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Journal articles on the topic 'Q-deformed Heisenberg'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

-MONTEIRO, MARCO A. R., ITZHAK RODITI, and LIGIA M. C. S. RODRIGUES. "HIGHLY DEFORMED q-OSCILLATOR SYSTEMS." Modern Physics Letters B 07, no. 29n30 (1993): 1897–902. http://dx.doi.org/10.1142/s0217984993001909.

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We consider the large q limit of systems made of deformed Heisenberg operators. When the deformation parameter is infinite the Fock space and the statistical properties have a fermionic behaviour. We also investigate the ideal q-gas and find the virial expansion of its equation of state.

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2

Chung, Won Sang, and Hassan Hassanabadi. "Fermi energy in the q-deformed quantum mechanics." Modern Physics Letters A 35, no. 11 (2020): 2050074. http://dx.doi.org/10.1142/s0217732320500741.

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In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrödinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.

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3

Swamy, P. Narayana. "Deformed Heisenberg algebra: origin of q-calculus." Physica A: Statistical Mechanics and its Applications 328, no. 1-2 (2003): 145–53. http://dx.doi.org/10.1016/s0378-4371(03)00518-1.

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4

Ben Geloun, Joseph, and Mahouton Norbert Hounkonnou. "q-graded Heisenberg algebras and deformed supersymmetries." Journal of Mathematical Physics 51, no. 2 (2010): 023502. http://dx.doi.org/10.1063/1.3272545.

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5

Cantuba, Rafael Reno S. "Lie polynomials in q-deformed Heisenberg algebras." Journal of Algebra 522 (March 2019): 101–23. http://dx.doi.org/10.1016/j.jalgebra.2018.12.008.

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6

SHABANOV, SERGEI V. "q-OSCILLATORS, NON-KÄHLER MANIFOLDS AND CONSTRAINED DYNAMICS." Modern Physics Letters A 10, no. 12 (1995): 941–48. http://dx.doi.org/10.1142/s0217732395001034.

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It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second- (or first-) class constraints.

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7

JOHAL, RAMANDEEP S. "q-DEFORMED DYNAMICS AND JOSEPHSON JUNCTION." Modern Physics Letters B 14, no. 27n28 (2000): 961–66. http://dx.doi.org/10.1142/s0217984900001166.

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We define a generalized rate equation for an observable in quantum mechanics, that involves a parameter q and whose limit q→1 gives the standard Heisenberg equation. The generalized rate equation is used to study dynamics of current-biased Josephson junction. It is observed that this toy model incorporates diffraction-like effects in the critical current. Physical interpretation for q is provided which is also shown to be a q-deformation parameter.

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8

GAVRILIK, A. M., and I. I. KACHURIK. "THREE-PARAMETER (TWO-SIDED) DEFORMATION OF HEISENBERG ALGEBRA." Modern Physics Letters A 27, no. 21 (2012): 1250114. http://dx.doi.org/10.1142/s0217732312501143.

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A three-parametric two-sided deformation of Heisenberg algebra (HA), with p, q-deformed commutator in the L.H.S. of basic defining relation and certain deformation of its R.H.S., is introduced and studied. The third deformation parameter μ appears in an extra term in the R.H.S. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p, q, μ)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor μ in the considered deformed HA inevitably depends explicitly

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9

Fiore, Gaetano. "Embedding Q-deformed Heisenberg algebras into undeformed ones." Reports on Mathematical Physics 43, no. 1-2 (1999): 101–8. http://dx.doi.org/10.1016/s0034-4877(99)80019-6.

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10

Pan, Hui-yun, and Zu Sen Zhao. "q-bosons and the Lie-deformed Heisenberg algebra." Physics Letters A 237, no. 6 (1998): 315–18. http://dx.doi.org/10.1016/s0375-9601(97)00764-0.

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11

Pan, Hui-Yun, and Zu Sen Zhao. "The q-deformed Heisenberg algebra and k-fermions." Physics Letters A 312, no. 1-2 (2003): 1–6. http://dx.doi.org/10.1016/s0375-9601(03)00376-1.

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12

Pan, Hui-yun, and Zu Sen Zhao. "Operator realizations of the q-deformed Heisenberg algebra." Physics Letters A 282, no. 4-5 (2001): 251–56. http://dx.doi.org/10.1016/s0375-9601(01)00053-6.

