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SIGMA, 2011, том 7, 110, 23 страниц (Mi sigma668)  

Эта публикация цитируется в 28 научных статьях (всего в 28 статьях)

Statistical Thermodynamics of Polymer Quantum Systems

Guillermo Chacón-Acostaa, Elisa Manriqueb, Leonardo Dagdugc, Hugo A. Morales-Técotlc

a Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana-Cuajimalpa, Artificios 40, México D. F. 01120, México
b Institut für Physik, Johannes-Gutenberg-Universität, D-55099 Mainz, Germany
c Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, México D. F. 09340, México

Аннотация: Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional polymer quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schrödinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. When the polymer length is small such corrections resemble those coming from the phenomenological generalized uncertainty relation approach based on the idea of the existence of a minimal length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$. In the case of the polymer oscillators this peak separates the vibrational and rotational regimes, while in the ideal polymer gas it reflects the band structure which allows the existence of negative temperatures.

Ключевые слова: statistical thermodynamics, canonical quantization, loop quantum gravity.

DOI: https://doi.org/10.3842/SIGMA.2011.110

Полный текст: PDF файл (830 kB)
Полный текст: http://emis.mi.ras.ru/.../110
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: 1109.0803
Тип публикации: Статья
MSC: 82B30; 81S05; 81Q65; 82B20; 83C45
Поступила: 1 сентября 2011 г.; в окончательном варианте 16 ноября 2011 г.; опубликована 2 декабря 2011 г.
Язык публикации: английский

Образец цитирования: Guillermo Chacón-Acosta, Elisa Manrique, Leonardo Dagdug, Hugo A. Morales-Técotl, “Statistical Thermodynamics of Polymer Quantum Systems”, SIGMA, 7 (2011), 110, 23 pp.

