Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model
157
0
0.0
(
0
)
Added by
Stijn De Baerdemacker
Publication date
2014
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.
rate research
Read More
The contraction of the Poincare group with respect to the space trans- lations subgroup gives rise to a group that bears a certain duality relation to the Galilei group, that is, the contraction limit of the Poincare group with respect to the time translations subgroup. In view of this duality, we call the former the dual Galilei group. A rather remarkable feature of the dual Galilei group is that the time translations constitute a central subgroup. Therewith, in unitary irreducible representations (UIR) of the group, the Hamiltonian appears as a Casimir operator proportional to the identity H = EI, with E (and a spin value s) uniquely characterizing the representation. Hence, a physical system characterized by a UIR of the dual Galilei group displays no non-trivial time evolution. Moreover, the combined U(1) gauge group and the dual Galilei group underlie a non- relativistic limit of Maxwells equations known as the electric limit. The analysis presented here shows that only electrostatics is possible for the electric limit, wholly in harmony with the trivial nature of time evolution governed by the dual Galilei group.
This thesis presents an introduction to the class of Richardson-Gaudin integrable models, with special focus on the Bethe ansatz wave function, and investigates ways of applying the properties of Richardson-Gaudin models both in and out of integrability. A framework is outlined for the numerical and theoretical treatment of these systems, exposing a duality allowing the Bethe equations to be solved numerically. This is extended to the calculation of inner products and correlation functions. Using this framework, the influence of particle exchange on the Bethe ansatz is discussed, after which it is shown how the Bethe ansatz is able to accurately model wave functions of non-integrable models in two different settings. First, a variational approach is outlined for stationary models where integrability-breaking perturbations are explicitly introduced. Second, an alternative way of breaking integrability is through the introduction of dynamics and periodic driving, where it is shown how integrability can be used to model the resulting Floquet many-body resonances. Throughout this work, it is shown how the clear-cut structure and relatively large freedom in Richardson-Gaudin models makes them ideal for an investigation of the general principles of integrability, as well as being a perfect testing ground for the development of new quantum many-body techniques beyond integrability.
We study the symplectic geometry of the Jaynes-Cummings-Gaudin model with $n=2m-1$ spins. We show that there are focus-focus singularities of maximal Williamson type $(0,0,m)$. We construct the linearized normal flows in the vicinity of such a point and show that soliton type solutions extend them globally on the critical torus. This allows us to compute the leading term in the Taylor expansion of the symplectic invariants and the monodromy associated to this singularity.
The fundamental solution of the Schrodinger equation for a free particle is a distribution. This distribution can be approximated by a sequence of smooth functions. It is defined for each one of these functions, a complex measure on the space of paths. For certain test functions, the limit of the integrals of a test function with respect to the complex measures, exists. We define the Feynman integral of one such function by this limit.
In this paper, we show that a generalization of the discrete Burgers equation can be obtained by a kind of discrete Cole--Hopf transformation to the discrete diffusion equation corresponding to the correlated random walk, which is also known as a generalization of the well known random walks. By applying the technique called ultradiscretization, we obtain the generalization of the ultradiscrete diffusion equation, the ultradiscrete Cole--Hopf transformation and the ultradiscrete Burgers equation. Moreover, we show that the resulting ultradiscrete Burgers equation yields cellular automata. The relationship of the ultradiscrete Burgers equation to the traffic flow is also discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
