice: Peierls equation and anomalous heat conductivity
- Relaxation of classical many-body hamiltonians in one dimension
- Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System
- Finite thermal conductivity in 1D models having zero Lyapunov exponents
- Can disorder induce a finite thermal conductivity in 1D lattices?
- On the universality of anomalous one-dimensional heat conductivity
- Diffusive-ballistic crossover in 1D quantum walks
- Quantum heat transfer through an atomic wire
- Dynamics by White-Noise Hamiltonians
- Damped Quantum Interference using Stochastic Calculus