|
In my talk I shall discuss a simple model of conductivity -- a quantum particle (an atom) in a lattice, subject
to a static field and interacting with the bath of Bose atoms. Results from direct numerical simulations
of the system dynamics and statistical analysis of the eigenstates are compared with predictions from
linear response theory, analytical solutions of the master equation, and the theory of quantum chaos.
It is shown, in particular, that the behavior of the current-current correlation function, entering Kubo's equation,
is entirely defined by the chaotic properties of the system and that the phenological relaxation constant,
entering the master equation, is actually encoded in this correlation function.
[1] A.V.Ponomarev, J.Mandronero, A.R.Kolovsky and A.Buchleitner, Atomic current across an optical lattice, Phys. Rev. Lett. 96, 050404 (2006). [2] A.R.Kolovsky, Atomic current in optical lattices: Reexamination of the Esaki-Tsu equation, Phys. Rev. A 77, 063604 (2008). [3] A.R.Kolovsky, Conductivity with cold atoms in optical lattices}, Journal of Statistical Mechanics -Theory and Experiments (JSTAT), doi:10.1088/1742-5468/2009/02/P02018 (2009). |
|