Annales Henri Poincaré

, Volume 16, Issue 8, pp 1713–1778 | Cite as

A Ballistic Motion Disrupted by Quantum Reflections

  • Jeremy Thane ClarkEmail author


I study a Lindblad dynamics modeling a quantum test particle in a Dirac comb that collides with particles from a background gas. The main result is a homogenization theorem in an adiabatic limiting regime involving large initial momentum for the test particle. Over the time interval considered, the particle would exhibit essentially ballistic motion if either the singular periodic potential or the kicks from the gas were removed. However, the particle behaves diffusively when both sources of forcing are present. The conversion of the motion from ballistic to diffusive is generated by occasional quantum reflections that result when the test particle’s momentum is driven through a collision near to an element of the half-spaced reciprocal lattice of the Dirac comb.


Test Particle Ballistic Motion Bloch Function Jump Rate Quantum Dynamical Semigroup 
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© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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