Riccati equation and the problem of decoherence

Abstract

The block operator matrix theory is used to investigate the problem of a single qubit. We will establish a connection between the Riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in question. The model of the half spin particle in the rotating magnetic field coupling with the external environment is discussed. We show that the model defined in such a way can be reduced to a time independent problem.

4 pages, accepted by Journal of Mathematical Physics,

References in corpus (2)

• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Adiabatic approximation in open quantum systems

Cited by in corpus (4)

• Exact solution of the Schrodinger equation with the spin-boson Hamiltonian
• Exact reduced dynamics for a qubit in a precessing magnetic field and in the contact with a heat-bath
• Riccati equation and the problem of decoherence II: Symmetry and the solution of the Riccati equation
• Stationary states of two-level open quantum systems