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13

Schmüdgen, Konrad. "Operator representations of a q-deformed Heisenberg algebra." Journal of Mathematical Physics 40, no. 9 (1999): 4596–605. http://dx.doi.org/10.1063/1.532989.

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14

Hellström, Lars, and Sergei Silvestrov. "Two-sided ideals in q-deformed Heisenberg algebras." Expositiones Mathematicae 23, no. 2 (2005): 99–125. http://dx.doi.org/10.1016/j.exmath.2005.01.003.

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15

PETERSEN, JENS U. H. "A QUADRATIC DEFORMATION OF THE HEISENBERG–WEYL AND QUANTUM OSCILLATOR ENVELOPING ALGEBRAS." International Journal of Modern Physics A 08, no. 20 (1993): 3479–93. http://dx.doi.org/10.1142/s0217751x93001399.

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A new two-parameter quadratic deformation of the quantum oscillator algebra and its one-parameter deformed Heisenberg subalgebra are considered. An infinite-dimensional Fock module representation is presented, which at roots of unity contains singular vectors and so is reducible to a finite-dimensional representation. The semicyclic, nilpotent and unitary representations are discussed. Witten's deformation of sl 2 and some deformed infinite-dimensional algebras are constructed from the 1d Heisenberg algebra generators. The deformation of the centerless Virasoro algebra at roots of unity is men

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16

ASCHIERI, PAOLO. "LIE ALGEBRA OF THE q-POINCARÉ GROUP AND q-HEISENBERG COMMUTATION RELATIONS." International Journal of Modern Physics B 13, no. 24n25 (1999): 2895–902. http://dx.doi.org/10.1142/s021797929900271x.

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We discuss quantum orthogonal groups and their real forms. We review the construction of inhomogeneous orthogonal q-groups and their q-Lie algebras. The geometry of the q-Poincaré group naturally induces a well defined q-deformed Heisenberg algebra of hermitian q-Minkowski coordinates xaand momenta pa.

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17

SHIRAISHI, JUN’ICHI. "A TRIAL TO FIND AN ELLIPTIC QUANTUM ALGEBRA FOR sl2 USING THE HEISENBERG AND CLIFFORD ALGEBRA." Modern Physics Letters A 09, no. 25 (1994): 2301–3. http://dx.doi.org/10.1142/s0217732394002161.

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A Heisenberg-Clifford realization of a deformed U (sl2) by two parameters p and q is discussed. The commutation relations for this deformed algebra have interesting connection with the theta functions.

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18

FALCO, L. DE, A. JANNUSSIS, R. MIGNANI, and A. SOTIROPOULOU. "Q-BOSON OSCILLATOR ALGEBRA WITH COMPLEX DEFORMATION PARAMETER." Modern Physics Letters A 09, no. 36 (1994): 3331–37. http://dx.doi.org/10.1142/s0217732394003154.

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We study a general q-deformed Heisenberg-Weyl algebra with complex deformation parameter. The q-boson realization of such an algebra is obtained by means of a complex generalization of the bosonization method. The real spectrum of the corresponding complex deformed oscillator is derived for two special cases of the q-commutation relations. The bosonic realization of the related SU(2) algebra is also briefly considered.

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19

Boucerredj, N., N. Mebarki, and A. Benslama. "Some aspects of a weak WeylHeisenberg algebra deformation." Canadian Journal of Physics 83, no. 9 (2005): 929–39. http://dx.doi.org/10.1139/p05-038.

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In the weak deformation (WD) approximation of the WeylHeisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaïchian et al. Q-deformed path integral approach (where Q is the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave fun

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20

NADERI, MOHAMMAD HOSSEIN, MAHMOOD SOLTANOLKOTABI, and RASOUL ROKNIZADEH. "DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH." International Journal of Modern Physics A 24, no. 10 (2009): 1963–86. http://dx.doi.org/10.1142/s0217751x09043043.

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In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construc

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21

JING, SICONG. "THE JORDAN-SCHWINGER REALIZATION OF TWO-PARAMETRIC QUANTUM GROUP slq,s(2)." Modern Physics Letters A 08, no. 06 (1993): 543–48. http://dx.doi.org/10.1142/s0217732393000568.

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The Jordan-Schwinger realization of two-parametric quantum group sl q,s(2), is presented by introducing two-parametric deformed harmonic oscillator. The Heisenberg commutation relations of the two-parametric deformed oscillator are derived by virtue of the Schwinger’s contraction procedure.

