A semiclassical theory in phase space for molecular processes: Formalism based on dynamical characteristic function

1985 ◽  
Vol 82 (6) ◽  
pp. 2573-2589 ◽  
Author(s):  
Kazuo Takatsuka ◽  
Hiroki Nakamura
Keyword(s):  
Phase Space ◽  
Characteristic Function ◽  
Dynamical Characteristic ◽  
Semiclassical Theory ◽  
Molecular Processes

scholarly journals Tutorial Notes on One-Party and Two-Party Gaussian States

2003 ◽  
Vol 01 (02) ◽  
pp. 153-188 ◽  
Author(s):  
Berthold-Georg Englert ◽  
Krzysztof Wódkiewicz
Keyword(s):  
Quantum Information ◽  
Phase Space ◽  
Characteristic Function ◽  
Information Science ◽  
Operator Method ◽  
Two Dimensional ◽  
Quantum Information Science ◽  
Gaussian States ◽  
One Dimensional ◽  
Practical Applications

Gaussian states — or, more generally, Gaussian operators — play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial manner, a systematic operator method for first characterizing such states and then investigating their properties. The central numerical quantities are the covariance matrix that specifies the characteristic function of the state, and the closely related matrices associated with Wigner's and Glauber's phase space functions. For pedagogical reasons, we restrict the discussion to one-dimensional and two-dimensional Gaussian states, for which we provide illustrating and instructive examples.

Stochasticity in the Josephson map

1996 ◽  
Vol 56 (3) ◽  
pp. 493-506 ◽  
Author(s):  
Y. Nomura ◽  
Y. H. Ichikawa ◽  
A. T. Filipov
Keyword(s):  
Nonlinear Dynamics ◽  
Diffusion Coefficient ◽  
Phase Space ◽  
Characteristic Function ◽  
Numerical Investigation ◽  
Stochastic Diffusion ◽  
Standard Map ◽  
External Bias ◽  
Stochastic Parameter ◽  
Phase Space Portrait

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

Phase space interpretation of semiclassical theory

1977 ◽  
Vol 67 (7) ◽  
pp. 3339-3351 ◽  
Author(s):  
Eric J. Heller
Keyword(s):  
Phase Space ◽  
Semiclassical Theory

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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