Related papers: Second virial coefficient for a d-dimensional Lenn…
We study a quasi two dimensional dipolar gas at finite, but ultralow temperatures using the classical field approximation. The method, already used for a contact interacting gas, is extended here to samples with a weakly interacting…
We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length…
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D, with…
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method, we calculate the energy eigenvalues of the 1S, 2P- and 3D- levels. We compare the computed…
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a genera lization of virial theorem, which consists in scaling the wave function, we…
We extend to general dimension $n\ge1$ the virial identity proved by Boussaid-D'Ancona-Fanelli for the 3D magnetic Dirac equation. As an application we deduce smoothing and Strichartz estimates for an $n$-dimensional Dirac equation…
Selfconsistent equations which describe the order parameter and chemical potential behaviour in $2D$ metalic system as functions of external magnetic field, $H$, temperature, $T$, and carrier density, $n$, are obtained. It is shown that for…
A compact analytical form is derived via an integration approach for the interaction between a sphere and a thin rod of both finite and infinite lengths, with each object treated as a continuous medium of materials points interacting by the…
We consider the non-positivity of the Hilbert coefficients for a parameter ideal of a commutative Noetherian local ring. In particular, we show that the second Hilbert coefficient of a parameter ideal of depth at least d-1 is always…
The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by $E = \mathcal{B}/r_s$ where…
We study the influence of the dimension of space on the thermodynamics of the classical and quantum self-gravitating gas. We consider Hamiltonian systems of self-gravitating particles described by the microcanonical ensemble and…
The method of intertwining with n-dimensional (nD) linear intertwining operator L is used to construct nD isospectral, stationary potentials. It has been proven that differential part of L is a series in Euclidean algebra generators.…
The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of…
In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general 2-dimensional regions. We consider some examples and the numerical results and fitting…
The purpose of this paper is to study thermodynamic length of an isochoric two dimensional thermodynamic system with constant heat capacity. We find that length is related to the heat flow into the substance. We give examples of Ideal gas…
Assume that the generalized Ramanujan conjecture holds on the automorphic $L$-function $L(s, \pi)$ on $\GL_d$ over $\mathbb{Q}$ with $d\geq 3$, we can obtain a small log-saving non-trivial bound on the second integral moment of $L(1/2+it,…
We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We…
We prove that for any norm |*| in the d-dimensional real vector space V and for any odd n>0 there is a non-negative polynomial p(x), x in V of degree 2n such that p^{1/2n}(x) < |x| < c(n,d) p^{1/2n}(x), where c(n,d)={n+d-1 choose n}^{1/2n}.…
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological…
We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full…