Abstract
We consider a family of time-dependent dephasing Lindblad generators which model the monitoring of the instantaneous Hamiltonian of a system by a Markovian bath. In this family the time dependence of the dephasing operators is (essentially) governed by the instantaneous Hamiltonian. The evolution in the adiabatic limit admits a geometric interpretation and can be solved by quadrature. As an application we derive an analog of the Landau-Zener tunneling formula for this family.
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References
Lindblad G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119–130 (1976)
Gorini V., Kossakowski A., Sudarshan E.C.G.: Completely positive semigroups of N-level systems. J. Math. Phys. 17, 821–825 (1976)
Gardiner C.W., Zoller P.: Quantum noise. Springer, Berlin (2004)
Davies E.B.: Quantum theory of open systems. Academic Press, London (1976)
Breuer H.P., Petruccione F.: The theory of open quantum systems. Oxford University Press, Oxford (2002)
Åberg J., Kult D., Sjöqvist E.: Robustness of the adiabatic quantum search. Phys. Rev. A 71, 060312 (2005)
Misra B., Sudarshan E.C.G.: The Zeno’s paradox in quantum theory. J. Math. Phys. 18(4), 756–763 (1977)
Avron J., Fraas M., Graf G.M., Grech P.: Optimal time schedule for adiabatic evolution. Phys. Rev. A 82, 040304(R) (2010)
Nenciu G., Rasche G.: On the adiabatic theorem for nonself-adjoint Hamiltonians. J. Phys. A 25, 5741–5751 (1992)
Joye A.: General adiabatic evolution with a gap condition. Commun. Math. Phys. 275, 139–162 (2007)
Abou Salem W.K.: On the quasi-static evolution of nonequilibrium steady states. Ann. H. Poincaré 8, 569–596 (2007)
Landau L.: Zur Theorie der Energieübertragung. II. Phys. Z. Sowjet. 2, 46–51 (1932)
Zener C.: Non-adiabatic crossing of energy levels. Proc. Roy. Soc. London, Series A 137, 692–702 (1932)
Majorana E.: Atomi orientati in campo magnetico variabile. Nuovo Cimento 9, 43–50 (1932)
Stückelberg E.C.G.: Theorie der unelastischen Stösse zwischen Atomen. Helv. Phys. Acta 5, 369 (1932)
Leggett A.J., et al.: Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59(1), 1–85 (1987)
Shimshoni E., Gefen Y.: Onset of dissipation in Zener dynamics: relaxation versus dephasing. Ann. Phys. 210, 16–80 (1991)
Wubs M., Saito K., Kohler S., Hänggi P., Kayanuma Y.: Gauging a quantum heat bath with dissipative Landau-Zener transitions. Phys. Rev. Lett. 97, 200404 (2006)
Shimshoni E., Stern A.: Dephasing of interference in Landau-Zener transitions. Phys. Rev. B 47, 9523–9536 (1993)
Pokrovsky V.L., Sun D.: Fast quantum noise in the Landau-Zener transition. Phys. Rev. B 76, 024310 (2007)
Berry M.V.: Histories of adiabatic quantum transitions. Proc. Roy. Soc. London, Series A 429, 61–72 (1990)
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Communicated by M. Aizenman
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Avron, J.E., Fraas, M., Graf, G.M. et al. Landau-Zener Tunneling for Dephasing Lindblad Evolutions. Commun. Math. Phys. 305, 633–639 (2011). https://doi.org/10.1007/s00220-011-1269-y
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DOI: https://doi.org/10.1007/s00220-011-1269-y