2,251 research outputs found
Fluctuations of the Fermi condensate in ideal gases
We calculate numerically and analytically the fluctuations of the fermionic
condensate and of the number of particles above the condensate for systems of
constant density of states. We compare the canonical fluctuations, obtained
from the equivalent Bose condensate fluctuation, with the grandcanonical
fermionic calculation. The fluctuations of the condensate are almost the same
in the two ensembles, with a small correction comming from the total particle
number fluctuation in the grandcanonical ensemble. On the other hand the number
of particles above the condensate and its fluctuation is insensitive to the
choice of ensemble.Comment: 10 pages with 3 figs. IOP styl
An ansatz for the exclusion statistics parameters in macroscopic physical systems described by fractional exclusion statistics
I introduce an ansatz for the exclusion statistics parameters of fractional
exclusion statistics (FES) systems and I apply it to calculate the statistical
distribution of particles from both, bosonic and fermionic perspectives. Then,
to check the applicability of the ansatz, I calculate the FES parameters in
three well-known models: in a Fermi liquid type of system, a one-dimensional
quantum systems described in the thermodynamic Bethe ansatz and quasiparticle
excitations in the fractional quantum Hall (FQH) systems. The FES parameters of
the first two models satisfy the ansatz, whereas those of the third model,
although close to the form given by the ansatz, represent an exception. With
this ocasion I also show that the general properties of the FES parameters,
deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters
of the FQH liquid.Comment: 6 pages, EPL styl
Quantization of the elastic modes in an isotropic plate
We quantize the elastic modes in a plate. For this, we find a complete,
orthogonal set of eigenfunctions of the elastic equations and we normalize
them. These are the phonon modes in the plate and their specific forms and
dispersion relations are manifested in low temperature experiments in
ultra-thin membranes.Comment: 14 pages, 2 figure
The thermodynamic limit for fractional exclusion statistics
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev.
Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the
calculation of the particle distribution that maximizes the partition function.
These inconsistencies appear when mutual exclusion statistics is manifested
between different subspecies of particles in the system. In order to eliminate
these inconsistencies, I introduce new mutual exclusion statistics parameters,
which are proportional to the dimension of the Hilbert sub-space on which they
act. These new definitions lead to properly defined particle distributions and
thermodynamic properties. In another paper (arXiv:0710.0728) I show that
fractional exclusion statistics manifested in general systems with interaction
have these, physically consistent, statistics parameters.Comment: 8 page
Condensation in ideal Fermi gases
I investigate the possibility of condensation in ideal Fermi systems of
general single particle density of states. For this I calculate the probability
of having exactly particles in the condensate and analyze its
maxima. The existence of such maxima at macroscopic values of indicates a
condensate. An interesting situation occurs for example in 1D systems, where
may have two maxima. One is at and another one may exist at
finite (for temperatures bellow a certain condensation temperature). This
suggests the existence of a first order phase transition. % The calculation of
allows for the exploration of ensemble equivalence of Fermi systems
from a new perspective.Comment: 8 pages with 1 figure. Will appear in J. Phys. A: Math. Gen. Changes
(minor): I updated Ref. [9] and its citation in the text. I introduced
citation for figure 1 in the tex
Nonlinear supratransmission in multicomponent systems
A method is proposed to solve the challenging problem of determining the
supratransmission threshold (onset of instability of harmonic boundary driving
inside a band gap) in multicomponent nonintegrable nonlinear systems. It is
successfully applied to the degenerate three-wave resonant interaction in a
birefringent quadratic medium where the process generates spatial gap solitons.
No analytic expression is known for this model showing the broad applicability
of the method to nonlinear systems.Comment: 4 pages, 3 figure
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