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Journal articles on the topic 'Quantum torus'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Hajac, Piotr M., and Tetsuya Masuda. "Quantum double-torus." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 327, no. 6 (1998): 553–58. http://dx.doi.org/10.1016/s0764-4442(98)89162-3.

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2

Liu, Wenna, and Chuanzhong Li. "Symmetries of the q-NKdV hierarchy." International Journal of Modern Physics A 36, no. 06 (2021): 2150040. http://dx.doi.org/10.1142/s0217751x21500408.

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In this paper, the additional symmetries and the string equation of the [Formula: see text]-NKdV hierarchy are established basing on the Orlov–Shulman’s [Formula: see text] operator, and then some properties are also given. Next, we construct the quantum torus symmetry of the [Formula: see text]-NKdV hierarchy and further derive the quantum torus constraints on the tau function of the [Formula: see text]-NKdV hierarchy. Comparing to the [Formula: see text] infinite-dimensional Lie symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Finally, we study the gh

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3

Neeb, Karl-Hermann. "On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups." Canadian Mathematical Bulletin 51, no. 2 (2008): 261–82. http://dx.doi.org/10.4153/cmb-2008-027-7.

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AbstractAn n-dimensional quantum torus is a twisted group algebra of the group ℤn. It is called rational if all invertible commutators are roots of unity. In the present note we describe a normal form for rational n-dimensional quantum tori over any field. Moreover, we show that for n = 2 the natural exact sequence describing the automorphism group of the quantum torus splits over any field.

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4

Gizbert-Studnicki, J. "Quantum Gravity on a Torus." Acta Physica Polonica B Proceedings Supplement 13, no. 2 (2020): 223. http://dx.doi.org/10.5506/aphyspolbsupp.13.223.

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5

ISIDRO, JOSÉ M. "QUANTUM-MECHANICAL DUALITIES ON THE TORUS." Modern Physics Letters A 19, no. 23 (2004): 1733–44. http://dx.doi.org/10.1142/s0217732304014860.

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On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e. independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting

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6

LI, DINGPING. "HIERARCHICAL WAVE FUNCTIONS AND FRACTIONAL STATISTICS IN FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS." International Journal of Modern Physics B 07, no. 15 (1993): 2779–94. http://dx.doi.org/10.1142/s0217979293003036.

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One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clearly reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.

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7

Lü, Rencai, and Kaiming Zhao. "Verma Modules over Quantum Torus Lie Algebras." Canadian Journal of Mathematics 62, no. 2 (2010): 382–99. http://dx.doi.org/10.4153/cjm-2010-022-1.

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AbstractRepresentations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras . The center of now is generally infinite dimensional.In this paper, Z-graded Verma modules over and their corresponding irreducible highest weight modules are defined for some linear functions . Necessary and sufficient conditions for to have all finite dimensional weight spaces are giv

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8

Li, Chuanzhong, Xinyue Li, and Fushan Li. "Quantum Torus Lie Algebra in the q-Deformed Kadomtsev–Petviashvili System." Algebra Colloquium 26, no. 04 (2019): 579–88. http://dx.doi.org/10.1142/s1005386719000439.

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Based on the W∞ symmetry of the q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy, which is a q-deformation of the KP hierarchy, we construct the quantum torus symmetry of the q-KP hierarchy, which further leads to the quantum torus constraint of its tau function. Moreover, we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.

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9

HO, CHOON-LIN, and YUTAKA HOSOTANI. "ANYON EQUATION ON A TORUS." International Journal of Modern Physics A 07, no. 23 (1992): 5797–831. http://dx.doi.org/10.1142/s0217751x92002647.

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Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gau

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10

TANIMURA, SHOGO. "QUANTIZATION ON A TORUS WITHOUT POSITION OPERATORS." Modern Physics Letters A 18, no. 38 (2003): 2755–65. http://dx.doi.org/10.1142/s0217732303012301.

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We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct an irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field and prove that any irreducible representation of the algebra is unitarily equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.

