Evolving states in nonlocal type dynamics of composite systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Sowa, Artur

关键词: Nonlocal quantum dynamics;    Nonlinear evolution equations;    Operator equations;    Composite quantum systems;    Nondissipative interaction;   

DOI  :  10.1016/j.geomphys.2010.09.006

来源: Elsevier

【 摘 要 】

We discuss a model of nonlocal dynamics describing non-dissipative interaction of quantum systems. Within this framework, the evolution of the composite system is governed by an operator equation -i(K) over dot = KH + (H) over capK + beta Kf (K*K). Here, H and (H) over cap are time-independent self-adjoint Hamiltonians, x bar right arrow f(x) is a real analytic function, and beta is a real parameter. We demonstrate that the equation is completely solvable in the sense that a solution K = K (t) may be represented as a composition of three factors, each determined from a decoupled linear problem. Namely, if K(0) = K-0 then K(t) = exp[i (H) over capt] o K-0 o exp[i beta f (K-0*K-0)t] o exp[iHt]. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free