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International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin

On a quantum heavy particle

Dmitrii Valer'evich Treschev

Published Jan 1, 2018• 0 citations
Publisher
DOI
10.4213/proc22850

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Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass usually assures that the coherence length of the incident particle in the direction of the propagation of the particle (the parallel direction) will be much shorter than the characteristic lattice length of the surface, thus leading to a classical description. Recent work on molecular interferometry has shown that extreme collimation of the beam creates a perpendicular coherence length which is sufficiently long so as to observe interference of very heavy species passing through a grating. Here we show, using quantum mechanical simulations, that the same effect will lead to quantum diffraction of heavy particles colliding with a surface. The effect is robust with respect to the incident energy, the angle of incidence, and the mass of the particle.
We investigate the quantum walk of two interacting particles of different mass in a one dimensional lattice. We show that the inter-particle interaction together with the mass imbalance exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the heavy and light particles perform independent particle quantum walks for small interaction. However, stronger interactions lead to the quantum walk of the repulsively bound pair. For a different initial states when the walkers are on different sites initially, the heavy particle performs quantum walk almost independently and the light particle shows reflected and transmitted components across the heavy particle for small interactions. After a critical interaction strength, the light particle wave function ceases to penetrate through the heavy particle. However, when the quantum walkers are initially kept at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both heavy and light particles from each other. We analyze these features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.
We consider a simple one-dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent superposition of two spatially separated wave packets with opposite momentum and the light particle localized in the region between the two wave packets. We characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. We derive the corresponding reduced density matrix for the heavy particle and explicitly compute the (partial) decoherence effect for the heavy particle induced by the presence of the light one for a particular set up of the parameters.