# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field. (English) Zbl 1152.82322
Summary: For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.

##### MSC:
 82C31 Stochastic methods in time-dependent statistical mechanics 81S25 Quantum stochastic calculus
Full Text:
##### References:
 [1] H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems, Oxford, 2002. · Zbl 1053.81001 [2] Stefanescu, E.: Physica A. 350, 227 (2005) [3] Li, Ke-Hsueh: Physics of open systems. Phys. rept. 134 (1986) [4] Lindblad, G.: Commun. math. Phys.. 48, 119 (1976) [5] Sandulescu, A.; Scutaru, H.: Ann. phys.. 173, 277 (1987) [6] Stefanescu, E.; Liotta, R. J.; Sandulescu, A.: Phys. rev. C. 57, 798 (1998) [7] Stefanescu, E.; Scheid, W.; Sandulescu, A.; Greiner, W.: Phys. rev. C. 53, 3014 (1996) [8] Sandulescu, A.; Stefanescu, E.: Physica A. 161, 525 (1989) [9] Atkins, D. J.; Wiswman, H. M.; Warszawski, P.: Phys. rev. A. 67, 023802 (2003) [10] Weiss, U.: Quantum dissipative systems. (1999) · Zbl 1137.81301 [11] Mahler, G.; Weberuss, V. A.: Quantum networks--dynamics of open nanostructures. (1995) [12] Gainutdinov, R. Kh.; Mutygullina, A. A.; Scheid, W.: Phys. lett. A. 306, 1 (2002) [13] Hu, B. L.; Paz, J. P.; Zhang, Y.: Phys. rev. D. 45, 2843 (1992) [14] Halliwell, J. J.; Yu, T.: Phys. rev. D. 53, 2012 (1996) [15] Kanokov, Z.; Palchikov, Yu.V.; Adamian, G. G.; Antonenko, N. V.; Scheid, W.: Phys. rev. E. 71, 016121 (2005) [16] Palchikov, Yu.V.; Kanokov, Z.; Adamian, G. G.; Antonenko, N. V.; Scheid, W.: Phys. rev. E. 71, 016122 (2005) [17] Ford, G. W.; Lewis, J. T.; O’connell, R. F.: Ann. phys.. 252, 362 (1996) [18] Stefanescu, E.; Sandulescu, A.; Scheid, W.: Int. J. Mod. phys. E. 9, 17 (2000) [19] Stefanescu, E.; Sandulescu, A.: Int. J. Mod. phys. E. 11, 119 (2002) [20] Stefanescu, E.; Sandulescu, A.: Int. J. Mod. phys. E. 11, 379 (2002) [21] Feynman, R. P.; Vernon, F. L.; Hellvarth, R. W.: J. appl. Phys.. 28, 49 (1957) [22] Belyanin, A. A.; Kocharovsky, V. V.; Kocharovsky, Vl.V.: Q. semiclass. Opt.. 10, L13 (1998) [23] Stefanescu, E.; Scheid, W.: Physica A. 374, 203 (2007)