scholarly journals Quantum tetrachotomous states: Superposition of four coherent states on a line in phase space

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
Namrata Shukla ◽  
Naeem Akhtar ◽  
Barry C. Sanders
Keyword(s):  
Phase Space ◽  
Coherent States

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

Reply to  Comment on   Semiclassical approximations in phase space with coherent states   

2002 ◽  
Vol 35 (44) ◽  
pp. 9493-9497 ◽  
Author(s):  
M Baranger ◽  
M A M de Aguiar ◽  
F Keck ◽  
H J Korsch ◽  
B Schellhaa 
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Semiclassical Approximations

An Extra Phase for Two-Mode Coherent States Displaced in Noncommutative Phase Space

2012 ◽  
Vol 29 (4) ◽  
pp. 041102
Author(s):  
Long Yan ◽  
Xun-Li Feng ◽  
Zhi-Ming Zhang ◽  
Song-Hao Liu
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Noncommutative Phase Space

COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS

1993 ◽  
Vol 08 (18) ◽  
pp. 1735-1738 ◽  
Author(s):  
JOHN R. KLAUDER
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
Wide Class ◽  
Coherent States ◽  
Path Integrals ◽  
Killing Vector ◽  
Single Variable ◽  
Holomorphic Representation ◽  
Representation Spaces ◽  
State Path

A wide class of single-variable holomorphic representation spaces are constructed that are associated with very general sets of coherent states defined without the use of transitively acting groups. These representations and states are used to define coherent-state path integrals involving phase-space manifolds having one Killing vector but a quite general curvature otherwise.

scholarly journals Quantum dynamics in phase space: from coherent states to the Gaussian representation

2007 ◽  
Vol 54 (16-17) ◽  
pp. 2499-2512 ◽  
Author(s):  
P. D. Drummond ◽  
P. Deuar ◽  
T. G. Vaughan ◽  
J. F. Corney
Keyword(s):  
Phase Space ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Gaussian Representation

SUPERPOSITIONS OF SQUEEZED COHERENT STATES: PROPERTIES AND GENERATION

1999 ◽  
Vol 13 (17) ◽  
pp. 2299-2312 ◽  
Author(s):  
A.-S. F. OBADA ◽  
G. M. ABD AL-KADER
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Coherent States ◽  
Phase Distribution ◽  
Coherence Function ◽  
Photon Number ◽  
Distribution Functions ◽  
Numerical Results ◽  
Quadrature Component ◽  
Photon Number Distribution

The s-parameterized charactristic function for the superposition of squeezed coherent states (SCS's) is given. The s-parameterized distribution functions for the superposition of SCS's are investigated. Various moments are calculated by using this charactristic function. The Glauber second-order coherence function is calculated. The photon number distribution of the superposition of SCS's studied. Analytical and numerical results for the quadrature component distributions for the superposition of a pair of SCS's are presented. The phase distribution calculated from the integration of s-parameterized distribution function over the phase space. A generation scheme is discussed.

scholarly journals COHERENT STATES AND THE QUANTIZATION OF (1+1)-DIMENSIONAL YANG–MILLS THEORY

2001 ◽  
Vol 13 (10) ◽  
pp. 1281-1305 ◽  
Author(s):  
BRIAN C. HALL
Keyword(s):  
Phase Space ◽  
Gauge Symmetry ◽  
Coherent States ◽  
Complex Structure ◽  
Canonical Quantization ◽  
Point Of View ◽  
Joint Work ◽  
Bargmann Transform ◽  
Yang Mills ◽  
New Family

This paper discusses the canonical quantization of (1+1)-dimensional Yang–Mills theory on a spacetime cylinder from the point of view of coherent states, or equivalently, the Segal–Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal–Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction.

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