On the resonances near the continua boundaries of the Dirac equation with a short-range interaction

Krylov, K. S.; Mur, V. D.; Fedotov, A. M.

doi:10.1140/epjc/s10052-020-7833-x

Cited by 5 publications

(9 citation statements)

References 36 publications

(84 reference statements)

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“…5 (Fig. 2a in [47]). The pole closest to the physical region will be called the Breit-Wigner pole, k + ≡ k BW .…”

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

“…So, for example, for the partial phase of elastic scattering δ κ in states with κ = −1, i.e. for s-states, we have [47] δ…”

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

“…6 (Fig. 4 in [47]) shows the phase of elastic scattering of a positron as a function of its energy ε = −ε. It can be seen that when energy ε is close to the resonance position ε (s) 0 , the phase changes abruptly across the width γ (s) , which ensures the appearance of a resonance in the scattering in the same way as in the nonrelativistic theory of scattering [48].…”

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

See 2 more Smart Citations

Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics

Krylov,

Kuleshov,

Lozovik

et al. 2021

Preprint

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Physical problems for which the existence of non-trivial topological Pauli phase (i.e. fractional quantization of angular orbital angular momenta that is possible in 2D case) is essential are discussed within the framework of two-dimensional Helmholtz, Schroedinger and Dirac equations.As examples in classical field theory we consider a "wedge problem" -a description of a field generated by a point charge between two conducting half-planes -and a Fresnel diffraction from knife-edge.In few-electron circular quantum dots the choice between integer and half-integer quantization of orbital angular momenta is defined by the Pauli principle. This is in line with precise experimental data for the ground state energy of such quantum dots in a perpendicular magnetic field.In a gapless graphene, as in the case of gapped one, in the presence of overcharged impurity this problem can be solved experimentally, e.g., using the method of scanning tunnel spectroscopy.

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“…5 (Fig. 2a in [47]). The pole closest to the physical region will be called the Breit-Wigner pole, k + ≡ k BW .…”

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

“…So, for example, for the partial phase of elastic scattering δ κ in states with κ = −1, i.e. for s-states, we have [47] δ…”

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

Section: Scattering Phase and Poles Of The Scattering Matrix Of S-statesmentioning

confidence: 99%

See 1 more Smart Citation

Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics

Krylov,

Kuleshov,

Lozovik

et al. 2021

Preprint

Self Cite

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show abstract

“…Complex-energy solutions for the differential equation are obtained using the appropriate boundary conditions, analogous to states in the discrete region. This has, for example, been studied for the spectrum of the Dirac equation with a spherical well potential [201][202][203] and for a Coulomb cut-off potential [28,151,194,203,204], for which the solutions can be analytically expressed. Alternatively, solutions to the Dirac equation can be analytically continued into the complex plane by complex scaling or by introducing a complex absorbing potential [205][206][207][208][209].…”

Section: Analytical Continuationmentioning

confidence: 99%

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Preprint

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We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Z crit ≈ 170, where levels such as the 1s shell dive into the negative energy continuum (E nκ < −m e c 2 ). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.* Here we define the starting point of the superheavy element region at the transactinides, Z ≥ 103

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“…However, due to the self-adjointness of the radial Dirac Hamiltonian, see Reference [ 39 ] and the mathematically rigorous paper [ 69 ], the one-particle approximation for the Dirac equation is valid not only for

, but also for

(see References [ 35 , 70 ] for the case of short-range potential [ 71 ]). Qualitatively, this can be understood using the semiclassical approximation, when the system (1) near the boundary of the lower continuum of solutions to the Dirac equation is equivalent to the Schrödinger equation [ 41 , 42 ] with effective energy

and potential

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

On the Impact of Substrate Uniform Mechanical Tension on the Graphene Electronic Structure

et al. 2020

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Employing density functional theory calculations, we obtain the possibility of fine-tuning the bandgap in graphene deposited on the hexagonal boron nitride and graphitic carbon nitride substrates. We found that the graphene sheet located on these substrates possesses the semiconducting gap, and uniform biaxial mechanical deformation could provide its smooth fitting. Moreover, mechanical tension offers the ability to control the Dirac velocity in deposited graphene. We analyze the resonant scattering of charge carriers in states with zero total angular momentum using the effective two-dimensional radial Dirac equation. In particular, the dependence of the critical impurity charge on the uniform deformation of graphene on the boron nitride substrate is shown. It turned out that, under uniform stretching/compression, the critical charge decreases/increases monotonically. The elastic scattering phases of a hole by a supercritical impurity are calculated. It is found that the model of a uniform charge distribution over the small radius sphere gives sharper resonance when compared to the case of the ball of the same radius. Overall, resonant scattering by the impurity with the nearly critical charge is similar to the scattering by the potential with a low-permeable barrier in nonrelativistic quantum theory.

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On the resonances near the continua boundaries of the Dirac equation with a short-range interaction

Cited by 5 publications

References 36 publications

Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics

Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

On the Impact of Substrate Uniform Mechanical Tension on the Graphene Electronic Structure

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