scholarly journals Phase probability distributions of Roy-type even and odd nonlinear coherent states

2004 ◽  
Vol 53 (11) ◽  
pp. 3729
Author(s):  
Wang Ji-Suo ◽  
Liu Tang-Kun ◽  
Feng Jian ◽  
Sun Jin -Zuo
Keyword(s):  
Coherent States ◽  
Probability Distributions

scholarly journals COHERENT STATES IN GRAVITATIONAL QUANTUM MECHANICS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350004 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Quantum Gravity ◽  
Coherent States ◽  
Scale Effects ◽  
Black Hole Physics ◽  
Probability Distributions ◽  
Planck Scale ◽  
Experimental Tests ◽  
Heisenberg Algebra ◽  
Adjoint Representation ◽  
Weight Functions

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.

scholarly journals Generalized Binomial Probability Distributions Attached to Landau Levels on the Riemann Sphere

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
A. Ghanmi ◽  
A. Hafoud ◽  
Z. Mouayn
Keyword(s):  
Coherent States ◽  
Riemann Sphere ◽  
Probability Distributions ◽  
Photon Number ◽  
Landau Levels ◽  
Binomial Probability ◽  
Statistical Parameters ◽  
Generalized Coherent States

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As an application, photon number statistics related to coherent states under consideration are discussed.

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (1) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (01) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

scholarly journals New mathematics for the nonadditive Tsallis’ scenario

2017 ◽  
Vol 31 (21) ◽  
pp. 1750151 ◽  
Author(s):  
G. L. Ferri ◽  
F. Pennini ◽  
A. plastino ◽  
M. C. Rocca
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Mean Values

In this paper, we investigate quantum uncertainties in a Tsallis’ nonadditive scenario. To such an end we appeal to [Formula: see text]-exponentials (qEs), that are the cornerstone of Tsallis’ theory. In this respect, it is found that some new mathematics is needed and we are led to construct a set of novel special states that are the qE equivalents of the ordinary coherent states (CS) of the harmonic oscillator (HO). We then characterize these new Tsallis’ special states by obtaining the associated (i) probability distributions (PDs) for a state of momentum [Formula: see text], (ii) mean values for some functions of space an momenta and (iii) concomitant quantum uncertainties. The latter are then compared to the usual ones.

PROBABILITY DISTRIBUTIONS ATTACHED TO GENERALIZED BARGMANN–FOCK SPACES IN THE COMPLEX PLANE

2010 ◽  
Vol 13 (02) ◽  
pp. 257-271 ◽  
Author(s):  
ZOUHAÏR MOUAYN ◽  
AHMED TOUHAMI
Keyword(s):  
Complex Plane ◽  
Coherent States ◽  
Probability Distributions ◽  
Photon Counting ◽  
Fock Spaces ◽  
Statistical Parameters ◽  
Generalized Coherent States ◽  
Counting Statistics ◽  
Photon Counting Statistics

Probability distributions attached to generalized Bargmann–Fock spaces in the complex plane are introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As application, quantum photon counting statistics related to the coherent states under consideration are discussed.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

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