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Quantum Stochastic Systems in Terms of Non-Equilibrium Thermo Field Dynamics

In: Quantum Communication, Computing, and Measurement

Author

Listed:
  • T. Arimitsu

    (University of Tsukuba, Institute of Physics)

  • T. Saito

    (University of Tsukuba, Institute of Physics)

  • T. Imagire

    (University of Tsukuba, Institute of Physics)

Abstract

With the help of Non-Equilibrium Thermo Field Dynamics, a unified framework of the canonical operator formalism for quantum stochastic differential equations is constructed where the stochastic Liouville equation and the Langevin equation are, respectively, equivalent to the Schrödinger equation and the Heisenberg equation in quantum mechanics. It was found that there exist at least two attractive formulations; one is based on a non-Hermitian martingale (a realization of the conservation of probability), and the other on a Hermitian martingale (a realization of the conservation of norm of a wave function). In this paper, the structures of two formulations are investigated in a systematic manner by means of the difference of martingale operators.

Suggested Citation

  • T. Arimitsu & T. Saito & T. Imagire, 1997. "Quantum Stochastic Systems in Terms of Non-Equilibrium Thermo Field Dynamics," Springer Books, in: O. Hirota & A. S. Holevo & C. M. Caves (ed.), Quantum Communication, Computing, and Measurement, pages 371-380, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-5923-8_39
    DOI: 10.1007/978-1-4615-5923-8_39
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