Decoherence in open quantum systems

Systems that interact with an environment are referred to as open quantum systems. During the evolution of such systems, decoherence occurs: the superposition of quantum states breaks down, the system effectively becomes more classical, and information about the system passes into the medium. In fact, this happens when the following physical assumptions are fulfilled: the interaction of the system with the medium is weak, the correlations iside the system rapidly decay, and the rate of relaxation in the system is high. Using these assumptions, I will derive the Born-Markov and Lindblad equations* that describe the evolution of an open quantum system. Then I will tell about the article [1], in which we solve the Lindblad equation for the Hilbert space of dimension 2. We show that any initial state of the system tends to a finite one, which does not depend of the initial conditionas. Thus, we see that the system "forgets" about the initial state in the process of evolution.
*In addition to Lindblad, this equation was obtained independently by the Soviet scientist Franke V.A. and by Gorini V. & co. [3–5]

References

1. A. A. Andrianov, M. V. Ioffe, E. A. Izotova, O. O. Novikov, under review
2. A. A. Andrianov, M. V. Ioffe, E. A. Izotova, O. O. Novikov, Eur. Phys. J. Plus, 135 (2020), 531, arXiv: 2002.00410
3. V. A. Franke, Theor. Math. Phys., 27 (1976), 406
4. V. Gorini, A. Kossakowski, E. C. G. Sudarshan, J. Math. Phys., 17 (1976), 821
5. G. Lindblad, Commun. Math. Phys., 48 (1976), 119