Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

Elizalde, E.; Odintsov, Sergei D.; Saharian, A. A.

doi:10.1103/physrevd.79.065023

Cited by 105 publications

(118 citation statements)

References 73 publications

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“…(15b), one needs to evaluate first the momentum wave function Φ n (k) according to Eq. (8). In known to me literature [91,92,[96][97][98] there are no analytical expressions for the integrals in Eqs.…”

Section: Quantum Information Entropymentioning

confidence: 99%

“…(1) (with the appropriate change of its parameters) and the BC from Eq. (2) describe the processes in acoustics [2], electrodynamics [3], plasma [4], scalar field theory [5][6][7][8], superconductivity [9][10][11][12] where the coefficient Λ is called the de Gennes distance [13], and others [14,15]. Nonexhaustive list of the relevant research efforts can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Quantum Information Entropymentioning

confidence: 99%

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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“…This expression holds for arbitrary temperature, for arbitrary p ∈ [1,3] and for arbitrary integers q, when all the L i are equal. As is usual, F refers to unit surface area.…”

Section: Introductionmentioning

confidence: 99%

“…We are led to a Casimir piston model in which spacetime is flat. This model has attracted considerable attention in the recent literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. One reason for the current interest is obviously the mathematical elegance of the formalism; the efficiency of regularization procedures like the zeta function regularization is quite striking.…”

Section: Introductionmentioning

confidence: 99%

Finite temperature Casimir effect and dispersion in the presence of compactified extra dimensions

Rypestøl¹,

Brevik²

2010

Phys. Scr.

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Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and in addition an arbitrary number q of extra compacified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar 'refractive index' N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces we focus on the low temperature case, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q = 1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.

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“…The in-depth reason responsible for the Casimir effect is an existence of the zero-point and thermal fluctuations of the electromagnetic field whose spectrum is modified by the boundary conditions. Applications of the Casimir effect extend from the nanoscale science [4][5][6], atomic physics [7][8][9][10], condensed matter physics [11][12][13][14][15][16], to the elementary particles, astrophysics and cosmology [17][18][19][20]. The basic theory describing the Casimir effect is the Lifshitz theory of dispersion forces [3,21].…”

Section: Introductionmentioning

confidence: 99%

Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches

Mostepanenko

2015

Phys. Rev. A

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We investigate the Casimir free energy of a metallic film either sandwiched between two dielectric plates or in vacuum. It is shown that even for a thin film of several tens of nanometer thickness the Casimir free energy and pressure calculated with the Lifshitz theory using the Drude model and the plasma model approaches take significantly different values and can be easily discriminated.According to our results, the classical limit is already achieved for films of about 100 nm thickness if the Drude model approach is used in calculations. In this case the classical expressions for the Casimir free energy and pressure are common for both configurations considered. If the plasma model approach is used, the classical limit is not achieved for any film thickness. Instead, the Casimir free energy and pressure are decreasing exponentially to zero. When the plasma frequency goes to infinity, the Casimir free energy obtained using the Drude model approach goes to a nonzero limit in contradiction with expectations. If the plasma model approach is used the free energy of metallic film goes to zero in the limit of infinitely large plasma frequency. All analytic results are accompanied by numerical computations performed for a Au film and sapphire plates. The possibilities to observe the predicted effects discriminating between the Drude and plasma model approaches are discussed.

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Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

Cited by 105 publications

References 73 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

Finite temperature Casimir effect and dispersion in the presence of compactified extra dimensions

Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches

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