Related papers: Particle distribution tail and related energy form…
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
An ion held in a radiofrequency trap interacting with a uniform buffer gas of neutral atoms develops a steady-state energy distribution characterised by a power-law tail at high energies instead of the exponential decay characteristic of…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We compute tail contributions to the conservative dynamics of a generic self-gravitating system, for every multipole order, of either electric and magnetic parity. Such contributions arise when gravitational radiation is backscattered by…
Recently, Benedikter and the author proved an approximate formula for the momentum distribution of a 3d fermionic gas interacting by a short-range pair potential in the mean-field regime, within a trial state close to the ground state.…
The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of…
Magnetic reconnection is an explosive energy release event. It plays an important role in accelerating particles to high non-thermal energies. These particles often exhibit energy spectra characterized by a power-law distribution. However,…
Transformation equations for the kinetic energy of a tardyon are derived in the limits of classical and of special relativity theory. Two formulas are presented. In the first one the energy of the particle in one of the involved reference…
In this paper we prove the existence of the high-energy tails for electron distribution function of the Boltzmann equation for semiconductors, in the stationary and homogeneous regime, in the analytic band approximation and scattering with…
Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…
We derive the full set of universal relations for spin-polarized Fermi gases with $p$-wave interaction in two dimensions, simply using the short-range asymptotic behavior of fermion-pair wave functions. For $p$-wave interactions, an…
The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
We study the Sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape. We consider the particular case of discrete energy landscapes made of random +/- 1 jumps on the semi infinite line Z+ with a…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for…
In our previous paper, we have investigated the thermodynamics of the quantum ultra-cold neutron gas trapped in the two-dimensional square-well potential on the Earth's gravitational field. We have pointed out that they have strong…
In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity…
A classical Lagrangian model of the Pauli potential is introduced. It is shown that the kinematic kinetic energy ($\sum \frac{1}{2} m v^2$) in the model approximately reproduces the energy of a free Fermi gas at low temperatures and at…