Decay and Recurrences of Wave Packets in Nonlinear Quantum Systems

1994 ◽  
Vol 98 (13) ◽  
pp. 3285-3289 ◽  
Author(s):  
A. A. Stuchebrukhov ◽  
R. A. Marcus
Keyword(s):  
Wave Packets ◽  
Quantum Systems ◽  
Nonlinear Quantum

Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV

1978 ◽  
Vol 64 (1) ◽  
pp. 1-34 ◽  
Author(s):  
P. Deift ◽  
W. Hunziker ◽  
B. Simon ◽  
E. Vock
Keyword(s):  
Wave Packets ◽  
Quantum Systems

scholarly journals Non-dispersive wave packets in periodically driven quantum systems

2002 ◽  
Vol 368 (5) ◽  
pp. 409-547 ◽  
Author(s):  
Andreas Buchleitner ◽  
Dominique Delande ◽  
Jakub Zakrzewski
Keyword(s):  
Wave Packets ◽  
Quantum Systems ◽  
Dispersive Wave ◽  
Periodically Driven

THE DIFFEOMORPHISM GROUP APPROACH TO NONLINEAR QUANTUM SYSTEMS

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1905-1916 ◽  
Author(s):  
GERALD A. GOLDIN
Keyword(s):  
Nonlinear Effects ◽  
Quantum Systems ◽  
Incompressible Fluids ◽  
Diffeomorphism Groups ◽  
Group Approach ◽  
Quantum Vortex ◽  
Nonlinear Quantum ◽  
New Applications ◽  
Fundamental Physical ◽  
Natural Description

Unitary representations of diffeomorphism groups predict some unusual possibilities in quantum theory, including non-standard statistics and certain nonlinear effects. Many of the fundamental physical properties of “anyons” were first derived from their study by R. Menikoff, D.H. Sharp, and the author. This paper surveys new applications in two other domains: first (with Menikoff and Sharp) some surprising conclusions about the nature of quantum vortex configurations in ideal, incompressible fluids; second (with H.-D. Doebner) a natural description of dissipative quantum mechanics by means of a nonlinear Schrödinger equation different from the sort usually studied. Our equation follows from including a diffusion current in the equation of continuity.

Simplified P-representation operator correspondence applied to quantum systems with generalized Kerr nonlinearity

2019 ◽  
Vol 33 (28) ◽  
pp. 1950340 ◽  
Author(s):  
S. Chiangga ◽  
S. Pitakwongsaporn ◽  
Till D. Frank
Keyword(s):  
Energy Levels ◽  
Kerr Nonlinearity ◽  
Quantum Systems ◽  
Matter Wave ◽  
Quantum Oscillator ◽  
Text Representation ◽  
Nonlinear Quantum ◽  
Quantum Optical ◽  
Field Oscillation ◽  
Quadratic And Cubic Nonlinearities

A simplified operator correspondence scheme is derived to address nonlinear quantum systems within the framework of the [Formula: see text]-representation. The simplified method is applied to a general nonlinear quantum oscillator model that has been used in the literature to describe nonlinear quantum optical and matter wave systems. The [Formula: see text]-representation evolution equation for the model is derived for arbitrary nonlinearity exponents. It is shown that in the high temperature case, the [Formula: see text]-representation is sufficient to describe the model and its associated systems such that there is no need to use alternative, mathematically more involved representations. Systems with quadratic and cubic nonlinearities are considered in more detail. Distributions for the energy levels and photon and particle numbers are obtained within the framework of the [Formula: see text]-representation. Moreover, the electrical field oscillation frequency dependency is studied numerically when interpreting the model as model for quantum optical nonlinear oscillators.

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