Generalized Heisenberg commutation relations and uncertainty inequality for relativistic harmonic oscillators

1996 ◽  
Vol 210 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
Jau Tang
Keyword(s):  
Harmonic Oscillators ◽  
Commutation Relations ◽  
Uncertainty Inequality

Fermionic Gaussians

1995 ◽  
Vol 118 (3) ◽  
pp. 543-554 ◽  
Author(s):  
P. L. Robinson
Keyword(s):  
Quantum Theory ◽  
Ground States ◽  
Harmonic Oscillators ◽  
Considerable Importance ◽  
Boson Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Schrödinger Representation ◽  
Free Boson ◽  
Complex Wave

The notion of a Gaussian as the exponential of a quadratic is rather familiar. Such functions are of considerable importance in a number of contexts, for example within quantum theory. Thus, in the Schrödinger representation of the canonical commutation relations they alone minimize uncertainty and they appear as ground states for harmonic oscillators. Also in the complex-wave representation of a free boson field they arise as transforms of the Fock vacuum under certain Bogoliubov automorphisms.

THE p, q-OSCILLATORS REPRESENTATION OF QUANTUM ALGEBRA SU(3)pq

1995 ◽  
Vol 10 (40) ◽  
pp. 3083-3086
Author(s):  
LE VIET DUNG ◽  
NGUYEN THI HA LOAN
Keyword(s):  
Quantum Algebra ◽  
Harmonic Oscillators ◽  
Commutation Relations ◽  
Two Parameter

The representation, à la Schwinger, of quantum algebra SU(3)pq is considered by constructing quantum commutation relations for p, q-deformed harmonic oscillators. The obtained results can be seen as a two-parameter extension of the quantum algebra SU(3)q studied in Ref. 1.

On the Calculation of Polynomially Perturbed Harmonic Oscillators

PIERS Online ◽  
2007 ◽  
Vol 3 (4) ◽  
pp. 485-489 ◽  
Author(s):  
P. Peidaee ◽  
Alireza Baghai-Wadji
Keyword(s):  
Harmonic Oscillators

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

scholarly journals Noisy effects in interferometric quantum gravity tests

2017 ◽  
Vol 15 (08) ◽  
pp. 1740014 ◽  
Author(s):  
F. Benatti ◽  
R. Floreanini ◽  
S. Olivares ◽  
E. Sindici
Keyword(s):  
Quantum Gravity ◽  
Weak Coupling ◽  
Scale Effects ◽  
External Environment ◽  
Planck Scale ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Photon Propagation ◽  
Gravity Theories ◽  
Planck Scale Effects

Quantum-enhanced metrology is boosting interferometer sensitivities to extraordinary levels, up to the point where table-top experiments have been proposed to measure Planck-scale effects predicted by quantum gravity theories. In setups involving multiple photon interferometers, as those for measuring the so-called holographic fluctuations, entanglement provides substantial improvements in sensitivity. Entanglement is however a fragile resource and may be endangered by decoherence phenomena. We analyze how noisy effects arising either from the weak coupling to an external environment or from the modification of the canonical commutation relations in photon propagation may affect this entanglement-enhanced gain in sensitivity.

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