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11

Keating, J. P., F. Mezzadri, and J. M. Robbins. "Quantum boundary conditions for torus maps." Nonlinearity 12, no. 3 (1999): 579–91. http://dx.doi.org/10.1088/0951-7715/12/3/010.

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12

Hackett-Jones, Emily, and George Moutsopoulos. "Quantum mechanics of the doubled torus." Journal of High Energy Physics 2006, no. 10 (2006): 062. http://dx.doi.org/10.1088/1126-6708/2006/10/062.

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13

Gupta, Ashish. "Representations of then-Dimensional Quantum Torus." Communications in Algebra 44, no. 7 (2016): 3077–87. http://dx.doi.org/10.1080/00927872.2015.1065876.

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14

Morariu, Bogdan, and Alexios P. Polychronakos. "Quantum mechanics on the noncommutative torus." Nuclear Physics B 610, no. 3 (2001): 531–44. http://dx.doi.org/10.1016/s0550-3213(01)00294-2.

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15

Kramer, P. "Space groups on the quantum torus." Journal of Physics A: Mathematical and General 28, no. 22 (1995): 6405–15. http://dx.doi.org/10.1088/0305-4470/28/22/016.

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16

Hudson, R. L., and P. Robinson. "Quantum diffusions and the noncommutative torus." Letters in Mathematical Physics 15, no. 1 (1988): 47–53. http://dx.doi.org/10.1007/bf00416571.

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17

Menotti, Pietro. "Torus classical conformal blocks." Modern Physics Letters A 33, no. 28 (2018): 1850166. http://dx.doi.org/10.1142/s0217732318501663.

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After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus, we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing the classical conformal blocks for the sphere topology to the tours topology. We give the explicit results for the classical blocks up to the third-order in the nome included and compare them with the classical limit of the quantum conformal blocks. The extension to higher orders is straightforward.

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18

Kim, Hoil. "Quantum super torus and super mirror symmetry." Journal of Mathematical Physics 58, no. 5 (2017): 053502. http://dx.doi.org/10.1063/1.4982636.

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19

Zodinmawia and P. Ramadevi. "quantum Racah coefficients and non-torus links." Nuclear Physics B 870, no. 1 (2013): 205–42. http://dx.doi.org/10.1016/j.nuclphysb.2012.12.020.

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20

Iengo, Roberto, and Kurt Lechner. "Quantum mechanics of anyons on a torus." Nuclear Physics B 346, no. 2-3 (1990): 551–75. http://dx.doi.org/10.1016/0550-3213(90)90292-l.

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21

Nakatsu, Toshio, and Kanehisa Takasaki. "Melting Crystal, Quantum Torus and Toda Hierarchy." Communications in Mathematical Physics 285, no. 2 (2008): 445–68. http://dx.doi.org/10.1007/s00220-008-0583-5.

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22

Zeqian, Chen, and Yin Zhi. "Analytic Hardy spaces on the quantum torus." Acta Mathematica Scientia 31, no. 5 (2011): 1985–96. http://dx.doi.org/10.1016/s0252-9602(11)60376-7.

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23

Banica, Teodor, and Issan Patri. "Maximal torus theory for compact quantum groups." Illinois Journal of Mathematics 61, no. 1-2 (2017): 151–70. http://dx.doi.org/10.1215/ijm/1520046213.

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24

SATO, HARU-TADA. "QUANTUM GROUP SYMMETRY AND QUANTUM HALL WAVE FUNCTIONS ON A TORUS." Modern Physics Letters A 09, no. 20 (1994): 1819–25. http://dx.doi.org/10.1142/s0217732394001672.

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We generalize the quantum group structure of two-dimensional nonrelativistic electron in a uniform magnetic field into the case of a many-particle system on a torus. We verify the conjecture that the deformation parameter of the quantum algebra is given by the filling factor ν=1/p (p odd) on the basis of the Haldane-Rezayi’s wave functions.

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25

Yeşiltaş, Özlem. "Dirac Equation on the Torus and Rationally Extended Trigonometric Potentials within Supersymmetric QM." Advances in High Energy Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/6891402.

