engleski

Exact treatment of open infinite-dimensional quantum systems : I. Time-independent case

Closed quantum systems that do not interact with the surrounding are described by an eigenvalue equation such as the Schrödinger equation. In particular, one can describe in this way a finite closed quantum system Saρ that contains ρ eigenvalues and ρ eigenstates. Open quantum systems that interact with surrounding are usually treated within a perturbation expansion method. In a consistent quantum approach this “surrounding” should be treated as another (usually infinite) quantum system Sb∞ . In formal mathematical terms one has to find a solution of the combined system S∞≡Saρ⊕Sb∞ with emphasize on the properties of the subsystem Saρ . A new approach for the solution of this problem is presented. One finds that combined system S ∞ contains embedded eigenstates |Ψ(ε, …)⟩ with continuous eigenvalues ε, and in addition it may contain isolated eigenstates |Ψr⟩ with discrete eigenvalues ε r . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. In almost all cases those two equations produce a complete and exact description of the open quantum system Saρ . The extremely rare exceptional cases can be also treated accordingly. The suggested method produces correct results, however strong the interaction between quantum systems Saρ and Sb∞ . Two examples are presented in order to illustrate various aspects of this method.

interaction of quantum systemsm ; time-independent perturbation ; open quantum systems

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