Abstract
We construct Lindbladians associated with controlled stochastic Hamiltonians in the weak coupling regime. This construction allows us to determine the power spectrum of the noise from measurements of dephasing rates. Moreover, by studying the derived equation it is possible to optimize the control as well as to test numerical algorithms that solve controlled stochastic Schrödinger equations. A few examples are worked out in detail.
Highlights
Lindbladians in the weak coupling limit have been rigorously studied in [6, 13, 10, 4, 5, 18, 1, 16, 7] in the time independent setting
This article describes Lindbladians associated with controlled stochastic Hamiltonians in weak coupling
Ε is the phase acquired by the wave function during one correlation time
Summary
This article describes Lindbladians associated with controlled stochastic Hamiltonians in weak coupling. A careful derivation of the Lindbladians for the controlled stochastic evolutions and in particular Eq (3.8) for general and in Eq (1.10) for stationary control are new. The case where the direction of the field is stochastic is modeled by several α’s and gives rise to noise that is non-commutative (not been treated before.) Hc, a time-dependent (Hermitian) matrix, represents the control. By stationary controls we shall mean that HαI (t) has a finite number of Fourier coefficients.
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