9,841 research outputs found
A Parafermionic Generalization of the Jaynes Cummings Model
We introduce a parafermionic version of the Jaynes Cummings Hamiltonian, by
coupling Fock parafermions (nilpotent of order ) to a 1D harmonic
oscillator, representing the interaction with a single mode of the
electromagnetic field. We argue that for and there is no
difference between Fock parafermions and quantum spins . We
also derive a semiclassical approximation of the canonical partition function
of the model by assuming to be small in the regime of large enough
total number of excitations , where the dimension of the Hilbert space of
the problem becomes constant as a function of . We observe in this case an
interesting behaviour of the average of the bosonic number operator showing a
single crossover between regimes with different integer values of this
observable. These features persist when we generalize the parafermionic
Hamiltonian by deforming the bosonic oscillator with a generic function
; the deformed bosonic oscillator corresponds to a specific choice
of the deformation function . In this particular case, we observe at most
crossovers in the behavior of the mean bosonic number operator,
suggesting a phenomenology of superradiance similar to the atoms Jaynes
Cummings model.Comment: to appear on J.Phys.
On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions
We present decompositions of various positive kernels as integrals or sums of
positive kernels. Within this framework we study the reproducing kernel Hilbert
spaces associated with the fractional and bi-fractional Brownian motions. As a
tool, we define a new function of two complex variables, which is a natural
generalization of the classical Gamma function for the setting we conside
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