Kinetic model for q-deformed bosons and fermions

Abstract

We have studied the kinetics of $q$-deformed bosons and fermions, within a semiclassical approach. This investigation is realized by introducing a generalized exclusion-inclusion principle, intrinsically connected with the quantum $q$-algebra by means of the creation and annihilation operators matrix elements. In this framework, we have derived a non-linear Fokker-Planck equation for $q$-deformed bosons and fermions which can be seen as a time evolution equation, appropriate to consider non-equilibrium or near-equilibrium systems in a semiclassical approximation. The steady state of this equation reproduces in a simple mode the $q$-oscillators equilibrium statistics.

revtex, 4 pages, to appear in Phys. Lett. A

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• H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
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• The k-generalized distribution: A new descriptive model for the size distribution of incomes
• Thermodynamic Geometry of Deformed Bosons and Fermions
• Relativistic Entropy and Related Boltzmann Kinetics
• High temperature behavior of a deformed Fermi gas obeying interpolating statistics
• Thermostatistics of deformed bosons and fermions
• A generalized statistical model for the size distribution of wealth
• Classical and quantum q-deformed physical systems
• Intermediate statistics as a consequence of deformed algebra
• Basic-deformed quantum mechanics
• A k-generalized statistical mechanics approach to income analysis
• A comparative study on q-deformed fermion oscillators
• Calculating statistical distributions from operator relations: the statistical distributions of various intermediate statistics
• From creation and annihilation operators to statistics
• Deformed quantum statistics in two-dimensions
• Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model
• Bose Einstein condensation in a gas of the Fibonacci oscillators
• Non-extensive entropy of bosonic Fibonacci oscillators
• $q$-deformed Fermion in Many-Particle Systems and Its Application to BCS Theory
• Nonlinear Schroedinger Equations within the Nelson Quantization Picture
• $q$-graded Heisenberg algebras and deformed supersymmetries