Canonical transformations and exact invariants for dissipative systems

A simple treatment to the problem of finding exact invariants and related auxiliary equations for time‐dependent oscillators with friction is presented. The treatment is based on the use of a time‐dependent canonical transformation and an auxiliary transformation.

[1]  M. Lutzky,et al.  New nonlinear dynamical systems possessing invariants , 1981 .

[2]  L. Wollenberg.  Characterisation of homogeneous quadratic invariants for one-dimensional homogeneous quadratic hamiltonians , 1980 .

[3]  C. J. Eliezer,et al.  A Note on the Time-Dependent Harmonic Oscillator , 1976 .

[4]  B. Remaud,et al.  Constants of motion and non-stationary wave functions for the damped, time-dependent harmonic oscillator , 1980 .

[5]  J. R. Ray,et al.  Ermakov systems and quantum-mechanical superposition laws , 1981 .

[6]  S. V. Lawande,et al.  Time‐dependent invariants and quantum mechanics in two dimensions , 1986 .

[7]  W. Sarlet.  Further generalization of Ray-Reid systems , 1981 .

[8]  John R. Ray,et al.  More exact invariants for the time-dependent harmonic oscillator , 1979 .

[9]  W. Sarlet.  Exact invariants for time-dependent Hamiltonian systems with one degree-of-freedom , 1978 .

[10]  Invariants for dissipative nonlinear systems by using rescaling , 1985 .

[11]  J. R. Ray,et al.  Ermakov systems, nonlinear superposition, and solutions of nonlinear equations of motion , 1980 .

[12]  P. Leach.  An exact invariant for a class of time‐dependent anharmonic oscillators with cubic anharmonicity , 1981 .

[13]  P. Leach.  A theorem for time-dependent dynamical systems , 1983 .

[14]  J. R. Ray.  Minimum-uncertainty coherent states for certain time-dependent systems , 1982 .

[15]  A. Nassar.  Ermakov and non-Ermakov systems in quantum dissipative models , 1986 .

[16]  J. L. Reid.  Lie symmetries, nonlinear equations of motion and new Ermakov systems , 1982 .

[17]  P. Caldirola,et al.  Forze non conservative nella meccanica quantistica , 1941 .

[18]  H. Lewis,et al.  Exact invariants for a class of time-dependent nonlinear Hamiltonian systems , 1982 .

[19]  H. Lewis,et al.  Exact time-dependent solutions of the Vlasov--Poisson equations , 1984 .

[20]  J. R. Ray,et al.  Nonlinear superposition, higher‐order nonlinear equations, and classical linear invariants , 1982 .

[21]  M. Lutzky,et al.  Noether's theorem and the time-dependent harmonic oscillator , 1978 .

[22]  P. Leach.  On a Generalization of the Lewis Invariant for the Time-Dependent Harmonic Oscillator , 1978 .

[23]  M. Lutzky.  An application of Ray–Reid invariants , 1980 .

[24]  H. R. Lewis,et al.  An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field , 1969 .

[25]  P. Leach.  Towards an invariant for the time‐dependent anharmonic oscillator , 1979 .

[26]  J. R. Ray,et al.  Ermakov systems, velocity dependent potentials, and nonlinear superposition , 1981 .

[27]  H. J. Korsch,et al.  Dynamical Noether invariants for time-dependent nonlinear systems , 1981 .