Stochastic physical origin of the quantum operator algebra and phase space interpretation of the Hilbert space formalism: The relativistic spin zero case

1986 ◽  
Vol 113 (7) ◽  
pp. 359-364 ◽  
Author(s):  
C. Dewdney ◽  
P.R. Holland ◽  
A. Kyprianidis ◽  
Z. Marić ◽  
J.P. Vigier
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Operator Algebra ◽  
Physical Origin ◽  
Quantum Operator ◽  
Relativistic Spin ◽  
Space Formalism

CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

1991 ◽  
Vol 01 (03) ◽  
pp. 667-679 ◽  
Author(s):  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Phase Space ◽  
Measure Zero ◽  
Invariant Set ◽  
Time Dependent ◽  
Invariant Sets ◽  
Physical Origin ◽  
Chaotic Scattering ◽  
Periodic Oscillations ◽  
Surface Of Section ◽  
Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

The uniform exponential stability of a class of linear differential–difference equations in a Hilbert space

1981 ◽  
Vol 89 (3-4) ◽  
pp. 201-215 ◽  
Author(s):  
Richard Datko
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Exponential Stability ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Exponential Stability ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is given for the uniform exponential stability of certain autonomous differential–difference equations whose phase space is a Hilbert space. It is shown that this property is preserved when the delays depend homogeneously on a nonnegative parameter.

PROBLEMS WITH THE PATH-INTEGRAL DESCRIPTION OF THE TEMPORAL, LIGHT-CONE AND FOCK-SCHWINGER GAUGES

1992 ◽  
Vol 07 (03) ◽  
pp. 219-224 ◽  
Author(s):  
MARTIN LAVELLE ◽  
DAVID McMULLAN
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Light Cone ◽  
Space Formalism

Simple arguments are presented to show that the standard Faddeev-Popov formulations of the temporal, light-cone and Fock-Schwinger gauges are not unitary. We also demonstrate that the phase space formalism of these theories provide three counterexamples to the Fradkin-Vilkovisky theorem.

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