1,964 research outputs found
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
Universal behaviour of ideal and interacting quantum gases in two dimensions
I discuss ideal and interacting quantum gases obeying general fractional
exclusion statistics. For systems with constant density of single-particle
states, described in the mean field approximation, the entropy depends neither
on the microscopic exclusion statistics, nor on the interaction. Such systems
are called {\em thermodynamically equivalent} and I show that the microscopic
reason for this equivalence is a one-to-one correspondence between the excited
states of these systems. This provides a method, different from the
bosonisation technique, to transform between systems of different exclusion
statistics. In the last section the macroscopic aspects of this method are
discussed.
In Appendix A I calculate the fluctuation of the ground state population of a
condensed Bose gas in grandcanonical ensemble and mean field approximation,
while in Appendix B I show a situation where although the system exhibits
fractional exclusion properties on microscopic energy intervals, a rigorous
calculation of the population of single particle states reveals a condensation
phenomenon. This also implies a malfunction of the usual and simplified
calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same
content, with slight rephrasing. Apendices are new. In the original
submission I just mentioned the condensation, which is now detailed in
Appendix B. They were intended for a separate paper. Reason for changes:
rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge
Power grids vulnerability: a complex network approach
Power grids exhibit patterns of reaction to outages similar to complex
networks. Blackout sequences follow power laws, as complex systems operating
near a critical point. Here, the tolerance of electric power grids to both
accidental and malicious outages is analyzed in the framework of complex
network theory. In particular, the quantity known as efficiency is modified by
introducing a new concept of distance between nodes. As a result, a new
parameter called net-ability is proposed to evaluate the performance of power
grids. A comparison between efficiency and net-ability is provided by
estimating the vulnerability of sample networks, in terms of both the metrics.Comment: 16 pages, 3 figures. Figure 2 and table II modified. Typos corrected.
Version accepted for publication in Chao
Second order resonant Raman scattering in single layer tungsten disulfide (WS)
Resonant Raman spectra of single layer WS flakes are presented. A
second order Raman peak (2LA) appears under resonant excitation with a
separation from the E mode of only cm. Depending on the
intensity ratio and the respective line widths of these two peaks, any analysis
which neglects the presence of the 2LA mode can lead to an inaccurate
estimation of the position of the E mode, leading to a potentially
incorrect assignment for the number of layers. Our results show that the
intensity of the 2LA mode strongly depends on the angle between the linear
polarization of the excitation and detection, a parameter which is neglected in
many Raman studies.Comment: 6 pages, 4 figure
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
- …