Regularity of solutions to linear stochastic Schrodinger equations
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Date
2007
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WORLD SCIENTIFIC PUBL CO PTE LTD
Abstract
We develop linear stochastic Schrodinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution X-t to a LSS with regular initial condition. Moreover, we obtain that the mean value of the square norm of X-t is constant. We also treat the approximation of LSSs by ordinary stochastic differential equations. We apply our results to:
(i) models of quantum measurements of position and momentum; and
(ii) a system formed by fermions.
(i) models of quantum measurements of position and momentum; and
(ii) a system formed by fermions.
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Keywords
linear stochastic Schrodinger equation, stochastic evolution equation, regular solution, existence and uniqueness, QUANTUM, SEMIGROUPS