Casimir Theory for the Piecewise Uniform Relativistic String

Berntsen, Martin; Brevik, Iver; Odintsov, Sergei D.

doi:10.1006/aphy.1997.5679

Cited by 15 publications

(24 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…General reviews, containing more references, can be found in Refs. [33][34][35]. A generalization to the case of a nonrelativistic string, (the velocity of sound being different in the different pieces,) has been given in Ref.…”

Section: Analogy To the Theory Of The Piecewise Uniform Stringmentioning

confidence: 99%

Casimir energies of self-similar plate configurations

et al. 2016

View full text Add to dashboard Cite

We construct various self-similar configurations using parallel δ-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to the electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning δ-function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases, the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green's function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory.

show abstract

Section: Analogy To the Theory Of The Piecewise Uniform Stringmentioning

confidence: 99%

Casimir energies of self-similar plate configurations

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Usually the transition to finite temperature in calculations of vacuum energy is accomplished by substituting the integration over imaginary frequencies by summation over the discrete Matsubara frequencies in the integral representation for the Casimir energy at zero temperature [16,21,22]. However, following this way one should control how many times the integration by parts in the integral expression at hand has been done [23,24].…”

Section: Transition To the Finite Temperature In Calculations Of mentioning

confidence: 99%

Casimir effect for a dilute dielectric ball at finite temperature

Nesterenko¹,

Lambiase²,

Scarpetta³

2001

Phys. Rev. D

View full text Add to dashboard Cite

The Casimir effect at finite temperature is investigated for a dilute dielectric ball; i.e., the relevant internal and free energies are calculated. The starting point in this study is a rigorous general expression for the internal energy of a system of noninteracting oscillators in terms of the sum over the Matsubara frequencies. Summation over the angular momentum values is accomplished in a closed form by making use of the addition theorem for the relevant Bessel functions. For removing the divergences the renormalization procedure is applied that has been developed in the calculation of the corresponding Casimir energy at zero temperature. The behavior of the thermodynamic characteristics in the low and high temperature limits is investigated.

show abstract

“…(Ref. [8] contains a review of the various regularization methods.) As a physical result of the Casimir energy calculations it is also worth noticing that the energy is in general nonpositive, and is more negative the larger is the number of uniform pieces in the string.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of the piecewise uniform string

Brevik

Bytsenko

Nielsen³

1998

Class. Quantum Grav.

View full text Add to dashboard Cite

The thermodynamic free energy F is calculated for a gas whose particles are the quantum excitations of a piecewise uniform bosonic string. The string consists of two parts of length L I and L II , endowed with different tensions and mass densities, adjusted in such a way that the velocity of sound always equals the velocity of light. The explicit calculation is done under the restrictive condition that the tension ratio x = T I /T II approaches zero. Also, the length ratio s = L II /L I is assumed to be an integer. The expression for F is given on an integral form, in which s is present as a parameter. For large values of s, the Hagedorn temperature becomes proportional to the square root of s.

show abstract

Casimir Theory for the Piecewise Uniform Relativistic String

Cited by 15 publications

References 24 publications

Casimir energies of self-similar plate configurations

Casimir energies of self-similar plate configurations

Casimir effect for a dilute dielectric ball at finite temperature

Thermodynamic properties of the piecewise uniform string

Contact Info

Product

Resources

About