Related papers: Exact Partition Function for the Random Walk of an…
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for…
We derive the partition function of a non-relativistic quantum string which its ends are allowed to freely slide on the two angled straight solid rods. We first derive the classical solution of the model and then use it to derive the…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
In article the following tasks on computer modeling of electric fields are analyzed: 1) calculation of distribution of potential for the field created by two parallel plates and charged bodies in the non-uniform environment; 2) calculation…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…
We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described…
Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
We derive the partition function of the one-body and two-body systems of classical noncommutative harmonic oscillator in two dimensions. Then, we employ the path integral approach to the quantum noncommutative harmonic oscillator and derive…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
The problem concerning the form of the electrostatic field potential of the infinite charged metallic plane contacting with the metallic sphere is solved. The distributions of the surface charge densities both on the plane and the sphere…
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which…
As a first step to meet the challenge to calculate the electronic structure and total energy of charged states of atoms and molecules adsorbed on ultrathin-insulating films supported by a metallic substrate using density functional theory…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We introduce a random walk in random environment associated to an underlying directed polymer model in $1+1$ dimensions. This walk is the positive temperature counterpart of the competition interface of percolation and arises as the limit…
We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the…
We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions.…
The zeros of the size-$n$ partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as $n\to\infty$. Here we use weighted Dyck paths as a simple model of two-dimensional…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…