Exact energy spectrum for models with equally spaced point potentials

Caudrelier, Vincent; Crampé, Nicolas

doi:10.1016/j.nuclphysb.2005.12.014

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…On the other hand the advantage of this approach is the possibility of generalizing it to other specific boundary or initial conditions. In principle this formalism should allow one to include impurities [38] and can be extended to multi-component generalizations of the NSE [39].…”

Section: The Quantum Inverse Scattering Methodsmentioning

confidence: 99%

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

2010

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In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.

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Section: The Quantum Inverse Scattering Methodsmentioning

confidence: 99%

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

2010

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“…More recently there have been papers where, contact potentials have been used to study the effects of resonant tunneling [24,25], to study their properties under the effect of external fields [26], and their applications in the study of metamaterials [27]. In addition the effects of several contact potential barriers have been studied in [28,29,30,31,32,33] and extensions to arbitrary dimension have been considered in [34] generalising the approach by Jackiw in [15]. Mathematical properties of potentials decorated with contact interactions have also been the object of recent studies [35,36,37,38,39,40,41].…”

Section: Introductionmentioning

confidence: 99%

Band spectra of periodic hybrid $δ$-$δ^\prime$ structures

Gadella,

Guilarte,

Muñoz-Castañeda

et al. 2019

Preprint

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We present a detailed study of a generalised one-dimensional Kronig-Penney model using δ-δ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite array formed by identical δ-δ potentials standing at the linear lattice nodes. This case will be known throughout the paper as the one-species hybrid Dirac comb. We investigate the consequences of adding the δ interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac-δ combs and one-species hybrid Dirac combs. Secondly we study the quantum system that arises when the periodic potential is the one obtained from the superposition of two one-species hybrid Dirac combs displaced one with respect to the other and with different couplings. The latter will be known as the two-species hybrid Dirac comb. One of the most remarkable results is the appearance of a curvature change in the band spectrum when the δ couplings are above a critical value.

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“…• Chains of periodic δ-δ interactions have been considered in order to analyze a solvable Kronig-Penney model in solid state, where the behaviour of band spectrum has been thoroughly analyzed in order to obtain a better comprehension of dielectric and conducting phenomena [24,25]. • Although in principle we focused our attention in one dimensional nonrelativistic problems, work has been done also in the study of contact potentials in higher dimensions [26], or as perturbations of the Dirac equation or the Salpeter Hamiltonian [27].…”

Section: Introductionmentioning

confidence: 99%

Some recent results on contact or point supported potentials

Nieto¹,

Gadella²,

Mateos-Guilarte³

et al. 2020

Preprint

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We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the δ-δ interaction. After a simple general presentation in one dimension, we briefly discuss a one dimensional periodic potential with a δ-δ interaction at each node. The dependence of energy bands with the parameters (coefficients of the deltas) can be computed numerically. We also study the δ-δ interaction supported on spheres of arbitrary dimension. The spherical symmetry of this model allows us to obtain rigorous conclusions concerning the number of bound states in terms of the parameters and the dimension. Finally, a δ-δ interaction is used to approximate a potential of wide use in nuclear physics, and estimate the total number of bound states as well as the behaviour of some resonance poles with the lowest energy.

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Exact energy spectrum for models with equally spaced point potentials

Cited by 4 publications

References 21 publications

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

Band spectra of periodic hybrid $δ$-$δ^\prime$ structures

Some recent results on contact or point supported potentials

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