The parallel critical field of a type-II superconducting cylinder

Constantinou, N C; Masale, M

doi:10.1088/0953-8984/4/18/001

Cited by 15 publications

(18 citation statements)

References 7 publications

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“…Recent analysis [1] extended into the whole complex plane earlier theoretical research [2][3][4] on the influence of the real Robin parameter Λ [5] on the properties of spatially confined two-(2D) and three-dimensional (3D) domain Ω . Obtained dependencies on the example of the infinitely long cylinder and its circular crosssection generalized previously known results for different real Λ without [6][7][8][9][10][11] or with [7,[12][13][14][15][16][17][18][19][20][21][22][23][24] axial magnetic field B. Robin parameter also known as the extrapolation length appears in the boundary condition at the sample interface ∂Ω with its inward normal unit vector n…”

Section: Introductionsupporting

confidence: 60%

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Olendski¹

2012

Annals of Physics

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Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius ρ0 in the superposition of the longitudinal uniform magnetic field B and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths Λin and Λout, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part Ei of the total transverse energy E is discussed. The energy E turns real under special correlation between the imaginary parts of Λin and Λout with the opposite signs what corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy E on Λin and Λout. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy Ei is quenched by the strong intensities B, then for the annulus this takes place only when the inner Robin distance Λin is real; otherwise, it almost quadratically depends on B with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.

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Section: Introductionsupporting

confidence: 60%

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Olendski¹

2012

Annals of Physics

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“…All other properties of the above equations, in particular, their asymptotics in the vanishing fields, can be directly analyzed in the same way, as for the DD case. 58 Contrary to the systems with circular symmetry, 28,31,38,43,[70][71][72][73][74][75][76] in our case, the coefficients n are not real integers. An analysis shows that, similar to the DD configuration, 58 for each fixed energy E, a complete set of solutions of Eq.…”

Section: ͑21͒mentioning

confidence: 74%

Analytical and numerical study of a curved planar waveguide with combined Dirichlet and Neumann boundary conditions in a uniform magnetic field

Olendski

Mikhailovska

2008

Phys. Rev. B

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A model of a thin straight strip with a uniformly curved section and with different uniform boundary conditions on the opposite edges subjected to the homogeneous magnetic field B is theoretically analyzed within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers and superconducting films. In particular, for the inner Dirichlet and outer Neumann boundaries, it is shown that bend-induced enhancement of the superconductivity survives in the magnetic field with the order parameter ⌿͑r͒ being pushed stronger and stronger to the Neumann surface with increasing B and, simultaneously, the area where the nucleation of the superconductivity takes place is spread more and more in the straight arms. Various magnetotransport properties of the film such as interference blockade of the supercurrent flow at some special field-dependent temperatures are also discussed with special attention being paid to the formation and evolution of the vortices, which appear as a result of the bend-induced interaction between the different subbands; it is shown, in particular, that the number of vortices decreases with the field and some of them transform into the antivortices. A proof of the very close analogy between two kinds of strips, ͑1͒ pure Dirichlet condition on both edges and ͑2͒ inner Dirichlet and outer Neumann requirements, derived earlier for B = 0 is extended to the case of nonzero fields.

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“…Another exciting generalization is the influence of the transverse magnetic field B when its increasing magnitude pushes the position densities to the dot center, thus diminishing the confinement influence and converting the orbitals into the Landau levels, which means that its strong values should suppress both the Dirichlet and Neumann thresholds to zero, wiping out the difference between them in this way. Position waveforms and energy spectra of both Dirichlet [ 74–77 ] and Neumann [ 77,78 ] discs in the field B are known, but apparently, nobody considered momentum parts and associated quantum information measures in both spaces.…”

Section: Conclusion and Future Outlookmentioning

confidence: 99%

Comparative analysis of information measures of the Dirichlet and Neumann two‐dimensional quantum dots

Olendski

2020

Int J of Quantum Chemistry

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d-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schrödinger equation in position space and the Fourier transform of the corresponding wave function leads to the analytic form of its momentum counterpart too. This paves the way to an efficient computation in either space of Shannon, Rényi and Tsallis entropies, Onicescu energies and Fisher informations; for example, for the latter measure, some particular orbitals exhibit simple expressions in either space at any BC type. A comparative study of the influence of the edge requirement on the quantum information measures proves that the lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where one-parameter momentum entropies exist is equal to d/(d + 3) for the Dirichlet hyperball and d/(d + 1) for the Neumann one what means that at the unrestricted growth of the dimensionality both measures have their Shannon fellow as the lower verge. Simultaneously, this imposes the restriction on the upper value of the interval [1/2, α R ) inside which the Rényi uncertainty relation for the sum of the position R ρ (α) and wave vector R γ α 2α−1 components is defined: α R is equal to d/(d − 3) for the Dirichlet geometry and to d/(d − 1) for the Neumann BC. Some other properties are discussed from mathematical and physical points of view. Parallels are drawn to the corresponding properties of the hydrogen atom and similarities and differences are explained based on the analysis of the associated wave functions.

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The parallel critical field of a type-II superconducting cylinder

Cited by 15 publications

References 7 publications

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Analytical and numerical study of a curved planar waveguide with combined Dirichlet and Neumann boundary conditions in a uniform magnetic field

Comparative analysis of information measures of the Dirichlet and Neumann two‐dimensional quantum dots

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