Phonon Random Walks: Using Classical Chains to Simulate Quantum Dynamics
Year: 2016
Type: preprint
Abstract: Inspired by quantum walks (QW), we propose the concept of classical phonon random walks (PRW). With this we show a correspondence between classical and quantum dynamics. To be specific, we explain how a classical chain of particles with linear interactions can be used to simulate a quantum like wave function $\psi_{m}(t)$. In particular, the real (imaginary) part of $\psi_{m}(t)$ is the normalized classical momentum (a new $\pi/2$ shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared $\left|\psi_{m}(t)\right|^{2}$. We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.
Source: arXiv (Cornell University)
Authors: Daxing Xiong, Eli Barkai
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2560936634