Quantum dynamics with source boundary condition

ERNESTO P. DANIELI; GONZALO A. ÁLVAREZ; LUIS E. F. FOA TORRES; HORACIO M. PASTAWSKI

Búzios, Brazil

Workshop; Pan American Advanced Studied Institute (PASI) and Workshop on Physics of Information - PASI 2003; 2003

Pan American Advanced Studied Institute

A situation which is quite overlooked in the literature is the Schrödinger equation with a time dependent source. Examples of this are the electrodes in an a.c. electrical conductivity experiment, the non-equilibrium chemical kinetics for slow rates of laser pumping into the excited state; the cross-polarization transfer in NMR, etc. We use the keldysh formalism to study the solutions of the Schrödinger equation with a source. We solve the two extreme cases in which the boundary condition results in either a coherent or an incoherent injection of quantum waves. For the coherent case, we find a relation between the source boundary condition and the initial value problem that enables proper normalization and establishes their equivalence. we propose a "gedanken" experiment where the evolution of a quantum wave-packet is reverted by the local injection. The incoherent injection was used to represent environmental interactions accounting for dynamical feedback effects that go beyond the Fermi Golden Rule. We address the problem of cross-polarization transfer in NMR, in which the nuclear spin system 13C-1H is in contact with a spin reservoir. For a solvable model of this system, the result of the Keldysh equation with a decoherent source is shown to give the exact dynamics.