Statistical Thermodynamics of Polymer Quantum Systems

Abstract

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 {\em 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. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$.

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• Propagators in Polymer Quantum Mechanics
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Boundary conditions in quantum mechanics on the discretized half-line
• Classical polymerization of the Schwarzschild metric
• Polymer quantization versus the Snyder noncommutative space
• Tunneling in Polymer Quantization and the Quantum Zeno Effect
• The Polymer Bouncer
• Quasi-probability distributions in Loop Quantum Cosmology
• Instanton solutions on the polymer harmonic oscillator
• An open scattering model in polymerized quantum mechanics
• Geometrical and Topological Aspects of Quantum Information Systems
• Strong Equivalence Principle in Polymer Quantum Mechanics and deformed Heisenberg Algebra