Canonical Transformations for Time Evolution and Their Representation in Wigner Distribution Phase Space

2000 ◽  
Vol 282 (1) ◽  
pp. 138-153 ◽  
Author(s):  
Marcos Moshinsky ◽  
Anju Sharma
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Wigner Distribution ◽  
Canonical Transformations ◽  
Distribution Phase

scholarly journals Phase-space studies of backscattering diffraction of defective Schrödinger cat states

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Damian Kołaczek ◽  
Bartłomiej J. Spisak ◽  
Maciej Wołoszyn
Keyword(s):  
Phase Space ◽  
Dispersive Medium ◽  
Wigner Distribution ◽  
Interference Term ◽  
Wigner Distribution Function ◽  
The Subject ◽  
Schrödinger Cat ◽  
Cat States ◽  
Schrodinger Cat State ◽  
Space Approach

AbstractThe coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.

scholarly journals Wigner Distributions of Quark

2016 ◽  
Vol 40 ◽  
pp. 1660055
Author(s):  
Asmita Mukherjee ◽  
Sreeraj Nair ◽  
Vikash Kumar Ojha
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Distribution Functions ◽  
Space Distribution ◽  
Parton Distributions ◽  
Transverse Momentum Dependent ◽  
Phase Space Distribution ◽  
Generalized Parton Distributions ◽  
Wigner Distributions ◽  
Classical Phase Space

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

The phase space time evolution method

1971 ◽  
Vol 1 (2) ◽  
pp. 115-143
Author(s):  
Morton A. Tavel ◽  
Martin S. Zucker
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Space Time ◽  
Space Time Evolution

QUANTUM DEFORMATIONS OF QUANTUM MECHANICS

1993 ◽  
Vol 08 (01) ◽  
pp. 89-96 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Evolution ◽  
Function Space ◽  
Scalar Product ◽  
Hypergeometric Functions ◽  
Quantum Mechanical ◽  
Basic Hypergeometric Functions ◽  
Quantum Deformations ◽  
The One

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

scholarly journals Brightness of synchrotron radiation from undulators and bending magnets

2015 ◽  
Vol 22 (2) ◽  
pp. 288-316 ◽  
Author(s):  
Gianluca Geloni ◽  
Vitali Kocharyan ◽  
Evgeni Saldin
Keyword(s):  
Electron Beam ◽  
Phase Space ◽  
Synchrotron Radiation ◽  
Wigner Distribution ◽  
Geometrical Optics ◽  
Single Electron ◽  
Beam Divergence ◽  
Photon Flux ◽  
Photon Flux Density ◽  
Beam Size

The maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields is considered as a possible definition of SR source brightness. Such a figure of merit was originally introduced in the SR community by Kim [(1986),Nucl. Instrum. Methods Phys. Res. A,246, 71–76]. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as the maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In these asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more to the maximum photon flux density in phase space. In these intermediate regimes a significant numerical disagreement is found between exact calculations and the approximation for undulator brightness currently used in the literature. The WD formalism is extended to a satisfactory theory for the brightness of a bending magnet. It is found that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically.

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

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