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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.


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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
\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
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    Эта публикация цитируется в следующих статьяx:
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    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
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