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22

Cerchiai, B. L., R. Hinterding, J. Madore, and J. Wess. "A calculus based on a q-deformed Heisenberg algebra." European Physical Journal C 8, no. 3 (1999): 547–58. http://dx.doi.org/10.1007/s100529901097.

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23

Cheng, Yongsheng, and Yucai Su. "Quantum Deformations of the Heisenberg-Virasoro Algebra." Algebra Colloquium 20, no. 02 (2013): 299–308. http://dx.doi.org/10.1142/s1005386713000266.

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In this paper, the authors develop an approach to construct a q-deformed Heisenberg-Virasoro algebra which is a Hom-Lie algebra, and investigate its central extensions and second cohomology group. Finally, quantum deformations of the Heisenberg-Virasoro algebra which provide a non-trivial Hopf structure are presented.

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24

Larsson, Daniel, and Sergei D. Silvestrov. "Burchnall-Chaundy Theory for q-Difference Operators and q-Deformed Heisenberg Algebras." Journal of Nonlinear Mathematical Physics 10, sup2 (2003): 95–106. http://dx.doi.org/10.2991/jnmp.2003.10.s2.8.

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25

MORARIU, BOGDAN. "QUANTUM ALGEBRA OF THE PARTICLE MOVING ON THE q-DEFORMED MASS-HYPERBOLOID." International Journal of Modern Physics A 15, no. 21 (2000): 3277–86. http://dx.doi.org/10.1142/s0217751x00002329.

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I introduce a reality structure on the Heisenberg double of Fun q( SL (N,C)) for q phase, which for N=2 can be interpreted as the quantum phase space of the particle on the q-deformed mass-hyperboloid. This construction is closely related to the q-deformation of the symmetric top. Finally, I conjecture that the above real form describes zero modes of certain noncompact WZNZ-models.

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26

Chung, Won Sang. "Holstein–Primakoff realization of Higgs algebra and its q-extension." Modern Physics Letters A 29, no. 10 (2014): 1450050. http://dx.doi.org/10.1142/s0217732314500503.

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In this paper, Holstein–Primakoff realization of Higgs algebra is obtained by using the linear (or quadratic) deformation of Heisenberg algebra and q-deformed Higgs algebra is proposed. Some applications such as Kepler problem in a two-dimensional curved space and SUSY quantum mechanics are also discussed.

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27

Fabo, Wang, and Kuang Leman. "Even and Odd Q -coherent State Representations of the Q -deformed Heisenberg-Weyl Algebra." Chinese Physics Letters 9, no. 12 (1992): 629–32. http://dx.doi.org/10.1088/0256-307x/9/12/001.

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28

de Jeu, Marcel, Christian Svensson, and Sergei Silvestrov. "Algebraic curves for commuting elements in the q-deformed Heisenberg algebra." Journal of Algebra 321, no. 4 (2009): 1239–55. http://dx.doi.org/10.1016/j.jalgebra.2008.10.021.

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29

Gavrilik, Alexandre, and Ivan Kachurik. "Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators." Modern Physics Letters A 34, no. 01 (2019): 1950007. http://dx.doi.org/10.1142/s021773231950007x.

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The recently introduced by us, two- and three-parameter (p, q)- and (p, q, [Formula: see text])-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper, we explore certain Hermitian Hamiltonians build in terms of non-Hermitian position and momentum operators obeying definite [Formula: see text](N)-pseudo-hermiticity properties. A generalized nonlinear (with the coefficients depending on the particle number operator N) one-mode Bogoliubov transformation is developed

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30

Cheng, Yongsheng, and Hengyun Yang. "Low-dimensional cohomology of q-deformed Heisenberg-Virasoro algebra of Hom-type." Frontiers of Mathematics in China 5, no. 4 (2010): 607–22. http://dx.doi.org/10.1007/s11464-010-0063-z.

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31

Hou, Bo-Yuan, and Lian-Chao Xu. "The Hopf Algebraic Structure of q -Deformed Heisenberg Algebra when q Is a Root of Unity." Communications in Theoretical Physics 24, no. 4 (1995): 481–82. http://dx.doi.org/10.1088/0253-6102/24/4/481.

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32

Palladino, B. E., and P. Leal Ferreira. "Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra." Brazilian Journal of Physics 28, no. 4 (1998): 00. http://dx.doi.org/10.1590/s0103-97331998000400019.