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The exact solutions of the (2+1)-dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Pöschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum mechanics techniques are used to get the extended potentials when the inner and outer radii of the torus are both equal and inequal. In addition, using the aspects of the Lie algebraic approaches, the iso(2,1) algebra is also applied to the system where we have arrived at the spectrum solutions of the extended potentials using the Casimir operator that matches

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26

Nelson, J. E., and R. F. Picken. "Quantum geometry from 2 + 1 AdS quantum gravity on the torus." General Relativity and Gravitation 43, no. 3 (2010): 777–95. http://dx.doi.org/10.1007/s10714-010-1095-0.

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27

EZAWA, KIYOSHI. "TRANSITION AMPLITUDE IN (2+1)-DIMENSIONAL CHERN-SIMONS GRAVITY ON A TORUS." International Journal of Modern Physics A 09, no. 27 (1994): 4727–45. http://dx.doi.org/10.1142/s0217751x94001898.

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In the framework of the Chern-Simons gravity proposed by Witten, a transition amplitude of a torus universe in (2+1)-dimensional quantum gravity is computed. This amplitude has the desired properties as a probability amplitude of the quantum mechanics of a torus universe, namely, it has a peak on the “classical orbit” and it satisfies the Schrödinger equation of the (2+1)-dimensional gravity. The discussion is given that the classical orbit dominance of the amplitude is not altered by taking the modular invariance into account and that this amplitude can serve as a covariant transition amplitu

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28

Artamonov, Viatcheslav A. "Actions of Pointed Hopf Algebras on Quantum Torus." ANNALI DELL UNIVERSITA DI FERRARA 51, no. 1 (2005): 29–60. http://dx.doi.org/10.1007/bf02824822.

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29

Goff, Owen. "The q-Onsager algebra and the quantum torus." Journal of Combinatorial Theory, Series A 208 (November 2024): 105939. http://dx.doi.org/10.1016/j.jcta.2024.105939.

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30

Chang-Young, Ee, and Hoil Kim. "Symmetry of quantum torus with crossed product algebra." Journal of Mathematical Physics 47, no. 7 (2006): 073508. http://dx.doi.org/10.1063/1.2219160.

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31

Dana, Itzhack, Mario Feingold, and Michael Wilkinson. "Band Distributions for Quantum Chaos on a Torus." Physical Review Letters 81, no. 15 (1998): 3124–27. http://dx.doi.org/10.1103/physrevlett.81.3124.

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32

KRAJEWSKI, THOMAS, and RAIMAR WULKENHAAR. "PERTURBATIVE QUANTUM GAUGE FIELDS ON THE NONCOMMUTATIVE TORUS." International Journal of Modern Physics A 15, no. 07 (2000): 1011–29. http://dx.doi.org/10.1142/s0217751x00000495.

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Using standard field theoretical techniques, we survey pure Yang–Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared singularity, the theory is ultraviolet divergent. Because of an invariant regularization scheme, this theory turns out to be renormalizable and the detailed computation of the one-loop counterterms is given, leading to an asymptotically free theory. Besides, it turns out that nonplanar diagrams are overall convergent when θ is irrational.

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33

Lesniewski, Andrzej, Ron Rubin, and Nathan Salwen. "Classical limits for quantum maps on the torus." Journal of Mathematical Physics 39, no. 4 (1998): 1835–47. http://dx.doi.org/10.1063/1.532266.

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34

Hikami, Kazuhiro. "Quantum Invariant for Torus Link and Modular Forms." Communications in Mathematical Physics 246, no. 2 (2004): 403–26. http://dx.doi.org/10.1007/s00220-004-1046-2.

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35

Rosenzweig, Lior. "Quantum Unique Ergodicity for Maps on the Torus." Annales Henri Poincaré 7, no. 3 (2006): 447–69. http://dx.doi.org/10.1007/s00023-005-0256-2.

