The third boundary condition—was it robin’s?

Gustafson, Karl; Abe, Takehisa

doi:10.1007/bf03024402

Cited by 94 publications

(77 citation statements)

References 7 publications

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“…Linear relation between the function Ψ and its spatial derivative is governed by the Robin length Λ [1] whose real value guarantees that no current with the density…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field E applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length Λ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schrödinger equation are derived and used for calculating energies, dipole moments, position Sx and momentum S k quantum information entropies and their Fisher information Ix and I k and Onicescu information energies Ox and O k counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, Λ = 0 (Neumann, Λ = ∞), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum Sx + S k . Analogously, at Λ = 0 and Λ = ∞ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as E 2/3 (E 1/3 ) and its inverse, respectively, leading to the field-independent product IxI k (OxO k ). Peculiarities of their transformations at the finite nonzero Λ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

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“…Linear relation between the function Ψ and its spatial derivative is governed by the Robin length Λ [1] whose real value guarantees that no current with the density…”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Olendski

2016

Annalen der Physik

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“…Analysis of the interaction between the electric field E applied perpendicularly to the plane S and the Robin boundary condition (BC) at it [1] …”

Section: Introductionmentioning

confidence: 99%

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Olendski

2016

Annalen der Physik

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A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field E that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage-free configuration support negative-energy bound state. For the canonical ensemble, the heat capacity at Λ < 0 exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as ln 2 E and its location being proportional to (− ln E ) −1 . For the Fermi-Dirac distribution, the specific heat per particle cN is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing E is defined as 3(N − 1)/(2N )kB, with N being a number of the particles. The maximum of cN is the largest for N = 1 and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose-Einstein ensemble, a formation of the sharp asymmetric feature on the cN -T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp-like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of cN (T ), is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature Tcr and ground-level population of the Bose-Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.

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“…There are many applications of Laplacian differential operator related to physical geodesy, electromagnetic, measurement 1,2 , and to specific boundary problems such as Dirichlet problem and Neumann problem 3 . The applications of the mixed boundary value problem in potential theory can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Solving a class of Robin problems in simply connected regions via integral equations with a generalized Neumann kernel

Al-Shatri¹,

Murid²,

Ismail³

2017

ScienceAsia

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This paper presents a new boundary integral equation method for the solution of a class of Robin problems in bounded and unbounded simply connected regions. We show how to reformulate the Robin problems as RiemannHilbert problems which lead to systems of integral equations, related differential equations, and normalizing conditions that give rise to unique solutions. Numerical results on several test regions are presented to illustrate the solution technique for the Robin problems when the boundaries are sufficiently smooth.

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The third boundary condition—was it robin’s?

Cited by 94 publications

References 7 publications

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum‐information measures

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

Solving a class of Robin problems in simply connected regions via integral equations with a generalized Neumann kernel

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