相关论文: Electron-hole symmetry and solutions of Richardson…
BCS superconductivity is explained by a simple Hamiltonian describing an attractive pairing interaction between pairs of electrons. The Hamiltonian may be treated using a mean-field method, which is adequate to study equilibrium properties…
The constant pairing Hamiltonian holds exact solutions worked out by Richardson in the early Sixties. This exact solution of the pairing Hamiltonian regained interest at the end of the Nineties. The discret complex-energy states had been…
Richardson equations can be mapped on the classical electrostatic problem in two dimensions. We have recently suggested a new analytical approach to these equations in the thermodynamical limit, which is based on the `probability' of the…
A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that…
We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to…
We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic translations commute. In the Hartree-Fock-Bogoliubov approximation, we solve the gap equation…
We investigate the possibility of excitonic superfluidity in electron-hole bilayers. We calculate the phase diagram of the system for the whole range of electron-hole density imbalance and for different degrees of electrostatic screening,…
The complete exact solution of the T=1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with non-degenerate single-particle levels and including isospin-symmetry breaking terms. The power…
We establish the general form of effective interacting Hamiltonian for LaOFeAs system based on the symmetry consideration. The peculiar symmetry property of the electron states yields unusual form of electron-electron interaction. Based on…
As a model which displays a picture of the symmetry energy as an energy of rotation in isospace of a Cooper pair condensate, a Hamiltonian with a pairing force and an interaction of isospins is analyzed in the Hartree-Bogolyubov (HB) plus…
We present a generalized Richardson solution for fermions interacting with the pairing interaction in both discrete and continuum parts of the single particle (s.p.) spectrum. The pairing Hamiltonian is based on the rational Gaudin (RG)…
This chapter gives an overview of Richardson-Gaudin states which represent weakly correlated pairs of electrons. They are parametrized by sets of numbers obtained from non-linear equations. The best method to solve these equations is…
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a…
Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constant interaction strength can be calculated by solving a set of non-linear coupled equations. However, in the case of Fermions these equations lead…
We introduce a Hamiltonian for two interacting $su(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin…
The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the physics of systems with strong pair correlations is reviewed. We begin with a brief discussion of Richardson's early work, which demonstrated the exact solvability…
We solve the Schr\"{o}dinger equation for two electrons plus one hole by writing it in the electron-exciton basis. The main advantage of this basis is to eliminate the exciton contribution from the trion energy in a natural way. The…
We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension $d$ and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons…
The physical pictures of the electron pairing structure and pairing mechanisms in superconductors are reviewed. An initial idea for a new physical picture of the origin and nature of the pairing is proposed. The idea is based on the…
The pairing in a system of electrons and holes in two spatially separated parallel planes is studied in the case of electron-hole asymmetry caused by the difference in the carriers masses and their chemical potentials. It is found that the…