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36

BENATTI, F., V. CAPPELLINI, M. DE COCK, M. FANNES, and D. VANPETEGHEM. "CLASSICAL LIMIT OF QUANTUM DYNAMICAL ENTROPIES." Reviews in Mathematical Physics 15, no. 08 (2003): 847–75. http://dx.doi.org/10.1142/s0129055x03001837.

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Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov–Sinai invariant is recovered on time scales that are logarithmic in the quantization parameter. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail.

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37

Yang, Jianwei, Gaohui Peng, Huiyun Hao, and Fengzhen Que. "Existence of global weak solution for quantum Navier–Stokes system." International Journal of Mathematics 31, no. 05 (2020): 2050038. http://dx.doi.org/10.1142/s0129167x2050038x.

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In this paper, the barotropic compressible quantum Navier–Stokes equations with a density-dependent viscosity in a three-dimensional torus is studied. By introducing a cold pressure to handle the convection term, we prove the global-in-time existence of weak solutions to quantum Navier–Stokes equations for large data in the sense of standard definition.

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38

Gomes, Diogo A., and Claudia Valls. "Wigner measures and quantum Aubry–Mather theory." Asymptotic Analysis 51, no. 1 (2007): 47–61. https://doi.org/10.3233/asy-2007-787.

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In this paper we investigate the quantum action problem using Wigner measures on the torus. We prove existence, study its main properties, and prove convergence to Mather measures in the semiclassical limit. We also indicate how to extend these techniques to the study of stochastic Mather measures.

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39

LIU, GENQIANG, and KAIMING ZHAO. "IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI." Glasgow Mathematical Journal 55, no. 3 (2013): 677–93. http://dx.doi.org/10.1017/s0017089512000845.

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AbstractLet d be a positive integer, q=(qij)d×d be a d×d matrix, ℂq be the quantum torus algebra associated with q. We have the semidirect product Lie algebra $\mathfrak{g}$=Der(ℂq)⋉Z(ℂq), where Z(ℂq) is the centre of the rational quantum torus algebra ℂq. In this paper, we construct a class of irreducible weight $\mathfrak{g}$-modules $\mathcal{V}$α (V,W) with three parameters: a vector α∈ℂd, an irreducible $\mathfrak{gl}$d-module V and a graded-irreducible $\mathfrak{gl}$N-module W. Then, we show that an irreducible Harish Chandra (uniformaly bounded) $\mathfrak{g}$-module M is isomorphic to

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40

LI, DINGPING. "HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS." International Journal of Modern Physics B 07, no. 14 (1993): 2655–65. http://dx.doi.org/10.1142/s0217979293002973.

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One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

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41

Iosue, Joseph T., T. C. Mooney, Adam Ehrenberg, and Alexey V. Gorshkov. "Projective toric designs, quantum state designs, and mutually unbiased bases." Quantum 8 (December 3, 2024): 1546. https://doi.org/10.22331/q-2024-12-03-1546.

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Toric t-designs, or equivalently t-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree t monomials over the full torus. Motivated by the projective structure of quantum mechanics, we develop the notion of t-designs on the projective torus, which have a much more restricted structure than their counterparts on full tori. We provide various new constructions of toric and projective toric designs and prove bounds on their size. We draw connections between projective toric designs and a diverse set of mathematical obj

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42

BILLIG, Y., and K. ZHAO. "VERTEX OPERATOR REPRESENTATIONS OF QUANTUM TORI AT ROOTS OF UNITY." Communications in Contemporary Mathematics 06, no. 01 (2004): 195–220. http://dx.doi.org/10.1142/s0219199704001252.

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As Lie algebra, we add the center c1 (and the outer derivation d1) to the quantum torus [Formula: see text] to give the extended torus Lie algebra [Formula: see text] (and [Formula: see text] respectively). Before the present paper, only some level 1 vertex operator representations for some [Formula: see text] (and [Formula: see text]) were constructed. In this paper, we first give vertex operator representations for [Formula: see text] where I is an arbitrary index set. By embedding some [Formula: see text] into [Formula: see text], we obtain a series of higher level vertex operator represent

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43

GURZADYAN, V. G., and A. A. KOCHARYAN. "ON PURE AND MIXED QUANTUM STATES OF THE UNIVERSE." Modern Physics Letters A 04, no. 06 (1989): 507–11. http://dx.doi.org/10.1142/s0217732389000617.

