Physical structure of point-like interactions for one-dimensional Schrödinger operator and the gauge symmetry

Kulinskii, V. L.; Panchenko, Dmitry

doi:10.1016/j.physb.2015.05.011

Cited by 23 publications

(39 citation statements)

References 19 publications

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“…In accordance with the spin-momentum nature of the r-couplings the physical reason of such factorization is that X 3 contact interaction does not include spatial inhomogeneity in electric field potential ϕ. This is quite consistent with the difference between X 2 and X 3 from the point of view of breaking the gauge symmetry [14,17].…”

Section: Contact Interactions For Spin 1/2 Casesupporting

confidence: 64%

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Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

Kulinskii

Panchenko

2019

Front. Phys.

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We consider singular self-adjoint extensions for the Schrödinger operator of spin-1/2 particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip mechanism, i.e. for these point-like interactions the spin operator does not commute with the Hamiltonian. One of these extensions is the analog of zero-range δ-potential. The other one is the analog of so called δ (1) -interaction. We show that in physical terms such contact interactions can be identified as the point-like analogues of Rashba Hamiltonian (spin-momentum coupling) due to material heterogeneity of different types. The dependence of the transmissivity of some simple devices on the strength of the Rashba coupling parameter is discussed. Additionally, we show how these boundary conditions can be obtained in the non-relativistic limit of Dirac Hamiltonian.

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Section: Contact Interactions For Spin 1/2 Casesupporting

confidence: 64%

“…layered system. The only demand consistent with the hermiticity of the Hamiltonian (1) is the conservation of current components (14).…”

Section: Contact Interactions For Spin 1/2 Casementioning

confidence: 99%

Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

Kulinskii

Panchenko

2019

Front. Phys.

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“…(16), however, for this type we assume that the limit sin(kr) → 0 proceeds faster (as a function of l 1 , l 2 ) than in the asymptotic representation (18). The limit diagonal elements λ 11 and λ 22 are given in this case by the same formulae (19).…”

Section: Three Types Of Resonant-tunneling Point Interactionsmentioning

confidence: 99%

“…On the sets (21) and (22), the asymptotic formulae (24) provide the finiteness of the arguments of the trigonometric functions in Eqs. (5) - (8), so that all the expressions (14) - (19) can be used in the following in the parametrized form. Thus, the resonance condition (14) can be rewritten as…”

Section: Sets Of the Existence Of The Distribution δ ′ (X)mentioning

confidence: 99%

A phenomenon of splitting resonant-tunneling one-point interactions

Zolotaryuk

2018

Annals of Physics

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The so-called δ ′ -interaction as a particular example in Kurasov's distribution theory developed on the space of discontinuous (at the point of singularity) test functions, is identified with the diagonal transmission matrix, continuously depending on the strength of this interaction. On the other hand, in several recent publications, the δ ′ -potential has been shown to be transparent at some discrete values of the strength constant and opaque beyond these values. This discrepancy is resolved here on the simple physical example, namely the heterostructure consisting of two extremely thin layers separated by infinitesimal distance. In the three-scale squeezing limit as the thickness of the layers and the distance between them simultaneously tend to zero, a whole variety of single-point interactions is realized. The key point is the generalization of the δ ′ -interaction to the family for which the resonance sets appear in the form of a countable number of continuous two-dimensional curves. In this way, the connection between Kurasov's δ ′ -interaction and the resonant-tunneling point interactions is derived and the splitting of the resonance sets for tunneling plays a crucial role.

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“…As already mentioned in Section 1, neither δ ′ nor δ (1) stand for a "genuine" derivative of a δ interaction-they simply refer to particular choices of parameters in the general point interaction [34][35][36] (a recent proposal for physically interpreting the boundary conditions given by single point interactions is given in Kulinskii and Panchenko [58]). …”

Section: Double Barrier Of Generalized Point Interactions: Symmetry Umentioning

confidence: 99%

Double General Point Interactions: Symmetry and Tunneling Times

et al. 2016

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We consider the one dimensional problem of a non-relativistic quantum particle scattering off a double barrier built from two generalized point interactions (each one characterized as a member of the four parameter family of point interactions). The properties of the double point barrier under parity transformations are investigated, using the distributional approach, and the constraints on the parameters necessary for the interaction to have a well-defined parity are obtained. We show that the limit of zero interbarrier distance of a renormalized odd arrangement with two δ ′ is either trivial or does not exist as a generalized point interaction. Finally, we specialize to double barriers with defined parity, calculate the phase and Salecker-Wigner-Peres clock times and argue that the emergence of the generalized Hartman effect is an artifact of the extreme opaque limit.

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Physical structure of point-like interactions for one-dimensional Schrödinger operator and the gauge symmetry

Cited by 23 publications

References 19 publications

Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension

A phenomenon of splitting resonant-tunneling one-point interactions

Double General Point Interactions: Symmetry and Tunneling Times

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