1,720,981 research outputs found
Schrödinger operators with multiple Aharonov-Bohm fluxes
Full text linkWe study the Schrödinger operator describing a two-dimensional quantum particle moving in presence of Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.28 pages, pdfLaTeX, minor change
Deficiency indices for singular magnetic Schr\"{o}dinger operators
Full text linkWe show that the deficiency indices of magnetic Schr\"odinger operators with
several local singularities can be computed in terms of the deficiency indices
of operators carrying just one singularity each. We discuss some applications
to physically relevant operators.Comment: 12 pages, pdfLaTe
The Casimir energy anomaly for a point interaction
No full textThe Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boundary term which is infinite despite renormalization. The intrinsic nature of this anomaly is briefly discussed
Vacuum polarization with zero-range potentials on a hyperplane
Full text linkThe quantum vacuum fluctuations of a neutral scalar field induced by background zero-range potentials concentrated on a flat hyperplane of co-dimension 1 in (d+1)-dimensional Minkowski spacetime are investigated. Perfectly reflecting and semitransparent surfaces are both taken into account, making reference to the most general local, homogeneous and isotropic boundary conditions compatible with the unitarity of the quantum field theory. The renormalized vacuum polarization is computed for both zero and non-zero mass of the field, implementing a local version of the zeta regularization technique. The asymptotic behaviors of the vacuum polarization for small and large distances from the hyperplane are determined to leading order. It is shown that boundary divergences are softened in the specific case of a pure Dirac delta potential
The semiclassical limit on a star-graph with Kirchhoff conditions
Full text linkWe consider the dynamics of a quantum particle of mass m on a n-edges star-graph with Hamiltonian HK= - (2 m) - 1ħ2Δ and Kirchhoff conditions in the vertex. We describe the semiclassical limit of the quantum evolution of an initial state supported on one of the edges and close to a Gaussian coherent state. We define the limiting classical dynamics through a Liouville operator on the graph, obtained by means of Kreĭn’s theory of singular perturbations of self-adjoint operators. For the same class of initial states, we study the semiclassical limit of the wave and scattering operators for the couple (HK,HD⊕), where HD⊕ is the Hamiltonian with Dirichlet conditions in the vertex
Pauli Hamiltonians with an Aharonov–Bohm flux
Full text linkWe study a two-dimensional Pauli operator describing a charged quantum particle with spin 1=2 moving on a plane in presence of an orthogonal Aharonov–Bohm magnetic flux. We classify all the admissible self-adjoint realizations and give a complete picture of their spectral and scattering properties. Symmetries of the resulting Hamiltonians are also discussed, as well as their connection with the Dirac operator perturbed by an Aharonov–Bohm singularity
Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators
Full text linkWe study the Hamiltonian describing two anyons moving in a plane in the presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrödinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov-Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions
Scattering from local deformations of a semitransparent plane
Full text linkWe study scattering for the couple (A F ,A 0 ) of Schrödinger operators in L 2 (R 3 ) formally defined as A 0 =−Δ+αδ π javax.xml.bind.JAXBElement@35266ea2 and A F =−Δ+αδ π javax.xml.bind.JAXBElement@56dd5bc1 , α>0, where δ π javax.xml.bind.JAXBElement@4dbab1e is the Dirac δ-distribution supported on the deformed plane given by the graph of the compactly supported, Lipschitz continuous function F:R 2 →R and π 0 is the undeformed plane corresponding to the choice F≡0. We provide a Limiting Absorption Principle, show asymptotic completeness of the wave operators and give a representation formula for the corresponding Scattering Matrix S F (λ). Moreover we show that, as F→0, ‖S F (λ)−1‖ B(L javax.xml.bind.JAXBElement@b81c41d (S javax.xml.bind.JAXBElement@dd4f8b1 )) 2 =O(∫ R javax.xml.bind.JAXBElement@316bb999 dx|F(x)| γ ), 0<γ<1
Corrigendum to “Scattering from local deformations of a semitransparent plane” [J. Math. Anal. Appl. 473 (1) (2019) 215–257]
Full text linkWe correct a minor mistake in the final formula for the scattering matrix
A time machine for free fall into the past
No full textInspired by some recent works of Tippett-Tsang and Mallary-Khanna-Price, we present a new spacetime model containing closed timelike curves (CTCs). This model is obtained postulating an ad hoc Lorentzian metric on R^4, which differs from the Minkowski metric only inside a spacetime region bounded by two concentric tori. The resulting spacetime is topologically trivial, free of curvature singularities and is both time and space orientable; besides, the inner region enclosed by the smaller torus is flat and displays geodesic CTCs. Our model shares some similarities with the time machine of Ori and Soen but it has the advantage of a higher symmetry in the metric, allowing for the explicit computation of a class of geodesics. The most remarkable feature emerging from this computation is the presence of future-oriented timelike geodesics starting from a point in the outer Minkowskian region, moving to the inner spacetime region with CTCs, and then returning to the initial spatial position at an earlier time; this means that time travel to the past can be performed by free fall across our time machine. The amount of time travelled into the past is determined quantitatively; this amount can be made arbitrarily large keeping non-large the proper duration of the travel. An important drawback of the model is the violation of the classical energy conditions, a common feature of many time machines. Other problems emerge from our computations of the required (negative) energy densities and of the tidal accelerations; these are small only if the time machine is gigantic
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