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Within the framework of Hawking's quantum cosmology, a problem of a topology change of the Universe allowing differentiation between pure and mixed quantum states, is discussed. It is shown that for the pure state Universe, the transition of the sphere to torus is strongly suppressed. The corresponding probabilities are of the same order in the case of the mixed states of the Universe.

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44

LIPIŃSKI, Z. "YANGIAN DEFORMATION OF THE LIE ALGEBRA dĩff(T2)." Modern Physics Letters A 13, no. 20 (1998): 1611–22. http://dx.doi.org/10.1142/s0217732398001698.

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New solution of a classical Yang–Baxter equation on a loop extended, "modified" Lie algebra of a diffeomorphism group of a torus dĩff(T2)[λ]is given. Lie bialgebra structure on dĩff(T2)[λ] is defined. By quantization of a defined Lie bialgebra, a Yangian algebra Y(dĩff(T2)) is obtained. Existence of a quantum double and a quantum R-matrix for Y(dĩff(T2)) is considered.

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45

LAVRINENKO, I. V., H. LÜ, C. N. POPE, and T. A. TRAN. "U DUALITY AS GENERAL COORDINATE TRANSFORMATIONS, AND SPACE–TIME GEOMETRY." International Journal of Modern Physics A 14, no. 31 (1999): 4915–42. http://dx.doi.org/10.1142/s0217751x99002323.

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We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity and of type IIB supergravity, with type IIA/IIB T duality providing an intertwining between the two pictures. At the quantum level, the part of the U duality group that corresponds to the surviving discretized internal general coordinate transformations in a given picture leaves the internal torus invariant, while the part that is not described by internal g

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46

Hoyer, Peter, and Zhan Yu. "Analysis of lackadaisical quantum walks." Quantum Information and Computation 20, no. 13&14 (2020): 1138–53. http://dx.doi.org/10.26421/qic20.13-14-4.

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The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other c

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47

Gauthier, Richard. "Relativistic superluminal quantum-vortex electron model internally crosses lightspeed." Journal of Physics: Conference Series 2197, no. 1 (2022): 012009. http://dx.doi.org/10.1088/1742-6596/2197/1/012009.

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Abstract This article continues the development of the relativistic quantum-vortex electron and positron models composed of a helically-circulating electrically-charged superluminal energy quantum (SEQ). Parametric equations similar to that of a coiled slinky toy are proposed and analyzed for the relativistic electron and positron models, which can each have either spin-up or spin-down. The point-like electric charge of the SEQ moves along a positively or negatively-turning helical trajectory, depending on the sign of the electric charge, to form the electron/positron model. At low electron-mo

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48

Morton, H. R. "The coloured Jones function and Alexander polynomial for torus knots." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 1 (1995): 129–35. http://dx.doi.org/10.1017/s0305004100072959.

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AbstractIn [2] it was conjectured that the coloured Jones function of a framed knot K, or equivalently the Jones polynomials of all parallels of K, is sufficient to determine the Alexander polynomial of K. An explicit formula was proposed in terms of the power series expansion , where JK, k(h) is the SU(2)q quantum invariant of K when coloured by the irreducible module of dimension k, and q = eh is the quantum group parameter.In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot.

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49

Chruściński, Dariusz. "Phase-Space Approach to Berry Phases." Open Systems & Information Dynamics 13, no. 01 (2006): 67–74. http://dx.doi.org/10.1007/s11080-006-7268-3.

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We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

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50

Hosoya, A., and K. i. Nakao. "(2+1)-Dimensional Quantum Gravity: Case of Torus Universe." Progress of Theoretical Physics 84, no. 4 (1990): 739–48. http://dx.doi.org/10.1143/ptp/84.4.739.

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