For citation:
??? Non-Markov theory of quantum fluctuations in the nonlinear dynamical systems with linear friction. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 2, pp. 131-145.
Non-Markov theory of quantum fluctuations in the nonlinear dynamical systems with linear friction
Properties of the operator Langevin forces in systems with linear friction are found with the help of fluctuation—dissipation theorems. The special attention is paid to greater singularity of these forces than in the quantum Markov theory. To avoid infinities, dynamic equations are represented in the integral form. Integral stochastic processes σk(t) with finite mean square related to the Langevin forces are introduced and applied. Such non-Gaussian characteristics as threefold and fourfold many-time cumulants are considered in the non-linear case and in the case of fluctuating friction coefficients.
- Kossakowski А. On quantum statistical mechanics of non-Hamiltonian systems. Rep. Math. Phys. 1972;3(4):247-274. DOI: 10.1016/0034-4877(72)90010-9.
- Lindblad G. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 1976;48:119-130. DOI: 10.1007/BF01608499.
- Gardiner CW. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Berlin: Springer; 1985. 442 p.
- Hudson RL, Parthasarathy KR. Quantum Ito’s Formula and Stochastic Evolutions. Commun. Math. Phys. 1984;93:301-323. DOI: 10.1007/BF01258530.
- Callen HB, Welton ТА. Irreversibility and Generalized Noise. Phys. Rev. 1951;83(1):34-40. DOI: 10.1103/PhysRev.83.34.
- Stratonovich RL. Nonlinear Nonequilibrium Thermodynamics. Berlin: Springer; 1992. 361 p. DOI: 10.1007/978-3-642-77343-3.
- Stratonovich RL, Chichigina OA. On the applicability of the theory of quantum Markov processes to Brownian motion. J. Exp. Theor. Phys. 1994;78(1):56–61.
- 116 reads