8 research outputs found
Thermodynamic geometry of a system with unified quantum statistics
We examine the thermodynamic characteristics of unified quantum statistics as
a novel framework that undergoes a crossover between Bose-Einstein and
Fermi-Dirac statistics by varying a generalization parameter . We find
an attractive intrinsic statistical interaction when where the
thermodynamic curvature remains positive throughout the entire physical range.
For the system exhibits predominantly Fermi-like behavior at
high temperatures, while at low temperatures, the thermodynamic curvature is
positive and the system behaves like bosons. As the temperature decreases
further, the system undergoes a transition into the condensate phase. We also
report on a critical fugacity () defined as the point at which the
thermodynamic curvature changes sign, i.e. for ), the
statistical behavior resembles that of fermions (bosons). Also, we extract the
variation of statistical behaviour of the system for different values of
generalization parameter with respect to the temperature. We evaluate the
critical fugacity and critical dependent condensation temperature of
the system. Finally, we investigate the specific heat as a function of
temperature and condensation phase transition temperature of the system for
different values of generalization parameter in different dimensions.Comment: 10 pages, 17 figure
An electronic avalanche model for metal–insulator transition in two dimensional electron gas
In this paper, we present an electronic avalanche model for the transport of electrons in the disordered two-dimensional (2D) electron gas which has the potential to describe the 2D metal–insulator transition (MIT) in the zero electron–electron interaction limit. The disorder is considered to be uncorrelated-Coulomb noise with a uniform distribution. In this model we sub-divide the system to some virtual cells each of which has a linear size of the order of phase coherence length of the system. Using Thomas-Fermi-Dirac theory we propose some simple energy functions for the cells and using the thermodynamics of 2DEG we develop some rules for the charge transfer between the cells. A second order transition line arises from our model with some similarities with the experiments. The compressibility of the system also diverges on this line. We characterize this (disorder-driven) phase transition which is between the non-percolating phase and the percolating phase (in which the system shows metallic behavior) and obtain some geometrical critical exponents. The fractal dimension of the exterior frontier of the electronic avalanches on the transition line is compatible with the percolation theory, whereas the other exponents are different. The exponents are robust against disorder in the low disordered 2DEGs and change considerably in the high disordered ones
Anomalous Self-Organization in Active Piles
Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity’s strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak–Tang–Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζζ*≈0.1