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Quantum dissipative dynamics a particle in a double-well potential

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Abstract

The results of analytical and numerical investigation of quantum dissipative dynamics a particle moving in a potential well with two equilibrium states is presented. A classical analogue of this problem is the capture into the resonance a particle in a double-well potential, when two states of equilibrium in the phase space are separated by a separatrix. The probability of finding the system in one of states of equilibrium for the quantum particle, depending on initial conditions and noise, is discussed.

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References

  1. V. I. Arnold, “Small denominators and problem of stability of motion in classical and celestial mechanics,” Russ. Math. Surv. 18 (6), 85–191 (1963).

    Article  MathSciNet  Google Scholar 

  2. I. M. Lifshitz, V. M. Nabutovskii, and A. A. Slutskin, “Motion of charged particles in a varying inhomogeneous electromagnetic field,” Sov. Phys. JETP 14, 669–675 (1962).

    Google Scholar 

  3. M. Scully and M. Zubairy, Quantum Optics (Cambridge Univ. Press, Cambridge, 1997).

    Book  MATH  Google Scholar 

  4. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Natl. Bureau of Standards, Washington, 1964).

    MATH  Google Scholar 

  5. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).

    Book  MATH  Google Scholar 

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Correspondence to C. S. Kim.

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Submitted by L. N. Shchur

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Kim, C.S., Pashin, D.S. & Satanin, A.M. Quantum dissipative dynamics a particle in a double-well potential. Lobachevskii J Math 38, 931–935 (2017). https://doi.org/10.1134/S1995080217050201

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  • DOI: https://doi.org/10.1134/S1995080217050201

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