scholarly journals Turning off quantum duality

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
X.-F. Qian ◽  
K. Konthasinghe ◽  
S. K. Manikandan ◽  
D. Spiecker ◽  
A. N. Vamivakas ◽  
...  
Keyword(s):  
Quantum Duality

scholarly journals Testing quantum duality using cold Rydberg atoms

2004 ◽  
Vol 602 (1-2) ◽  
pp. 144-148 ◽  
Author(s):  
J.L. Noronha ◽  
C. Wotzasek
Keyword(s):  
Rydberg Atoms ◽  
Quantum Duality

scholarly journals Classical and quantum duality of quasi-exactly solvable problems

2019 ◽  
Vol 52 (39) ◽  
pp. 395302
Author(s):  
Michael Kreshchuk ◽  
Tobias Gulden
Keyword(s):  
Exactly Solvable ◽  
Quantum Duality ◽  
Solvable Problems

Quantum duality in quantum deformations

2006 ◽  
Vol 148 (1) ◽  
pp. 968-979 ◽  
Author(s):  
V. D. Lyakhovsky
Keyword(s):  
Quantum Deformations ◽  
Quantum Duality

scholarly journals Quantum duality and Bethe ansatz for the Hofstadter problem on the hexagonal lattice

1996 ◽  
Vol 210 (1-2) ◽  
pp. 110-114 ◽  
Author(s):  
C.-A. Piguet ◽  
D.F. Wang ◽  
C. Gruber
Keyword(s):  
Bethe Ansatz ◽  
Hexagonal Lattice ◽  
Quantum Duality

scholarly journals THE SL(2,R) WZWN STRING MODEL AS A DEFORMED OSCILLATOR AND ITS CLASSICAL-QUANTUM STRING REGIMES

2007 ◽  
Vol 22 (16) ◽  
pp. 1133-1142 ◽  
Author(s):  
M. RAMÓN MEDRANO ◽  
N. G. SÁNCHEZ
Keyword(s):  
Quantum Mechanics ◽  
Mass Spectrum ◽  
Uncertainty Relation ◽  
String Model ◽  
Quantum Uncertainty ◽  
Deformed Oscillator ◽  
Classical Quantum ◽  
Usual Quantum ◽  
Quantum Duality ◽  
Semiclassical Regime

We study the SL (2,R) WZWN string model describing bosonic string theory in AdS3 spacetime as a deformed oscillator together with its mass spectrum and the string modified SL (2,R) uncertainty relation. The SL (2,R) string oscillator is far more quantum (with higher quantum uncertainty) and more excited than the non-deformed one. This is accompassed by the highly excited string mass spectrum which is drastically changed with respect to the low excited one. The highly excited quantum string regime and the low excited semiclassical regime of the SL (2,R) string model are described and shown to be the quantum-classical dual of each other in the precise sense of the usual classical-quantum duality. This classical-quantum realization is not assumed nor conjectured. The quantum regime (high curvature) displays a modified Heisenberg's uncertainty relation, while the classical (low curvature) regime has the usual quantum mechanics uncertainty principle.

scholarly journals A quantum duality principle for coisotropic subgroups and Poisson quotients

2006 ◽  
Vol 199 (1) ◽  
pp. 104-135 ◽  
Author(s):  
Nicola Ciccoli ◽  
Fabio Gavarini
Keyword(s):  
Duality Principle ◽  
Quantum Duality

Quantum homogeneous superspaces and quantum duality principle

2015 ◽  
Vol 106 ◽  
pp. 59-72 ◽  
Author(s):  
Rita Fioresi
Keyword(s):  
Duality Principle ◽  
Quantum Duality

scholarly journals A QUANTUM-GRAVITY PERSPECTIVE ON SEMICLASSICAL vs. STRONG-QUANTUM DUALITY

2006 ◽  
Vol 03 (07) ◽  
pp. 1293-1302
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
The Other ◽  
Length Scale ◽  
Specific Nature ◽  
Action Integral ◽  
Fundamental Length ◽  
Starting Point ◽  
Duality Groups ◽  
Quantum Duality

It has been argued that, underlying the M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this paper, we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.

Contractions in Deformed Lie-Poisson Structures

1997 ◽  
Vol 12 (01) ◽  
pp. 225-230 ◽  
Author(s):  
V. D. Lyakhovsky ◽  
A. M. Mirolyubov
Keyword(s):  
Significant Role ◽  
Deformation Quantization ◽  
Duality Principle ◽  
Poisson Structures ◽  
Lie Bialgebras ◽  
First Order ◽  
Natural Analogues ◽  
Explicit Realization ◽  
Quantum Duality ◽  
Initial Object

The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structures — natural analogues of classical Lie bialgebras for the case when the initial object is a quantized group. Special types of contractions — the so called first order contractions — play the significant role in the explicit realization of deformed Lie-Poisson structures. Such contractions can be naturally applied to the Drinfeld double. In the case of (u(1) ⊕ sl(2))q we investigate explicitly the deformed structures induced by the first order contractions.

Poisson-Lie groups. The quantum duality principle and the twisted quantum double

1992 ◽  
Vol 93 (2) ◽  
pp. 1292-1307 ◽  
Author(s):  
M. A. Semenov-Tyan-Shanskii
Keyword(s):  
Lie Groups ◽  
Duality Principle ◽  
Quantum Double ◽  
Poisson Lie Groups ◽  
Quantum Duality
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