Phase space quantization and the uncertainty principle

2003 ◽  
Vol 317 (5-6) ◽  
pp. 365-369 ◽  
Author(s):  
Maurice A de Gosson
Keyword(s):  
Phase Space ◽  
Uncertainty Principle

TOPOLOGICAL ASPECTS OF THE SPECIFIC HEAT

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4170-4185 ◽  
Author(s):  
C. M. SARRIS ◽  
A. N. PROTO
Keyword(s):  
Phase Space ◽  
Specific Heat ◽  
Quantum System ◽  
Uncertainty Principle ◽  
Positive Definite ◽  
Metric Tensor ◽  
Quantum Nature ◽  
Generalized Phase Space

We describe how the specific heat of a quantum system is related to a positive definite metric defined on the generalized phase space in which the dynamics and thermodynamics of the system take place. This relationship is given through the components of a second-rank covariant metric tensor, enhancing a topological nature of the specific heat. We also present two examples where it can be seen how the uncertainty principle imposes strong constraints on the values achieved by the specific heat showing its inherent quantum nature.

scholarly journals Phase-space noncommutative extension of the Robertson-Schrödinger formulation of Ozawa’s uncertainty principle

2015 ◽  
Vol 91 (6) ◽  
Author(s):  
Catarina Bastos ◽  
Alex E. Bernardini ◽  
Orfeu Bertolami ◽  
Nuno Costa Dias ◽  
João Nuno Prata
Keyword(s):  
Phase Space ◽  
Uncertainty Principle

scholarly journals Phase-space noncommutative formulation of Ozawa’s uncertainty principle

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
Catarina Bastos ◽  
Alex E. Bernardini ◽  
Orfeu Bertolami ◽  
Nuno Costa Dias ◽  
João Nuno Prata
Keyword(s):  
Phase Space ◽  
Uncertainty Principle

scholarly journals CURVATURE, PHASE SPACE, HOLOGRAPHY AND BLACK HOLE ENTROPY

2009 ◽  
Vol 18 (14) ◽  
pp. 2167-2171 ◽  
Author(s):  
C. SIVARAM ◽  
KENATH ARUN
Keyword(s):  
Black Hole ◽  
Phase Space ◽  
Surface Area ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Black Hole Entropy ◽  
Black Hole Masses ◽  
Interior Volume

This paper discusses the thermodynamics of a black hole with respect to Hawking radiation and the entropy. We look at a unified picture of black hole entropy and curvature and how this can lead to the usual black hole luminosity due to Hawking radiation. It is also shown how the volume inside the horizon, apart from the surface area (hologram!), can play a role in understanding the Hawking flux. In addition, holography implies a phase space associated with the interior volume and this happens to be just a quantum of phase space, filled with just one photon. The generalized uncertainty principle can be incorporated in this analysis. These results hold for all black hole masses in any dimension.

scholarly journals GERBES AND HEISENBERG'S UNCERTAINTY PRINCIPLE

2006 ◽  
Vol 03 (08) ◽  
pp. 1469-1480 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Phase Space ◽  
Field Strength ◽  
Uncertainty Principle ◽  
Path Integrals ◽  
Feynman Path ◽  
Feynman Path Integrals ◽  
Form Field ◽  
Classical Phase Space ◽  
Heisenberg's Uncertainty Principle

We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Čech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.

Coordinate uncertainty principle in a generalized phase space

2014 ◽  
Vol 90 (2) ◽  
pp. 628-630 ◽  
Author(s):  
B. I. Sadovnikov ◽  
E. E. Perepelkin ◽  
N. G. Inozemtseva
Keyword(s):  
Phase Space ◽  
Uncertainty Principle ◽  
Generalized Phase Space

WIGNER FUNCTION IN THE SYMMETRIC GAUGE: DE HAAS-VAN ALPHEN OSCILLATIONS, MAGNETIC FIELD LOCALIZATION AND UNCERTAINTY PRINCIPLE

2003 ◽  
Vol 17 (26) ◽  
pp. 4683-4732 ◽  
Author(s):  
TOMAS B. MATERDEY ◽  
CHARLES E. SEYLER
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Wigner Function ◽  
Uncertainty Principle ◽  
Pure State ◽  
Interaction Picture ◽  
Gaussian Potential ◽  
Constant Type ◽  
The Matrix ◽  
Symmetric Gauge

Since the Wigner function (WF) is related to a Lindard-constant type linear dielectric function derived in the symmetric gauge,7 it is expected to show de Haas-van Alphen (dHvA) oscillations. Starting with the symmetric eigenfunctions, we derived the pure-state WF in a magnetic field, whose plots in phase space and in term of B-1 for increasing n are consistent with the dHvA effect. Furthermore the asymptotic expansion of WF at large n show periodic oscillations with a period related to the Fermi energy. The phase space plots of WF also show that dHvA and similar oscillations could be a consequence of Nature's strategy for increasing the effective spatial range without violating the uncertainty principle. Properties of the symmetric eigenfunctions were derived. The dynamics of WF can be obtained from the solution of the time-dependent Schrödinger equation (SE). A new method to solve the SE in a magnetic field in the interaction picture based on expansion in term of symmetric eigenfunctions has been developed. The matrix element for a Gaussian potential were derived explicitly, plotted against B-1, and showed oscillations. The total WF was shown to be a linear combination of the diagonal pure-state WF's by using the orthogonality for symmetric eigenfunctions. The no-special-point property for WF was confirmed, which is important for the construction of a numerical algorithm to solve the SE in a magnetic field.

scholarly journals Generalized uncertainty principle corrections to the simple harmonic oscillator in phase space

2016 ◽  
Vol 94 (1) ◽  
pp. 139-146 ◽  
Author(s):  
Saurya Das ◽  
Matthew P.G. Robbins ◽  
Mark A. Walton
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Uncertainty Principles ◽  
Marginal Probability ◽  
Wigner Functions ◽  
Simple Harmonic Oscillator ◽  
Probability Densities

We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.

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