Related papers: Energy Functions in Box Ball Systems
It is shown that within a quantum system, the wave field has a (potential) energy content that can be exchanged with quantum particles. Energy conservation in quantum systems holds if potential energy is correctly taken to be a field…
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This…
L\"uscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame.…
The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
The quantum properties of solitons at one loop can be related to phase shifts of waves on the soliton background. These can be combined with heat kernel methods to calculate various parameters. The vacuum energy of a CP(1) soliton in 2+1…
We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The…
The hadronic quark structure is investigated in the frame of high energy electron proton scattering. A phenomenological model based on the Born approximation is used to calculate the transition matrix element for the quark system forming…
We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities,…
A box-ball system (BBS) is a discrete dynamical system consisting of n balls in an infinite strip of boxes. During each BBS move, the balls take turns jumping to the first empty box, beginning with the smallest-numbered ball. The one-line…
The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an…
Liquid-solid phase transition and the change of the frictional force of a system with two hard spheres in a two-dimensional rectangular box are discussed. Under controlling the pressure or the supply of energy from the wall, the solid like…
Total energies of crystal structures can be calculated to high precision using quantum-based density functional theory (DFT) methods, but the calculations can be time consuming and scale badly with system size. Cluster expansions of total…
A critical study of the wave mechanics of a particle trapped in a 1-D box having infinite potential walls and small flexibility in its size reveals its several important and hither to unknown aspects which could be relevant for better…
We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and…
A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly…
We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom…
This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.
A system with a metastable phase and a pseudo continuous set of the heterogeneous centers is considered. An analytical theory for kinetics of the process of condensation in such a system is constructed. The free energy of formation of the…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
The properties of Q-balls in the general case of a sixth order potential have been studied using analytic methods. In particular, for a given potential, the initial field value that leads to the soliton solution has been derived and the…