The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie

Microwave device investigations Semiannual progress report, 1 Apr. - 1 Oct. 1968

Beam-plasma interactions, cyclotron harmonic instabilities, harmonic generation in beam-plasma system, relativistic electron beam studies, and materials test

Frequency multiplication in high-energy electron beams Semiannual progress report, 1 Oct. 1967 - 31 Mar. 1968

Electron beam-plasma interactions, cyclotron harmonic instabilities, paramagnetic and semiconductor materials, and harmonic current generatio

Richardson-Gaudin integrability in the contraction limit of the quasispin

Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is exactly diagonalizable by means of a Bethe Ansatz wavefunction, provided the free variables in the Ansatz are the solutions of the set of Richardson-Gaudin equations. On the one side, the Bethe Ansatz is a simple product state of generalised pair operators. On the other hand, the Richardson-Gaudin equations are strongly coupled in a non-linear way, making them prone to singularities. Unfortunately, it is non-trivial to give a clear physical interpretation to the Richardson-Gaudin variables because no physical operator is directly related to the individual variables. Purpose: The purpose of this paper is to shed more light on the critical behavior of the Richardson-Gaudin equations, and how this is related to the product wave structure of the Bethe Ansatz. Method: A pseudo-deformation of the quasi-spin algebra is introduced, leading towards a Heisenberg-Weyl algebra in the contraction limit of the deformation parameter. This enables an adiabatic connection of the exact Bethe Ansatz eigenstates with pure bosonic multiphonon states. The physical interpretation of this approach is an adiabatic suppression of the Pauli exclusion principle. Results: The method is applied to a so-called "picket-fence" model for the BCS Hamiltonian, displaying a typical critical behavior in the Richardson-Gaudin variables. It was observed that the associated bosonic multiphonon states change collective nature at the critical interaction strengths of the Richardson-Gaudin equations. Conclusions: The Pauli exclusion principle is the main responsible for the critical behavior of the Richardson-Gaudin equations, which can be suppressed by means of a pseudo deformation of the quasispin algebra.Comment: PACS 02.30.Ik, 21.10.Re, 21.60.Ce, 74.20.F

Coarse-grained computations of demixing in dense gas-fluidized beds

We use an "equation-free", coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable