Coherence factors beyond the BCS expressions—a derivation

Gorohovsky, Gregory; Bettelheim, Eldad

doi:10.1088/1751-8113/47/2/025001

Cited by 5 publications

(12 citation statements)

References 22 publications

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“…One can often convert the computation matrix elements of operators into the computation of Slavnov-type overlaps as was done here following Refrs. [2,5,16], but a similar procedure may be possible in additional models, such that the method here may be applied to compute interesting physical observables. After all, physical observables in and out of equilibrium can invariably be written through matrix elements and expectation values.…”

Section: Discussionmentioning

confidence: 99%

“…In fact such a program has been undertaken in Refrs. [4,5], however in those papers, c was taken to be of order 1/N or smaller, which is not the approach taken here. The advantage of our approach is that we can use our techniques to find the matrix elements for finite c, whereas Refrs.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of our approach is that we can use our techniques to find the matrix elements for finite c, whereas Refrs. [4,5] are limited to small c, and thus restricted to the semiclassical limit. In our approach however we do not reproduce the full semiclassical result, due to the fact that, in order to use the steepest descent method, we cannot let c be of order 1/N .…”

Section: Introductionmentioning

confidence: 99%

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Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

Bettelheim

2021

Preprint

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

Bettelheim

2021

Preprint

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“…For an example of a recent application of this exact solution for the evaluation of form factors, see Ref. [23], while the extension of this approach to other pairing models was reported in Ref. [24].…”

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confidence: 99%

Exact solution for the inhomogeneous Dicke model in the canonical ensemble: Thermodynamical limit and finite-size corrections

Pogosov¹,

Shapiro²,

Bork³

et al. 2017

Nuclear Physics B

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We consider an exactly solvable inhomogeneous Dicke model which describes an interaction between a disordered ensemble of two-level systems with single mode boson field. The existing method for evaluation of Richardson-Gaudin equations in the thermodynamical limit is extended to the case of Bethe equations in Dicke model. Using this extension, we present expressions both for the ground state and lowest excited states energies as well as leading-order finite-size corrections to these quantities for an arbitrary distribution of individual spin energies. We then evaluate these quantities for an equally-spaced distribution (constant density of states). In particular, we study evolution of the spectral gap and other related quantities. We also reveal regions on the phase diagram, where finite-size corrections are of particular importance. PACS numbers: 02.30Ik, 42.50.Ct, 03.65.Fd I. INTRODUCTIONRecent progress in engineering of artificial quantum systems for information technologies renewed an interest to Dicke (Tavis-Cummings) model [1] and its exact solution, already well known for a long time [2][3][4][5][6][7]. Dicke model describes an interaction between a collection of two-level systems and single mode radiation field, while physical realizations range from superconducting qubits coupled to microwave resonators to polaritons in quantum wells, see e.g. Refs. [8,9] and references therein; furthermore, it can be also applied to Fermi-Bose condensates near the Feshbach resonance [10].The characteristic feature of macroscopic artificial quantum systems such as superconducting qubits is a disorder in excitation frequencies and inhomogeneous broadening of the density of states. This feature is due to fundamental mechanisms: for example, an excitation energy of flux qubits depends exponentially on Josephson energies [11], which makes it extremely sensitive to characteristics of nanometer-scale Josephson junctions. Inhomogeneous broadening appears even in the case of microscopic two-level systems, such as NV-centers, where it is induced by spatial fluctuations of background magnetic moments [12]. In the case of NV-centers, the density of states is characterized by the q-Gaussian distribution [13]. Moreover, there are prospect to utilize the broadening for the construction of a multimodal quantum memory [14]. It is also possible to engineer a density of states profile by using, e.g., a so-called spectral arXiv:1612.01774v2 [cond-mat.stat-mech]

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“…Apart from the general interest, our results might be useful for the resolution of BE or computing correlations functions, since they provide additional tools to tackle these complex problems 16,18,22 . This paper is organized as follows.…”

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confidence: 99%

Particle–hole duality, integrability, and Russian doll BCS model

Bork

Pogosov

2015

Nuclear Physics B

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We address a generalized Richardson model (Russian doll BCS model), which is characterized by the breaking of time-reversal symmetry. This model is known to be exactly solvable and integrable.We point out that the Russian doll BCS model, on the level of Hamiltonian, is also particle-hole symmetric. This implies that the same state can be expressed both in the particle and hole representations with two different sets of Bethe roots. We then derive exact relations between Bethe roots in the two representations, which can hardly be obtained staying on the level of Bethe equations. In a quasi-classical limit, similar identities for usual Richardson model, known from literature, are recovered from our results. We also show that these relations for Richardson roots take a remarkably simple form at half-filling and for a symmetric with respect to the middle of the interaction band distribution of one-body energy levels, since, in this special case, the rapidities in the particle and hole representations up to the translation satisfy the same system of equations. PACS numbers: 02.30Ik, 74.20.Fg, 03.65.Fd I. INTRODUCTIONBasic properties of conventional superconductors can be described by the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, which assumes that pairing between electrons is due to their interaction through phonons. The simplest possible Hamiltonian, known as a reduced BCS Hamiltonian, accounts only couplings between the spin up and spin down electrons having opposite momenta; moreover, these couplings are supposed to be constant. Within the BCS theory, this Hamiltonian is solved approximately by using a mean-field treatment 1,2 .It was shown by Richardson long time ago that the same Hamiltonian can be solved exactly 3 . The approach to the problem, developed by Richardson, resembles a coordinate Bethe ansatz method. The Hamiltonian eigenstates and eigenvalues are expressed through the set of energy-like quantities (rapidities). They satisfy the set of nonlinear algebraic equations, which are now widely referred to as Richardson equations. The system described by the reduced BCS Hamiltonian is closely related to the so-called Gaudin ferromagnet 4 , for which the exact solution is also known.Unfortunately, the resolution of Richardson equations is a formidable task, so that very few explicit results have been obtained so far. However, in the case of a system, which contains a limited number of pairs, the equations can be solved numerically. Nowadays, this approach is used to investigate pairing correlations in ultrasmall metallic grains at low temperatures 5 .In addition, the reduced BCS Hamiltonian is integrable and exactly solvable through the algebraic Bethe anzats (ABA) method 6-10 , so that Richardson equations can be treated as Bethe equations (BE). In Ref. 11 , the confromal

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Coherence factors beyond the BCS expressions—a derivation

Cited by 5 publications

References 22 publications

Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

Exact solution for the inhomogeneous Dicke model in the canonical ensemble: Thermodynamical limit and finite-size corrections

Particle–hole duality, integrability, and Russian doll BCS model

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