Thermodynamics of a non-commutative fermion gas

Abstract

Building on the recent solution for the spectrum of the non-commutative well in two dimensions, the thermodynamics that follows from it is computed. In particular the focus is put on an ideal fermion gas confined to such a well. At low densities the thermodynamics is the same as for the commutative gas. However, at high densities the thermodynamics deviate strongly from the commutative gas due to the implied excluded area resulting from the non-commutativity. In particular there are extremal macroscopic states, characterized by area, number of particles and angular momentum, that correspond to a single microscopic state and thus have vanishing entropy. When the system size and excluded area are comparable, thermodynamic quantities, such as entropy, exhibit non-extensive features.

18 pages, 11 figures

References in corpus (20)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• The quantum structure of spacetime at the Planck scale and quantum fields
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Quantum Cosmology
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• Non-Commutative Inflation
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Testing the Noncommutative Standard Model at a Future Photon Collider
• The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
• Spectrum of the non-commutative spherical well
• Twisted Galilean symmetry and the Pauli principle at low energies
• Pair Production by a Constant External Field in Noncommutative QED
• Some consequences of a noncommutative space-time structure
• Some Phenomenological Consequences of the Time-Ordered Perturbation Theory of QED on Noncommutative Spacetime
• The noncommutative degenerate electron gas
• On the role of twisted statistics in the noncommutative degenerate electron gas
• Interacting Quantum Topologies and the Quantum Hall Effect

Cited by in corpus (15)

• Topics in Noncommutative Geometry Inspired Physics
• Spectrum of the three dimensional fuzzy well
• Quantum entanglement in a non-commutative system
• Twist Deformation of Rotationally Invariant Quantum Mechanics
• Statistical mechanics of free particles on space with Lie type noncommutativity
• Noncommutative spaces and covariant formulation of statistical mechanics
• Fate of the Superconducting Ground State on the Moyal Plane
• Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales
• The entropy of dense non-commutative fermion gases
• Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Entropy bound for the photon gas in noncommutative spacetime
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
• Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space