Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach

Abstract

Long-time tails, or algebraic decay of time-correlation functions, have long been known to exist both in many-body systems and in models of non-interacting particles in the presence of quenched disorder that are often referred to as Lorentz models. In the latter, they have been studied extensively by a wide variety of methods, the best known example being what is known as weak-localization effects in disordered systems of non-interacting electrons. This paper provides a unifying, and very simple, approach to all of these effects. We show that simple modifications of the diffusion equation due to either a random diffusion coefficient, or a random scattering potential, accounts for both the decay exponents and the prefactors of the leading long-time tails in the velocity autocorrelation functions of both classical and quantum Lorentz models.

16pp, 3 figs

References in corpus (10)

• Anderson Transitions
• Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• Theory of diffusive fluctuations
• Hydrodynamic Long-Time tails From Anti de Sitter Space
• Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly
• Density Expansion for the Mobility in a Quantum Lorentz Model
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Density Expansion for the Mobility of Electrons in Helium Gas
• Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background