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Physica Scripta

Two interacting particles in deformed nanolayer: discrete spectrum and particle storage

S I Popov, Maxim Gavrilov, I. Yu. Popov

Published Aug 16, 2012• 8 citations
Publisher

Abstract

The problem of particle storage in a nanolayered structure is considered. Local perturbations of the nanolayers can lead to the appearance of eigenvalues of the corresponding one-particle Hamiltonian. To study the particle storage it is necessary to deal with a multi-particle problem. The Hartree method and the finite element method are used. The discrete spectrum of the Hamiltonian of two interacting particles is considered. Two different types of the perturbation are treated: deformation of the layer boundary and a small window in a wall between two layers. The relation between the system parameters (interaction intensity–waveguide deformation) ensuring the existence of a non-empty discrete spectrum is studied. Comparison of particle storage efficiencies in these two cases is made.

DOI
10.1088/0031-8949/86/03/035003

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The problem of particle storage in a nanolayered structure is considered. Local perturbations of the nanolayers can lead to the appearance of eigenvalues of the corresponding one-particle Hamiltonian. To study the particle storage it is necessary to deal with a multi-particle problem. The Hartree method and the finite element method are used. The discrete spectrum of the Hamiltonian of two interacting particles is considered. Two different types of the perturbation are treated: deformation of the layer boundary and a small window in a wall between two layers. The relation between the system parameters (interaction intensity–waveguide deformation) ensuring the existence of a non-empty discrete spectrum is studied. Comparison of particle storage efficiencies in these two cases is made.
The problem of particle storage in nanolayered structures will be considered. Local perturbations of nanolayers can lead to the appearanceof eigenvalues of the corresponding one-particle Hamiltonian. To study particle storage it is necessary to deal with the multi-particle problem. This problem faces essential computational difficulties due to the great increase of the spatial dimension. Using a composite of natural physical models, analytical methods and computational approaches allows one to simplify the problem and to obtain useful results for application. Particularly, the Hartree method and Finite Elements Method (FEM) are used. The discrete spectrum of the Hamiltonian for two interacting particles is considered. Two different types of perturbation are considered: deformation of the layer boundary and a small window in a wall between two layers. The relation between the system parameters (interaction intensity - waveguide deformation) ensuring the existence of a non-empty discrete spectrum is studied. A comparison of particle storage efficiencies is made for these two cases.
Problem of particles storage in nanolayered structure is considered. Local deformations of the nanolayers leads to appearance of eigenvalues of the corresponding one-particle Hamiltonian. The cardinality of the discrete spectrum is used to estimate the maximal number of non-interacting fermions stored in the nanolayers. The discrete spectrum of the Hamiltonian of two interacting particles is considered. Relation between the system parameters (interaction intensity - waveguide deformation) ensuring the existence of non-empty discrete spectrum is studied. Hartree method and FEM are used.
The paper deals with the problem of quantum particle storage in a nanolayered structures. The system of a few electrons interacting via a -potential is considered. The particles are placed into a two-dimensional deformed waveguide. From a mathematical point of view, the bound state of the system means that the corresponding Hamiltonian will have eigenvalues. To treat a multi-particle problem, the Hartree-Fock approach and the finite element method are used. Three different types of the perturbation are considered: deformation of the layer boundary, a small window in a wall between two layers and a bent layer. The systems of 2‐10 particles with various total spins are studied. The dependence of the minimal deformation parameter, which keeps bound state on the number of particles, is given. Comparison of the storage efficiencies in those cases is made.
Deformation of the Heisenberg-Weyl algebra W s of creation-annihilation operators is studied and the problem of eigenvalues of the Hamiltonian for s deformed oscillators with interaction is solved within this algebra. At first, types of deformation are found for which solutions could be presented analytically and a simple q−deformation is considered by the means of the perturbation theory. Cases of reducing Hamiltonians which do not preserve the total particle number to that studied here are indicated. Investigations of new types of symmetries in different areas of mathematical physics by using the Inverse Scattering Method (ISM) and nonlinear differential equations, led to the appearance of notions ”Quantum Group”, ”Quantum Algebra” [1]. Nowadays, the deformed quantum statistics, parastatistics and corresponding algebras of creation-annihilation operators are widely studied. The common Heisenberg-Weyl algebra W s consists of generators ai, a + , ni, i =1 ,...,s ,
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the ‘pantographic’ case (same shape of the box through the entire process) and the case with deformation.