Statistical physics in deformed spaces with minimal length

Abstract

We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat capacity for ideal gas and harmonic oscillators using this method. The obtained results are in good agreement with the exact quantum ones. We also showed that the minimal length introduction reduces degrees of freedom of an arbitrary system in the high temperature limit significantly.

16 pages, 2 figures; several mistakes are corrected

References in corpus (35)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum Field Theory on Noncommutative Spaces
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Dirac oscillator with nonzero minimal uncertainty in position
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Minimal Length Uncertainty Relation and gravitational quantum well
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Self-consistency in Theories with a Minimal Length
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Perturbation hydrogen-atom spectrum in deformed space with minimal length
• The Casimir Effect in the Presence of a Minimal Length
• Casimir Effect in the Presence of Minimal Lengths
• One dimensional Coulomb-like problem in deformed space with minimal length
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
• About maximally localized states in quantum mechanics
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• Mimimal Length Uncertainty Principle and the Transplanckian Problem of Black Hole Physics
• Scattering problem in deformed space with minimal length
• WKB approximation in deformed space with minimal length and minimal momentum
• Ultraviolet cut off and Bosonic Dominance
• WKB approximation in deformed space with minimal length
• Ultraviolet cut off, black hole-radiation equilibrium and big bang

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• Effect of Generalized Uncertainty Principle on Main-Sequence Stars and White Dwarfs
• Deviation from the Standard Uncertainty Principle and the Dark Energy Problem
• The Minimal Length and the Quantum Partition Functions
• The quantum N-body problem with a minimal length
• New higher-order generalized uncertainty principle: Applications
• Thermostatistics of the Polymeric Ideal Gas
• A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations
• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
• The minimal length uncertainty and the nonextensive thermodynamics
• Generalized uncertainty principle and thermostatistics: a semiclassical approach
• Noncommutative spaces and covariant formulation of statistical mechanics
• Weakly interacting Bose gases with generalized uncertainty principle: Effects of quantum gravity
• Microscopic black hole and uncertainty principle with minimal length and momentum
• Entropy bound for the photon gas in noncommutative spacetime
• Linear-Quadratic GUP and Thermodynamic Dimensional Reduction
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• A minimal Length Uncertainty Approach to Cosmological Constant Problem
• Photon gas thermodynamics in dS and AdS momentum spaces
• Generalized uncertainty principle and burning stars
• Testing quantum gravity with dilute dipolar Bose gases
• The ideal gas of Bosons and Fermions in Harmonic Traps in the framework of Extended Uncertainty Principle
• Effect of the Minimal Length on Bose-Einstein Condensation in the Relativistic Ideal Bose Gas
• Effects of a Generalized Uncertainty Principle on the MIT Bag Model Equation of State
• Can Effects of a Generalized Uncertainty Principle Appear in Compact Stars?
• Theory of a many-boson system with deformed Heisenberg algebra
• Nonsingular universe from generalized thermostatistics
• Minimal-Length Corrections to Hyperon Polarization in Rotating Quark Gluon Plasma
• Dimensional Phenomenology in Polymeric Quantization Framework
• Chiral Vortical Transport under Minimal-Length Deformations in Rotating Relativistic Matter
• Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length
• Thermodynamic properties of ideal Bose gas trapped in different external power-law potentials under generalized uncertainty principle*