Quantum transport in chains with noisy off-diagonal couplings.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Dynamics

Background:

• Understanding transport phenomena in low-dimensional systems is crucial.
• Modeling energy and charge transport often involves complex Hamiltonians and noise effects.
• The Liouville-von Neumann equation describes system evolution but can be challenging to solve with noise.

Purpose of the Study:

• To develop a model for conductivity and energy diffusion in a linear chain system.
• To analyze the impact of Gaussian noise on system dynamics.
• To derive simplified equations of motion and identify transport coefficients.

Main Methods:

• Formulation of a quadratic Hamiltonian model with Gaussian noise.
• Derivation of the noise-averaged Liouville-von Neumann equation.
• Analysis of the system's density matrix for expectation values.
• Investigation of discrete heat and diffusion equations.

Main Results:

• The noise-averaged Liouville-von Neumann equation simplifies to the Lindblad equation under specific conditions (diagonal correlation matrix).
• Expectation values of energy and number densities satisfy discrete heat and diffusion equations.
• Transport coefficients are expressed via Hamiltonian parameters.
• Conditions for constant total energy and linear energy density gradients in heat reservoirs are discussed.

Conclusions:

• The model provides a framework for studying transport in noisy linear chains.
• The reduction to the Lindblad equation offers a more tractable approach for analysis.
• The derived discrete equations offer insights into heat and diffusion processes at a microscopic level.