Abstract:
A quantum Fokker–Planck equation is derived for a model system of a single-mode
laser based on two-level atoms with dynamics of the trajectories described by the
nonlinear differential Lorenz system. The trajectories are investigated in the
asymptotic limit of strong pumping, or large Rayleigh number, in the region of
applicability of averaging methods. Two bifurcations that arise when the damping
constant of the field is varied are described: the appearance of limit cycles and
Hopf inverse bifurcation.
Citation:
L. A. Pokrovskii, “Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers I”, TMF, 62:2 (1985), 272–290; Theoret. and Math. Phys., 62:2 (1985), 183–196
This publication is cited in the following 6 articles:
K. E. Morozov, “O nekonservativnykh vozmuscheniyakh trekhmernykh integriruemykh sistem”, Izvestiya vuzov. PND, 32:6 (2024), 766–780
A. N. Pchelintsev, “Numerical and physical modeling of the Lorenz system dynamics”, Num. Anal. Appl., 7:2 (2014), 159–167
Darryl D. Holm, Gregor Kovačič, Thomas A. Wettergren, “Homoclinic orbits in the Maxwell-Bloch equations with a probe”, Phys. Rev. E, 54:1 (1996), 243
Darryl D. Holm, Gregor Kovačič, Thomas A. Wettergren, “Near-integrability and chaos in a resonant-cavity laser model”, Physics Letters A, 200:3-4 (1995), 299
S. A. Moskalenko, A. Kh. Rotaru, Yu. M. Shvera, “Fokker–Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density”, Theoret. and Math. Phys., 75:2 (1988), 536–543
L. A. Pokrovskii, “Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers. II. Description of trajectories near a separatrix by the matching method”, Theoret. and Math. Phys., 67:2 (1986), 490–507
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