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Phase operator formalism in thermo field dynamics

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  • Ban, Masashi

Abstract

A phase operator formalism is presented within the framework of thermo field dynamics (TFD). It is shown that a unitary phase operator (or phase factor) can be defined as a canonical conjugate of the generator of phase shift in TFD since the generator has a lower bounded spectrum. The tilde conjugation plays an essential role in defining the unitary phase operator in TFD. The unitary phase operator is expressed in terms of the relative-number states. The properties of the unitary phase operator are investigated in detail. The relations to the Pegg-Barnett phase operator and to the polar decomposition of the operator which appears in the heterodyne detection are found. Furthermore, by making use of the phase operator method, a quantum phase measurement is considered and the relation to the optimal probability operator measure in the conventional theory is investigated.

Suggested Citation

  • Ban, Masashi, 1994. "Phase operator formalism in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 327-356.
    • Handle: RePEc:eee:phsmap:v:212:y:1994:i:3:p:327-356
    DOI: 10.1016/0378-4371(94)90337-9
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    1. Vallée Annie, 1975. "Singer-Kerel (Jeanne) - La New Economics et l'expansion américaine," Revue Économique, Programme National Persée, vol. 26(3), pages 518-519.
    2. Arimitsu, T. & Sudo, Y. & Umezawa, H., 1987. "Dynamical rearrangement of the thermal vacuum in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 433-451.
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