scholarly journals NEGATIVE PROBABILITY AND UNCERTAINTY RELATIONS

2001 ◽  
Vol 16 (37) ◽  
pp. 2381-2385 ◽  
Author(s):  
THOMAS CURTRIGHT ◽  
COSMAS ZACHOS
Keyword(s):  
Phase Space ◽  
Uncertainty Relations ◽  
Marginal Distributions ◽  
Negative Probability ◽  
Direct Use

A concise derivation of all uncertainty relations is given entirely within the context of phase-space quantization, without recourse to operator methods, to the direct use of Weyl's correspondence, or to marginal distributions of x and p.

scholarly journals COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS

2006 ◽  
Vol 21 (39) ◽  
pp. 2971-2976 ◽  
Author(s):  
SAYIPJAMAL DULAT ◽  
KANG LI
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space ◽  
Noncommutative Quantum Mechanics ◽  
Physical Observable ◽  
Noncommutative Quantum

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

scholarly journals Marginal distributions in (2N)-dimensional phase space and the quantum (N+1) marginal theorem

2004 ◽  
Vol 45 (12) ◽  
pp. 4832-4854 ◽  
Author(s):  
G. Auberson ◽  
G. Mahoux ◽  
S. M. Roy ◽  
Virendra Singh
Keyword(s):  
Phase Space ◽  
Marginal Distributions ◽  
Dimensional Phase Space

On uncertainty relations in noncommutative phase space

Open Physics ◽  
2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Guangjie Guo ◽  
Chaoyun Long ◽  
Shuijie Qin
Keyword(s):  
Phase Space ◽  
Natural Condition ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space ◽  
Noncommutative Plane

AbstractThe uncertainty relations are discussed on a noncommutative plane when noncommutativity of momentum spaces is considered. It is possible to construct normalizable states by simultaneously saturating two coordinate-momentum uncertainty relations. However, under the natural condition θη ≪ 4ħ2 one can not construct a normalizable state by simultaneously saturating any other pairs out of four basic nontrivial uncertainty relations.

scholarly journals Length in a Noncommutative Phase Space

2018 ◽  
Vol 63 (2) ◽  
pp. 102 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Lower Bound ◽  
Eigenvalue Problem ◽  
Minimal Length ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space

We study restrictions on the length in a noncommutative phase space caused by noncommutativity. The uncertainty relations for coordinates and momenta are considered, and the lower bound of the length is found. We also consider the eigenvalue problem for the squared length operator and find the expression for the minimal length in the noncommutative phase space.

scholarly journals Clustering and Uncertainty in Perfect Chaos Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sergey A. Kamenshchikov
Keyword(s):  
Phase Space ◽  
Transport Properties ◽  
Chaotic Systems ◽  
Dynamic Properties ◽  
Planck Equation ◽  
Uncertainty Relations ◽  
Nonlinear Dispersion ◽  
Fokker Planck Equation ◽  
Mutual Relations ◽  
Fokker Planck

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a nonstationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed us to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.

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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