IJPAM: Volume 85, No. 4 (2013)
A SOLVABLE QSDE THROUGH SEMIGROUPS
OF OPERATORS AND SOME PHYSICAL APPLICATIONS
OF OPERATORS AND SOME PHYSICAL APPLICATIONS
O. González-Gaxiola1, José A. Santiago2, G. Chacón-Acosta3
1,2,3Department of Applied Mathematics and Systems
UAM-Cuajimalpa
Artificios 40, México, D.F. 01120, MEXICO
1,2,3Department of Applied Mathematics and Systems
UAM-Cuajimalpa
Artificios 40, México, D.F. 01120, MEXICO
Abstract. In this paper we give a characterization, through semigroups theory, of the solution of a quantum stochastic differential equation (QSDE). In the physical interpretation of the problem, we show that the group that characterizes the quantum dynamics appears as the strong limit a family of translations perturbed by a Gaussian potential. Finally, we use the model to study a two-level atom in an electromagnetic field.
Received: November 4, 2012
AMS Subject Classification: 81Q10, 81Q80, 81V80
Key Words and Phrases: quantum stochastic differential equation, number process, evolution equation, exponential vector
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DOI: 10.12732/ijpam.v85i4.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 4
