Using Hilbert transform and classical chains to simulate quantum walks

Abstract

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular the quantum walks. Through this strategy, we obtain the quantum wave function from classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation indicates a concept of "phonon random walks", and thus it provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.

14 pages;13 figures; Finally published in Phys. Rev. E

References in corpus (11)

• Universal computation by quantum walk
• Quantum walks of correlated particles
• Heat Transport in low-dimensional systems
• Lévy walks
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Asymptotic densities of ballistic Lévy walks
• Dynamics of continuous-time quantum walks in restricted geometries
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Methods of exploring energy diffusion in lattices with finite temperature

Cited by in corpus (3)

• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• Accelerating the heat diffusion: fast thermal relaxation of a microcantilever