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Xiong D, Thiel F, Barkai E. Using Hilbert transform and classical chains to simulate quantum walks. Phys Rev E. 2017;96(2):022114doi: 10.1103/PhysRevE.96.022114.
Xiong, D., Thiel, F., & Barkai, E. (2017). Using Hilbert transform and classical chains to simulate quantum walks. Physical review. E, 96(2), 022114. https://doi.org/10.1103/PhysRevE.96.022114
Xiong, Daxing, et al. "Using Hilbert transform and classical chains to simulate quantum walks." Physical review. E vol. 96,2 (2017): 022114. doi: https://doi.org/10.1103/PhysRevE.96.022114
Xiong D, Thiel F, Barkai E. Using Hilbert transform and classical chains to simulate quantum walks. Phys Rev E. 2017 Aug;96(2):022114. doi: 10.1103/PhysRevE.96.022114. Epub 2017 Aug 08. PMID: 28950452.
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Phys Rev E. 2017 Aug;96(2):022114. doi: 10.1103/PhysRevE.96.022114. Epub 2017 Aug 08.

Using Hilbert transform and classical chains to simulate quantum walks.

Physical review. E

Daxing Xiong, Felix Thiel, Eli Barkai

Affiliations

  1. Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.
  2. Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel.

PMID: 28950452 DOI: 10.1103/PhysRevE.96.022114

Abstract

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the 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 a 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 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.

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