Evolving states in nonlocal type dynamics of composite systems

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 −iK̇=KH+HˆK+βKf(K∗K). Here, HH and Hˆ are time-independent self-adjoint Hamiltonians, x↦f(x)x↦f(x) is a real analytic function, and ββ is a real parameter. We demonstrate that the equation is completely solvable in the sense that a solution K=K(t)K=K(t) may be represented as a composition of three factors, each determined from a decoupled linear problem. Namely, if K(0)=K0K(0)=K0 then K(t)=exp[iHˆt]∘K0∘exp[iβf(K0∗K0)t]∘exp[iHt].