Factorization of the phase-space transformation produced by an arbitrary refracting surface

1986 ◽  
Vol 3 (3) ◽  
pp. 340 ◽  
Author(s):  
Miguel Navarro-Saad ◽  
Kurt Bernardo Wolf
Keyword(s):  
Phase Space ◽  
Space Transformation

Beamline optimization and phase space transformation (abstract)a)

1995 ◽  
Vol 66 (2) ◽  
pp. 2064-2064
Author(s):  
J. Bahrdt ◽  
U. Flechsig ◽  
F. Senf
Keyword(s):  
Phase Space ◽  
Space Transformation

scholarly journals Guiding-center recursive Vlasov and Lie-transform methods in plasma physics

2009 ◽  
Vol 75 (5) ◽  
pp. 675-696 ◽  
Author(s):  
A. J. BRIZARD ◽  
A. MISHCHENKO
Keyword(s):  
Phase Space ◽  
Plasma Physics ◽  
Hamiltonian Dynamics ◽  
Transform Methods ◽  
Lie Transform ◽  
Recursive Solution ◽  
Space Transformation

AbstractThe gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.

Quantum mechanics as a statistical theory

1949 ◽  
Vol 45 (1) ◽  
pp. 99-124 ◽  
Author(s):  
J. E. Moyal
Keyword(s):  
Quantum Mechanics ◽  
Statistical Theory ◽  
Phase Space ◽  
Quantum Dynamics ◽  
Transition Probabilities ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
Space Distribution ◽  
Statistical Dynamics ◽  
Space Transformation

An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the distribution functions of the complete set of dynamical variables specifying a mechanical system (phase-space distributions), which are fundamental in any form of statistical dynamics, are expressed in terms of the wave vectors of quantum theory. This is shown to be equivalent to specifying a theory of functions of non-commuting operators, and may hence be considered as an interpretation of quantum kinematics. In the second part, the laws governing the transformation with time of these phase-space distributions are derived from the equations of motion of quantum dynamics and found to be of the required form for a dynamical stochastic process. It is shown that these phase-space transformation equations can be used as an alternative to the Schrödinger equation in the solution of quantum mechanical problems, such as the evolution with time of wave packets, collision problems and the calculation of transition probabilities in perturbed systems; an approximation method is derived for this purpose. The third part, quantum statistics, deals with the phase-space distribution of members of large assemblies, with a view to applications of quantum mechanics to kinetic theories of matter. Finally, the limitations of the theory, its uniqueness and the possibilities of experimental verification are discussed.

scholarly journals Positive Phase Space Transformation Incompatible with Classical Physics

2009 ◽  
Vol 102 (11) ◽  
Author(s):  
Wonmin Son ◽  
Johannes Kofler ◽  
M. S. Kim ◽  
Vlatko Vedral ◽  
Časlav Brukner
Keyword(s):  
Phase Space ◽  
Positive Phase ◽  
Classical Physics ◽  
Space Transformation
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