1,720,977 research outputs found
Bosonic and fermionic realizations of an operator-deformed Heisenberg-Weyl algebra
No full textStarting from independent sets of one-dimensional ''bosonic'' and ''fermionic'' operators, we build up both a ''bosonic'' and a ''fermionic'' even-dimensional realization of an operatorial deformation of the Heisenberg-Weyl algebra, recently introduced to describe particles with intermediate statistics (guons). It is shown that these two deformed algebras are connected by unitary transformation. Mixed realizations are also generated by a simple change of representation
THERMODYNAMICS OF A WEAKLY DEFORMED CRYSTAL-LATTICE WITH Q-COMPLEX PARAMETER
No full textWe use a system of deformed harmonic oscillators with complex deformation parameter to describe, by means of a q-deformed analogous to the Debye model, a solid subjected to external perturbations or with some nonlinear effects inside the lattice. In the case of a weak deformation, the specific heat of the lattice exhibits a departure from the standard behavior only at low temperatures, whereas the usual Dulong-Petit law is recovered in the high-temperature limit
Heisenberg equation and constants of the motion for an anharmonic oscillator in the high-frequency limit
No full textUsing the best approximation of the time evolution operator of a quartic oscillator in the high-frequency limit, we derive its equation of the motion in the Heisenberg picture and show that such an anharmonic oscillator admits a wider class of constants of the motion than the standard harmonic oscillator
VARIATIONAL APPROACH TO GENERALIZED STATISTICS
No full textBy means of the Schwinger variational principle, we show that a field theory with a linearly realized symmetry admits the generalized g-statistics as a possible solution
APPROXIMATION METHOD FOR THE PARTITION-FUNCTION OF AN ANHARMONIC-OSCILLATOR GAS
No full textWe use an approximation procedure to find the partition function of a gas composed by anharmonic oscillators in a region where perturbation theory breaks down. The results are still quite accurate for small values of the coupling constant
HARMONIC OSCILLATOR WITH GENERALIZED STATISTICS
No full textUsing the formalism of g-operator we find a generalization of the harmonic-oscillator algebra, which contains as particular cases the boson and fermion oscillators. The form of the creation and annihilation operators is obtained as a function of two operators, alpha and beta, which satisfy a certain new algebra of the Lie-admissible type
q-parameter dependence of a gas in equilibrium with a deformed solid
No full textWe show that the main thermodynamical quantities of a gas in equilibrium with a deformed solid (composed by q-oscillators) exhibit a dependence on the deformation parameter of the lattice oscillators
AN ALTERNATIVE APPROACH TO DEFORMED STATISTICS
No full textStarting from general assumptions about creation and annihilation operators we propose a new generalized approach to deformed statistics, which permits to distinguish between two different situations; the first, in which we may define an intrinsically defined statistics, and the second one, in which this is not possible, because the symmetry properties of the system are determined by the vacuum state. The dynamical evolution of the generalized particles (guons) is derived by exploiting the Lie-admissible structure of the g-algebra
Fock space for generalized statistics and boson-fermion superselection rule
No full textWe introduce a generalized Pock space for a recently proposed operatorial deformation of the Heisenberg-Weyl (HW) algebra, aimed at describing statistics different from the Bose or Fermi ones. The new Fock space is obtained by the tensor product of the usual Pock space and the space spanned by the eigenstates of the deformation operator (g) over cap. We prove a ''statistical Ehrenfest-like theorem'', stating that the expectation values of the ladder operators of the generalized HW algebra - taken in the (g) over cap-subspace - are creation and annihilation operators defined in the usual Fock space and obeying the ordinary statistics, according to the (g) over cap-eigenvalues. Moreover, such a ''statistics'' operator (g) over cap can be regarded as the generator of a boson-fermion superselection rule. As a consequence, the generalized Pock space decomposes into incoherent sectors, and therefore one gets a density matrix diagonal in the (g) over cap eigenstates. This leads, under suitable conditions, to the possibility of continuously interpolating between different statistics. In particular, it is necessary to assume a nonstandard Liouville-Von Neumann equation for the density matrix, of the type already considered e.g. in the framework of quantum gravity. It is also preliminarily shown that our formalism leads in a natural way - due to the very properties of the operator (g) over cap - to a grading of the HW algebra, and therefore to a supersymmetrical scheme
Approximation procedure for an anharmonic oscillator with cubic and quartic terms
No full textWe use -after a shift transformation of the variable- the Burrows, Cohen and Feldmann approximation procedure to solve the problem of finding the energy eigenvalues for an anharmonic oscillator with cubic and quartic terms subjected to a linear external potential. Both low- and high-frequency limits are considered. A first application is given by deriving (in the high-frequency case) the partition function of a gas composed of such anharmonic oscillators. We also exploit the recently proved formal equivalence between a high-frequency anharmonic oscillator (in the approximation considered) and an infinitesimally deformed harmonic oscillator to introduce SU(2) and SU(1, 1) algebras for the anharmonic oscillator with cubic and quartic terms
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