The quantum Fokker-Planck equation for certain boson systems |
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| Institution: | 1. Nonlinear Optics Division, Institute of Physics, A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznań, Poland;2. Joint Laboratory of Optics, Palacký University, 771 46 Olomouc, Czechoslovakia;3. Institute for Higher Nervous Activity, Palacký University, 775 20, Olomouc, Czechoslovakia;1. Clifford Research Group, Department of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Krijgslaan 281–S8, 9000 Gent, Belgium;2. Department of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Krijgslaan 281–S9, 9000 Gent, Belgium;1. Faculty of Physics, Shahrood University of Technology, Shahrood, P.O. Box: 3619995161-316, Iran;2. Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, Jinju 52828, Republic of Korea;1. Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russia;2. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia;1. Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France;2. Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary prospect 7a, Moscow 117312, Russia;3. Moscow Institute of Physics and Technology, Institutsky per. 9, Dolgoprudny 141700, Russia;4. CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Prague 8, Czech Republic |
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| Abstract: | Quantum relations between a class of boson Langevin equations and the associated Fokker-Planck equations are derived. The Fokker-Planck equations for the Wigner distribution Φsym related with symmetric ordering of the boson operators, the distribution ΦA related with antinormal ordering, and the distribution ΦN related with normal ordering (P-representation) are given. |
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