2 research outputs found
Thermostatistics of deformed bosons and fermions
Based on the q-deformed oscillator algebra, we study the behavior of the mean
occupation number and its analogies with intermediate statistics and we obtain
an expression in terms of an infinite continued fraction, thus clarifying
successive approximations. In this framework, we study the thermostatistics of
q-deformed bosons and fermions and show that thermodynamics can be built on the
formalism of q-calculus. The entire structure of thermodynamics is preserved if
ordinary derivatives are replaced by the use of an appropriate Jackson
derivative and q-integral. Moreover, we derive the most important thermodynamic
functions and we study the q-boson and q-fermion ideal gas in the thermodynamic
limit.Comment: 14 pages, 2 figure
Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations
Let and let , . For and from , we define a function to be equal to if , and to if . Let , () be operator-valued distributions such that is the adjoint of . We say that , satisfy the anyon commutation relations (ACR) if for and for . In particular, for , the ACR become the canonical commutation relations and for , the ACR become the canonical anticommutation relations. We define the ACR algebra as the algebra generated by operator-valued integrals of , . We construct a class of gauge-invariant quasi-free states on the ACR algebra. Each state from this class is completely determined by a positive self-adjoint operator on the real space which commutes with any operator of multiplication by a bounded function . In the case ), we discuss the corresponding particle density . For , using a renormalization, we rigorously define a vacuum state on the commutative algebra generated by operator-valued integrals of . This state is given by a negative binomial point process. A scaling limit of these states as gives the gamma random measure, depending on parameter