Quantum Processes and Possibility of Their Control


  • Ashot S. Gevorkyan Institute for Informatics and Automation Problems of NAS RA


The dissipation and decoherence (for example, the e®ects of noise in quantum computations), interaction with thermostat or in general with physical vacuum, measurement and many other complicated problems of open quantum systems are a consequence of interaction of quantum systems with the environment. These problems are described mathematically in terms of complex probabilistic process (CPP). Particularly, treating the environment as a Markovian process we derive an LangevinSchrÄodinger type stochastic di®erential equation (SDE) for describing the quantum system interacting with environment. For the 1D randomly quantum harmonic oscillator (QHO) L-Sh equation has a solution in the form of orthogonal CPP. On the basis of orthogonal CPP the stochastic density matrix (SDM) method is developed and in its framework relaxation processes in the uncountable dimension closed system of "QHO+environment" is investigated. With the help of SDM method the thermodynamical potentials, like nonequilibrium entropy and the energy of ground state are exactly constructed. The dispersion for di®erent operators is calculated. In particular, the expression for uncertain relations depending on parameter of interaction between QHO and environment is obtained. The Weyl transformation for stochastic operators is speci¯ed. Ground state Winger function is developed in detail.


Proceedings of A driatico Research Conference and Miniworkshop Quantum Chaos, 4June-6July 1990,Trieste,Italy

C.Presilla,R.Onofrio,U Tambini, Ann.Phys.,v.248, p.95 (1996)

C.W. Gardiner,M.J.Collett,Phys.Rev.A,v.31,p.3761(1985)

N.Gisin,I.C.Percival,J.Phys.A,v.25, p.56-77 (1992)

N.Knauf, Y.G.Sinai,e-print N 232 http://www.math.tu-berlin.de

A .V.Bogdanov, A.S.Gevorkyan,Proceedings of Int. Workshop on Quantum Systems, Minsk,Belarus,p.26 (1996)

A.V.Bogdanov, A .S. Gevorkyan,A.G.Grigoryan,AMS/IP Studies in Advanced Mathematics,v.13,p.81(1999)

A.V .Bogdanov,A .S.Gevorkyan,A.G.Grigoryan,S.A.Matveev,Int.Journ.Bifurcation and Chaos,v.9,N.12,p.9(1999)

A.S.Gevorkyan,Exactly solvable models of stochastic quantum mechanics within the framework of Langevin-Schreodinger type equation, Analysis and applications.Proceeding of the NATO Advanced reserach worskshop, Yerevan 2002,Eds.by Barsegian G.and Begehr H.,NATO Science publications, pp. 415-442,Kluwer,(2004).

A .N . Baz', Ya. B.Zel'dovich and A.M.Perelomov, Scattering reactions and Decays in Nonrelativistic Quantum Mechanics,( in Russia) ,"Nauka",Moscow,1971.

D.N.Zubarev,Nonequilibrium statistical thermodinamics, Nauka,1971 (in russian).

I.M.Lifshitz, S.A .Gredeskul and L.P.Pastur, Introduction to the Theory of Non-Regular Systems, (in Russia) ,"Nauka",Moscow,1982.

C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences, Springer-Verlag Berlin New-York Tokyo,1985

J.Glimm,A .Jae, Quantum Physics. A Functional Integral Point of View, SpringerVerlag,1981.

W.M.Itano, D.J.Heinzen, J.J. Bollinger and D.J.Wineland,Phys.Rev.A,v.41,p.22-95 (1990).

V.Gorini,A.Kossakowski and E.C.G.Sudarshan,J.Math.Phys., v.17,p. 821(1976).

G.Lindblad,Comm.Math.phys., v48, p.119 -976) .




How to Cite

Gevorkyan, A. S. . (2021). Quantum Processes and Possibility of Their Control. Mathematical Problems of Computer Science, 26, 101–113. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/532

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