scholarly journals Representation-theoretic aspects of two-dimensional quantum systems in singular vector potentials: Canonical commutation relations, quantum algebras, and reduction to lattice quantum systems

1998 ◽  
Vol 39 (5) ◽  
pp. 2476-2498 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Singular Vector ◽  
Quantum Systems ◽  
Two Dimensional ◽  
Quantum Algebras ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Vector Potentials ◽  
Lattice Quantum

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.

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.

Neutron diffraction studies of two-dimensional quantum systems

1987 ◽  
Vol 65 (11) ◽  
pp. 1435-1439 ◽  
Author(s):  
H. J. Lauter ◽  
H. P. Schildberg ◽  
H. Godfrin ◽  
H. Wiechert ◽  
R. Haensel
Keyword(s):  
Neutron Diffraction ◽  
Domain Wall ◽  
Quantum Systems ◽  
Incommensurate Phase ◽  
Two Dimensional

The phases of D2 monolayers on graphite between the commensurate and the incommensurate phase have been investigated by neutron diffraction, revealing new features including domain-wall constructions. For the related systems, 3He and 4He adsorbed on graphite, the structure of the solid first and second layers and the interaction between them have been analyzed.

scholarly journals Deformation of the Wheeler–DeWitt equation

2014 ◽  
Vol 29 (20) ◽  
pp. 1450106 ◽  
Author(s):  
Mir Faizal
Keyword(s):  
Commutation Relation ◽  
Canonical Commutation Relation ◽  
Big Bang ◽  
Minimum Length ◽  
Second Quantization ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Big Bang ◽  
Big Bang Singularity ◽  
Modified Theory

In this paper, we will analyze the consequences of deforming the canonical commutation relations consistent with the existence of a minimum length and a maximum momentum. We first generalize the deformation of first quantized canonical commutation relation to second quantized canonical commutation relation. Thus, we arrive at a modified version of second quantization. A modified Wheeler–DeWitt equation will be constructed by using this deformed second quantized canonical commutation relation. Finally, we demonstrate that in this modified theory the big bang singularity gets naturally avoided.

scholarly journals Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

1997 ◽  
Vol 11 (10) ◽  
pp. 1281-1296 ◽  
Author(s):  
V. I. Man'ko ◽  
G. Marmo ◽  
F. Zaccaria ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Vector Field ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Heisenberg Picture ◽  
Commutation Relations

It is shown that for quantum systems the vector field associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schrödinger and Heisenberg picture. We illustrate these ambiguities in terms of simple examples.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

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