Dynamics of the open BCS model

Buffet, E.; Martin, Philippe A.

doi:10.1007/bf01011942

Cited by 7 publications

(51 citation statements)

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“…It is important to distinguish this type of interaction with the environment from other examples, e.g. [20] in the context of a heat bath, which facilitate a notion of entanglement with the environment. In our model there is no entanglement between the system and the environment, because the state space for the environment is not explicitly defined.…”

Section: Now Consider a More General Hamiltonian With An Extra Termmentioning

confidence: 99%

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An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Lukyanenko¹,

Isaac²,

Links³

2016

J. Phys. A: Math. Theor.

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We consider a generalisation of the p + ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation of particle number, present in the p + ip Hamiltonian, is broken. Nonetheless the generalised model is integrable. We establish integrability using the Boundary Quantum Inverse Scattering Method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe Ansatz Equations, the roots of which parametrise the exact solution for the energy spectrum.

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Section: Now Consider a More General Hamiltonian With An Extra Termmentioning

confidence: 99%

“…Thus, we obtain the following BAE in the quasi-classical limit (keeping in mind the parameters φ, ψ, α, β, γ, δ, λ and µ are defined in (20)):…”

Section: Bethe Ansatz Equationsmentioning

confidence: 99%

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Lukyanenko¹,

Isaac²,

Links³

2016

J. Phys. A: Math. Theor.

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“…in Section III we write the equations of motion for some macroscopic variables of the matter and we recover the same results as in [1]; our conclusions are contained in Section IV, while the Appendix is devoted to review some facts concerning the SLA, useful to keep the paper self contained. volume V = L 3 , with N lattice sites.…”

Section: Introductionmentioning

confidence: 99%

“…This is an easy consequence of the CCR (2.4). The free evolution of the spin operators is more difficult and its expression can be found in [1,2], for instance. Here it is shown how to obtain the time evolution in a semiclassical approximation, i.e., when the free time evolution of the intensive operators S α N is replaced by its limit (taken in the strong topology restricted to a certain family of relevant vectors, [8]).…”

Section: Introductionmentioning

confidence: 99%

The stochastic limit in the analysis of the open BCS model

Багарелло¹

2004

J. Phys. A: Math. Gen.

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In this paper we show how the perturbative procedure known as stochastic limit may be useful in the analysis of the Open BCS model discussed by Buffet and Martin as a spin system interacting with a fermionic reservoir. In particular we show how the same values of the critical temperature and of the order parameters can be found with a significantly simpler approach.PACS Numbers: 02.90.+p, 03.65.Db 1 This paper is dedicated with all my love to my sweet father

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“…It is important to distinguish this type of interaction with the environment from other examples, e.g. [BM78] in the context of a heat bath, which facilitate a notion of entanglement with the environ-ment. In our model there is no entanglement between the system and the environment, because the state space for the environment is not explicitly defined.…”

Section: Now Consider a More General Hamiltonian With Extra Termsmentioning

confidence: 99%

Richardson-Gaudin models from the Boundary Quantum Inverse Scattering Method

Lukyanenko¹

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Richardson-Gaudin models are a class of quantum integrable models connected to many physical systems, including pairing Hamiltonians from the theory of superconductivity. They can be obtained in the quasi-classical limit of the Quantum Inverse Scattering Method, which is based on an R-matrix and a Lax operator satisfying the Yang-Baxter equation. They can also be obtained from the Boundary Quantum Inverse Scattering Method, which relies on solutions of the reflection equations known as K-matrices. In this thesis we study these latter models systematically, explore the connections between them and investigate the interpretation of the "boundary".First of all, we consider Richardson-Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with diagonal K-matrices. We prove that the trigonometric boundary construction is equivalent to its rational limit, through a change of variables, rescaling, and a basis transformation. Moreover, we prove that the twisted-periodic and boundary constructions are equivalent in the trigonometric case, but not in the rational limit. Thus, including the "boundary" does not lead to a new model in this case.Next, we investigate Richardson-Gaudin models obtained from the spin-1/2 su(2) Boundary Quantum Inverse Scattering Method with non-diagonal K-matrices. Here the situation is different. The conserved operators in the boundary construction are no longer equivalent to the ones in the twisted-periodic construction. Also, the rational and the trigonometric boundary constructions are not equivalent. In the rational case this allows us to construct a generalisation of the p+ip pairing Hamiltonian with external interaction terms. In the trigonometric case the expressions for the conserved operators involve several free parameters, which can be adjusted to construct a variety of Hamiltonians. This result offers opportunities for future investigations.Finally, we study the case of the q-deformed bosonic Lax operator. This case is much more challenging than the case of the spin Lax operator. It is not straightforward to define the rational and quasi-classical limits of the bosonic Lax operator. Even after making modifications to the Lax operator for these limits to be well defined, it turns out that the limits do not commute. We state some open questions for future work.

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Dynamics of the open BCS model

Cited by 7 publications

References 1 publication

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

The stochastic limit in the analysis of the open BCS model

Richardson-Gaudin models from the Boundary Quantum Inverse Scattering Method

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