Quantum mechanics with a timedependent random unitary Hamiltonian: A perturbative study of the nonlinear Keldysh sigmamodel
Abstract
We analyze the perturbative series of the Keldyshtype sigmamodel proposed recently for describing the quantum mechanics with timedependent Hamiltonians from the unitary WignerDyson randommatrix ensemble. We observe that vertices of orders higher than four cancel, which allows us to reduce the calculation of the energydiffusion constant to that in a special kind of the matrix ϕ model. We further verify that the perturbative fourloop correction to the energydiffusion constant in the highvelocity limit cancels, in agreement with the conjecture of one of the authors.
 Publication:

Nuclear Physics B
 Pub Date:
 March 2006
 DOI:
 10.1016/j.nuclphysb.2006.01.006
 arXiv:
 arXiv:condmat/0511030
 Bibcode:
 2006NuPhB.737..304I
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 27 pages, 15 figures