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33

Fu, Hong-chen, and Mo-Lin Ge. "Cyclic Representation of the q -Deformed Heisenberg-Weyl Superalgebras and the q -Boson-Fermion Realization of Cyclic Representation of Quantum Superalgebra U q sl( m,n )." Communications in Theoretical Physics 20, no. 3 (1993): 291–98. http://dx.doi.org/10.1088/0253-6102/20/3/291.

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34

Li, Ping, Miao He, Jia-Cheng Ding, Xian-Ru Hu, and Jian-Bo Deng. "Thermodynamics of Charged AdS Black Holes in Rainbow Gravity." Advances in High Energy Physics 2018 (December 18, 2018): 1–6. http://dx.doi.org/10.1155/2018/1043639.

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In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including P and r) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge Q. Furthermore, we study the Gibbs function and fi

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35

SCHMÜDGEN, KONRAD. "A POLAR DECOMPOSITION FOR HOLOMORPHIC FUNCTIONS ON A STRIP." Bulletin of the London Mathematical Society 33, no. 3 (2001): 309–19. http://dx.doi.org/10.1017/s0024609301008013.

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Let f be a holomorphic function on the strip {z ∈ [Copf ] : −α < Im z < α}, where α > 0, belonging to the class [Hscr ](α,−α;ε) defined below. It is shown that there exist holomorphic functions w1 on {z ∈ [Copf ] : 0 < Im z < 2α} and w2 on {z ∈ [Copf ] : −2α < Im z < 2α}, such that w1 and w2 have boundary values of modulus one on the real axis, and satisfy the relationsw1(z)=f(z-αi)w2(z-2αi) and w2(z+2αi)=f(z+αi)w1(z)for 0 < Im z < 2α, where f(z) := f(z). This leads to a ‘polar decomposition’ f(z) = uf(z + αi)gf(z) of the function f(z), where uf (z + αi) and gf(z) ar

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36

JANNUSSIS, A., and G. BRODIMAS. "CONNECTION BETWEEN Q-ALGEBRAS AND NONCANONICAL HEISENBERG ALGEBRAS." Modern Physics Letters A 15, no. 21 (2000): 1385–90. http://dx.doi.org/10.1142/s0217732300001511.

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We stress the connection between [Formula: see text]-algebras and noncanonical Heisenberg algebras. We prove that the known Heisenberg–Weyl algebras for the deformed harmonic oscillators are partial cases of the Lie-admissible [Formula: see text]-algebras. We also point out the existence of a scale factor which plays an important role for the eigenvalue spectrum and for the generalized uncertainty Heisenberg relation. This factor has the form (Δx)(Δp) ≥ ℏ′/2 with ℏ′ = ℏκ and κ > 0.

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37

Chung, Won Sang, and Hassan Hassanabadi. "Three-dimensional quantum mechanics in a curved space based on the q-addition." International Journal of Modern Physics A 34, no. 29 (2019): 1950177. http://dx.doi.org/10.1142/s0217751x1950177x.

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In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

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38

RIBEIRO-SILVA, C. I., and N. M. OLIVEIRA-NETO. "GENERALIZED QUANTUM FIELD THEORY BASED ON A NONLINEAR DEFORMED HEISENBERG ALGEBRA." International Journal of Modern Physics A 23, no. 20 (2008): 3113–27. http://dx.doi.org/10.1142/s0217751x08040366.

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We consider a quantum field theory based on a nonlinear Heisenberg algebra which describes phenomenologically a composite particle. Perturbative computation, considering the λϕ4 interaction was done and we also performed some comparison with a quantum field theory based on the q-oscillator algebra.

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39

Gavrilik, Alexandre M., and Ivan I. Kachurik. "Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra." Symmetry, Integrability and Geometry: Methods and Applications, May 12, 2016. http://dx.doi.org/10.3842/sigma.2016.047.

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40

Cantuba, Rafael Reno S., and Mark Anthony C. Merciales. "An extension of a q-deformed Heisenberg algebra and its Lie polynomials." Expositiones Mathematicae, January 2020. http://dx.doi.org/10.1016/j.exmath.2019.12.001.

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41

"The Normal Ordering Procedure and Coherent State of the Q-Deformed Generalized Heisenberg Algebra." Journal of Generalized Lie Theory and Applications 08, no. 01 (2014). http://dx.doi.org/10.4172/1736-4337.1000213.

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