Non-Markovian Gaussian dissipative stochastic wave vector

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 63, Issue 1, 2001, Pages 012106-012101

  Budini, Adrián A ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; RANDOM PROCESSES; VECTORS; WAVE EQUATIONS;

STOCHASTIC WAVE FUNCTIONS (SWF);

QUANTUM THEORY;

EID: 4043075403     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.63.012106     Document Type: Article

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26. We have worked with an evolution that does not preserve the SWF norm in each realization of the noises. This property is necessary to work out numerically, and can be achieved by means of a Girsanov transformation of the noises [13], which leads to a nonlinear SWF evolution.
27. When the operator ℱ(t) is Hermitian, the SWF dynamics reduces to a stochastic Hamiltonian one. In this case most of the expressions obtained along the paper remain valid if we omit the "dissipative terms." In particular, the infinite hierarchy of equations result uncoupled, and the stochastic propagator loses its functional character. The expressions for the mean density matrix evolution remain the same.