Diffusion of a massive quantum particle coupled to a quasi-free thermal medium

Details Diffusion of a massive quantum particle coupled to a quasi-free thermal medium Diffusion of a massive quantum particle coupled to a quasi-free thermal medium

2009-06-28

arxiv.org/abs/0906.5178v4

Physics

Mathematical Physics

v3 to v4, layout changes, to appear in CMP

Scientific paper

We consider a heavy quantum particle with an internal degree of freedom moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with finitely many excited states). The particle is coupled to a thermal medium (bath) consisting of free relativistic bosons through an interaction of strength $\la$ linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order $\la^{-2}$, and we assume that the internal degree of freedom is coupled "effectively" to the thermal medium. We prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for $\la$ small enough.

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