Quantum vacuum interaction between two sine-Gordon kinks

Bordag, M.; Munõz-Castañeda, J. M.

doi:10.1088/1751-8113/45/37/374012

Cited by 21 publications

(40 citation statements)

References 19 publications

(36 reference statements)

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“…Therefore the condition ψ(0) = ψ(L) does not necessarily give rise to periodic boundary conditions. As an example it is worth to mention the case of Dirac delta potentials (see references [26][27][28] for recent developments in the interpretation of Dirac delta potentials as boundary conditions and infinitely thin kinks) where the condition ψ(0) = ψ(L) is satisfied but obviously the system does not satisfy periodic boundary conditions. Therefore in order to distinguish periodic boundary conditions from other types of point interactions it is necessary to include the second condition over the derivatives: ψ (0) = ψ (L).…”

Section: Heat Kernel Coefficients For Common Boundary Conditionsmentioning

confidence: 99%

QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions

2015

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Following the seminal works of Asorey-Ibort-Marmo and Muñoz-Castañeda-Asorey about selfadjoint extensions and quantum fields in bounded domains, we compute all the heat kernel coefficients for any strongly consistent selfadjoint extension of the Laplace operator over the finite line [0, L]. The derivative of the corresponding spectral zeta function at s = 0 (partition function of the corresponding quantum field theory) is obtained. To compute the correct expression for the a 1/2 heat kernel coefficient, it is necessary to know in detail which non-negative selfadjoint extensions have zero modes and how many of them they have. The answer to this question leads us to analyze zeta function properties for the Von Neumann-Krein extension, the only extension with two zero modes.Mathematics Subject Classification. 81S99, 81T20, 81T55, 81U99, 34B08, 35J25, 11M36, 47B25, 47A10.Keywords. Quantum Theory, Quantum field theory on curved space backgrounds, Casimir effect, Scattering theory, Parameter dependent boundary value problems, Boundary value problems for second-order elliptic equations, Zeta and L-functions: analytic theory, Symmetric and selfadjoint operators, General theory of linear operators.

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Section: Heat Kernel Coefficients For Common Boundary Conditionsmentioning

confidence: 99%

QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions

2015

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“…Particularly, they have calculated the vacuum energy and identified which boundary conditions generate attractive or repulsive Casimir forces between the plates. Bordag and Muñoz-Castañeda [66] have calculated the quantum vacuum interaction energy between two kinks of the sine-Gordon equation (for a review on nonlinear localized excitations including topological solitons see, e.g., the work [67]) and shown that this interaction induces an attractive force between the kinks in parallel to the Casimir force between conducting mirrors. A rigorous mathematical model of real metamaterials has been suggested in [68].…”

Section: Introductionmentioning

confidence: 99%

Point Interactions With Bias Potentials

2019

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We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation of multi-layered heterostructures that are subject to bias potentials. In this approach , the zero-thickness limit of the transmission matrices of specific structures is analyzed and shown to result in matrices connecting the two-sided boundary conditions of the wave function at the origin. The reflection and transmission amplitudes are computed in terms of these matrix elements as well as biased data. Several one-point interaction models of two-and three-terminal devices are elaborated. The typical transistor in the semiconductor physics is modeled in the "squeezed limit" as a δ-and a δ -potential and referred to as a "point" transistor. The basic property of these one-point interaction models is the existence of several extremely sharp peaks as an applied voltage tunes, at which the transmission amplitude is non-zero, while beyond these resonance values, the heterostructure behaves as a fully reflecting wall. The location of these peaks referred to as a "resonance set" is shown to depend on both system parameters and applied voltages. An interesting effect of resonant transmission through a δ-like barrier under the presence of an adjacent well is observed. This transmission occurs at a countable set of the well depth values.

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“…In particular, configurations of two pure delta potentials added to the free Schrödinger Hamiltonian have been used to describe scalar field fluctuations on external backgrounds [25], in terms of the corresponding scattering waves. Delta point interactions allow the implementation of some boundary conditions compatible with a scalar QFT defined on an interval [26]. The delta interaction is often multiplied by a real number a.…”

Section: Introductionmentioning

confidence: 99%

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

et al. 2018

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a b s t r a c tWe consider the one-dimensional Hamiltonian with a V-shaped, decorated with a point impurity of either δ-type, or local δ ′ -type or even nonlocal δ ′ -type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type −λ δ(x) or −λ δ(x − x 0 ) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ ′ interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type −λδ(x)+µδ ′ (x), and analyse in detail the discrete spectrum of the resulting selfadjoint Hamiltonian.

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Quantum vacuum interaction between two sine-Gordon kinks

Cited by 21 publications

References 19 publications

QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions

QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions

Point Interactions With Bias Potentials

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

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