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This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…

Quantum Physics · Physics 2024-07-10 Manjari Dutta , Shreemoyee Ganguly , Sunandan Gangopadhyay

The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…

High Energy Physics - Theory · Physics 2023-06-28 Pasquale Bosso , Luciano Petruzziello , Fabian Wagner

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…

Quantum Physics · Physics 2015-05-13 Ali Mostafazadeh

Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to…

High Energy Physics - Theory · Physics 2009-11-07 J. Beckers , J. F. Cariñena , N. Debergh , G. Marmo

We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…

High Energy Physics - Theory · Physics 2007-05-23 S. C. Jing , Q. Y. Liu , H. Y. Fan

In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…

Quantum Physics · Physics 2012-07-20 V. Chithiika Ruby , M. Senthilvelan

We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with…

A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…

High Energy Physics - Theory · Physics 2007-05-23 T. D. Palev

We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…

High Energy Physics - Theory · Physics 2010-04-06 A. Kempf

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to well known noncommutative algebra of canonical type. In…

Quantum Physics · Physics 2018-05-23 Kh. P. Gnatenko , O. V. Shyiko

We continue our previous application of supersymmetric quantum mechanical methods to eigenvalue problems in the context of some deformed canonical commutation relations leading to nonzero minimal uncertainties in position and/or momentum.…

Mathematical Physics · Physics 2011-07-19 C. Quesne , V. M. Tkachuk

We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…

High Energy Physics - Theory · Physics 2008-11-26 Marcos Rosenbaum , J. David Vergara , L. Roman Juarez

Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a…

Quantum Physics · Physics 2020-11-26 Abhishek Muhuri , Debdeep Sinha , Subir Ghosh

In this work we study the effective potential in noncommutative three-dimensional models where the noncommutativity is introduced through the coherent state approach. We discuss some important characteristics that seem to be typical to this…

High Energy Physics - Theory · Physics 2014-11-20 A. C. Lehum , J. R. Nascimento , A. Yu. Petrov

The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard…

Quantum Physics · Physics 2015-08-04 Alex E. Bernardini , Salomon S. Mizrahi

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…

Quantum Algebra · Mathematics 2018-02-14 Joakim Arnlind , Christoffer Holm

The aim of this paper is to find out how would possible space non-commutativity (NC) alter the QM solution of the Coulomb problem. The NC parameter lambda is to be regarded as a measure of the non-commutativity - setting lambda = 0 means a…

Mathematical Physics · Physics 2013-02-20 Veronika Gáliková , Peter Presnajder

Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…

General Relativity and Quantum Cosmology · Physics 2011-08-09 Eugenio Bianchi , Carlo Rovelli

The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature…

High Energy Physics - Theory · Physics 2009-11-11 N. A. Gromov , V. V. Kuratov

Wave turbulence describes the long-time statistical behavior of out-of-equilibrium systems composed of weakly interacting waves. Non-Hermitian media ranging from open quantum systems to active materials can sustain wave propagation in…