Цитирование в формате AMSBIB
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\by Guillermo Chac\'on-Acosta, Elisa Manrique, Leonardo Dagdug, Hugo A. Morales-T\'ecotl
\paper Statistical Thermodynamics of Polymer Quantum Systems
\jour SIGMA
\yr 2011
\vol 7
\papernumber 110
\totalpages 23
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Majumder B., Sen S., “Do the Modified Uncertainty Principle and Polymer Quantization Predict Same Physics?”, Phys. Lett. B, 717:4-5 (2012), 291–294  crossref  adsnasa  isi  scopus
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    3. Chacon-Acosta G., “Thermostatistics of a Gas of Hydrogen Atoms in the Polymer Representation”, Ix Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Society, AIP Conference Proceedings, 1473, eds. UrenaLopez L., BecerrilBarcenas R., LinaresRomero R., Amer Inst Physics, 2012, 153–162  crossref  isi  scopus
    4. Hernandez H.H., Chacon-Acosta G., “Effective Equations for the Quantum Pendulum From Momentous Quantum Mechanics”, Ix Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Society, AIP Conference Proceedings, 1473, eds. UrenaLopez L., BecerrilBarcenas R., LinaresRomero R., Amer Inst Physics, 2012, 168–177  crossref  isi  scopus
    5. Flores-Gonzalez E., Morales-Tecotl H.A., Reyes J.D., “Propagators in Polymer Quantum Mechanics”, Ann. Phys., 336 (2013), 394–412  crossref  mathscinet  adsnasa  isi  scopus
    6. Fernando Barbero G J., Prieto J., Villasenor E.J.S., “Band Structure in the Polymer Quantization of the Harmonic Oscillator”, Class. Quantum Gravity, 30:16 (2013), 165011  crossref  mathscinet  zmath  isi  scopus
    7. Husain V., Seahra S.S., Webster E.J., “High Energy Modifications of Blackbody Radiation and Dimensional Reduction”, Phys. Rev. D, 88:2 (2013), 024014  crossref  mathscinet  adsnasa  isi  elib  scopus
    8. Demarie T.F., Terno D.R., “Entropy and Entanglement in Polymer Quantization”, Class. Quantum Gravity, 30:13 (2013), 135006  crossref  mathscinet  adsnasa  isi  scopus
    9. Castellanos E., Chacon-Acosta G., “Polymer Bose–Einstein Condensates”, Phys. Lett. B, 722:1-3 (2013), 119–122  crossref  zmath  adsnasa  isi  elib  scopus
    10. Garcia-Chung A.A., Morales-Tecotl H.A., Reyes J.D., “Towards Polymer Quantum Mechanics for Fermionic Systems”, Ix Mexican School on Gravitation and Mathematical Physics: Cosmology for the Xxist Century, AIP Conference Proceedings, 1548, eds. UrenaLopez L., BecerrilBarcenas R., LinaresRomero R., Amer Inst Physics, 2013, 161–166  crossref  isi  scopus
    11. Chacon-Acosta G., Hernandez H.H., “One-Dimensional Polymer Fermi Gas at Zero Temperature”, Ix Mexican School on Gravitation and Mathematical Physics: Cosmology for the Xxist Century, AIP Conference Proceedings, 1548, eds. UrenaLopez L., BecerrilBarcenas R., LinaresRomero R., Amer Inst Physics, 2013, 179–182  crossref  isi  scopus
    12. Gorji M.A., Nozari K., Vakili B., “Polymeric Quantization and Black Hole Thermodynamics”, Phys. Lett. B, 735 (2014), 62–68  crossref  zmath  adsnasa  isi  elib  scopus
    13. Parra L., David Vergara J., “Polymer Quantum Mechanics Some Examples Using Path Integrals”, Recent Developments on Physics in Strong Gravitational Fields, AIP Conference Proceedings, 1577, eds. Macias A., Maceda M., Amer Inst Physics, 2014, 269–280  crossref  adsnasa  isi  scopus
    14. Martin-Ruiz A., “Diffraction in Time of Polymer Particles”, Phys. Rev. D, 90:12 (2014), 125027  crossref  adsnasa  isi  scopus
    15. Demir D.A., Sargin O., “Tunneling in Polymer Quantization and the Quantum Zeno Effect”, Phys. Lett. A, 378:44 (2014), 3237–3243  crossref  adsnasa  isi  scopus
    16. Gorji M.A., Nozari K., Vakili B., “Thermostatistics of the Polymeric Ideal Gas”, Phys. Rev. D, 90:4 (2014), 044051  crossref  adsnasa  isi  elib  scopus
    17. Chacon-Acosta G., Hernandez-Hernandez H.H., “Polymer Quantum Effects on Compact Stars Models”, Int. J. Mod. Phys. D, 24:5 (2015), 1550033  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. Martin-Ruiz A., Frank A., Urrutia L.F., “Analysis of the Quantum Bouncer Using Polymer Quantization”, Phys. Rev. D, 92:4 (2015), 045018  crossref  mathscinet  adsnasa  isi  elib  scopus
    19. Gorji M.A., Nozari K., Vakili B., “Polymer Quantization Versus the Snyder Noncommutative Space”, Class. Quantum Gravity, 32:15 (2015), 155007  crossref  mathscinet  zmath  adsnasa  isi  scopus
    20. Hosseinzadeh V., Gorji M.A., Nozari K., Vakili B., “Noncommutative Spaces and Covariant Formulation of Statistical Mechanics”, Phys. Rev. D, 92:2 (2015), 025008  crossref  mathscinet  adsnasa  isi  elib  scopus
    21. Martin-Ruiz A., Chan-Lopez E., Carbajal-Dominguez A., Bernal J., “Tunneling of Polymer Particles”, Rev. Mex. Fis., 61:3 (2015), 182–187  mathscinet  isi
    22. Chacon-Acosta G., Garcia-Chung A.A., Hernandez-Hernandez H.H., “Thermal Properties For An Ensemble of Polymer Fermi Oscillators”, X Mexican School on Gravitation and Mathematical Physics: ‘’Reaching a Century: Classical and Modified General Relativity'S Attempts To Explain de Evolution of the Universe", Journal of Physics Conference Series, 654, eds. Barcenas R., Hernandez H., Sabido M., IOP Publishing Ltd, 2015, 012002  crossref  isi  scopus
    23. Nozari, K.; Hosseinzadeh, V.; Gorji, M. A., “High temperature dimensional reduction in Snyder space”, PHYSICS LETTERS B, 750 (2015), 218-224  crossref  mathscinet  zmath  elib  scopus
    24. Kajuri N., “Strong equivalence principle in polymer quantum mechanics and deformed Heisenberg algebra”, Phys. Rev. D, 94:8 (2016), 084007  crossref  mathscinet  isi  elib  scopus
    25. Gorji M.A., Hosseinzadeh V., Nozari K., Vakili B., “Photon gas thermodynamics in dS and AdS momentum spaces”, J. Stat. Mech.-Theory Exp., 2016, 073107  crossref  mathscinet  isi  scopus
    26. Cumsille P., Reyes C.M., Ossandon S., Reyes C., “Polymer quantization, stability and higher-order time derivative terms”, Int. J. Mod. Phys. A, 31:9 (2016), 1650040  crossref  mathscinet  zmath  isi  elib  scopus
    27. Austrich-Olivares J.A., Garcia-Chung A., David Vergara J., “Instanton Solutions on the Polymer Harmonic Oscillator”, Class. Quantum Gravity, 34:11 (2017), 115005  crossref  mathscinet  zmath  isi  scopus
    28. Amirfakhrian M., Vakili B., “Polymer Deformation and Particle Tunneling From Schwarzschild Black Hole”, Int. J. Geom. Methods Mod. Phys., 16:3 (2019), 1950038  crossref  mathscinet  isi  scopus
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