5 research outputs found
Statistics of dressed modes in a thermal state
By a Wigner-function calculation, we evaluate the trace of a certain Gaussian
operator arising in the theory of a boson system subject to both finite
temperature and (weak) interaction. Thereby we rederive (and generalize) a
recent result by Kocharovsky, Kocharovsky, and Scully [Phys. Rev. A, vol. 61,
art. 053606 (2000)] in a way that is technically much simpler. One step uses a
special case of the response of Wigner functions to linear transformations, and
we demonstrate the general case by simple means. As an application we extract
the counting statistics for each mode of the Bose gas.Comment: to appear in Optics Communications, 10 page
Non-Linear Canonical Transformations in Classical and Quantum Mechanics
-Mechanics is a consistent physical theory which describes both classical
and quantum mechanics simultaneously through the representation theory of the
Heisenberg group. In this paper we describe how non-linear canonical
transformations affect -mechanical observables and states. Using this we
show how canonical transformations change a quantum mechanical system. We seek
an operator on the set of -mechanical observables which corresponds to the
classical canonical transformation. In order to do this we derive a set of
integral equations which when solved will give us the coherent state expansion
of this operator. The motivation for these integral equations comes from the
work of Moshinsky and a variety of collaborators. We consider a number of
examples and discuss the use of these equations for non-bijective
transformations.Comment: The paper has been improved in light of a referee's report. The paper
will appear in the Journal of Mathematical Physics. 24 pages, no figure