Casimir energy for a three-piece relativistic string

Brevik, Iver; Nielsen, H. B.; Odintsov, Sergei D.

doi:10.1103/physrevd.53.3224

Cited by 24 publications

(25 citation statements)

References 12 publications

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“…Vacuum polarization in the background of on a string was first considered in [19]. The generalized ζ-function has many interesting applications, e.g., in the piecewise string [20,21]. Similar analysis has been applied to noncommutative spacetime [22], monopoles [23], p-branes [24] or pistons [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Feng

Zhai

2014

Mod. Phys. Lett. A

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When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the "quasi-periodic" condition , is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional space-time case is also investigated.

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Section: Introductionmentioning

confidence: 99%

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Feng

Zhai

2014

Mod. Phys. Lett. A

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“…The theory for this case was given in Refs. [6] and [9]. Here, we shall consider instead a string divided into 2N pieces of equal length, of alternating type I (type II) material.…”

Section: N-piece Stringmentioning

confidence: 99%

“…Refs. [5,6,7,8,9,10,11,13,14]. As for possible physical applications of the model, we may also mention the paper of Lu and Huang [15], discussing the Casimir energy for a composite Green-Schwarz superstring.…”

Section: Introduction the Two-piece Stringmentioning

confidence: 99%

Casimir theory of the relativistic composite string revisited, and a formally related problem in scalar QFT

Brevik¹

2012

J. Phys. A: Math. Theor.

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The main part of this paper is to present an updated review of the Casimir energy at zero and finite temperature for the transverse oscillations of a piecewise uniform closed string. We make use of three different regularizations: the cutoff method, the complex contour integration method, and the zeta-function method. The string model is relativistic, in the sense that the velocity of sound is for each string piece set equal to the velocity of light. In this sense the theory is analogous to the electromagnetic theory in a dielectric medium in which the product of permittivity and permeability is equal to unity (an isorefractive medium). We demonstrate how the formalism works for a two-piece string, and for a 2N-piece string, and show how in the latter case a compact recursion relation serves to facilitate the formalism considerably. The Casimir energy turns out to be negative, and the more so the larger the number of pieces in the string. The two-piece string is quantized in D-dimensional spacetime, in the limit when the ratio between the two tensions is very small. We calculate the free energy and other thermodynamic quantities, demonstrate scaling properties, and comment finally on the meaning of the Hagedorn critical temperature for the two-piece string.Thereafter, as a novel development we present a scalar field theory for a real field in three-dimensional space in a potential rising linearly with a longitudinal coordinate z in the interval 0 < z < 1, and which is thereafter held constant on a horizontal plateau. The potential is taken as a rough 1 iver.h.brevik@ntnu.no 1 model of the two-piece string potential under simplifying conditions, when the length ratio between the pieces is replaced formally with the mentioned length parameter z. 2

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“…The generalized ζ-function has many interesting applications, e.g., in the piecewise string. 15,16 Similar analysis has been applied to monopoles, 17 p-branes 18 or pistons. [19][20][21][22] Recently, more attention has been paid to the Casimir effect due to the development of precise measurements, 23 and it has been applied to the fabrication of microelectromechanical systems (MEMS).…”

Section: Introductionmentioning

confidence: 99%

The Casimir Force of Quantum Spring in the (D+1)-Dimensional Spacetime

Zhai

Feng

2011

Mod. Phys. Lett. A

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The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper. 27 Here, the Casimir effect of the quantum spring is investigated in (D +1)-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any D, which indicate a Z 2 symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the ζfunction. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes.

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Casimir energy for a three-piece relativistic string

Cited by 24 publications

References 12 publications

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes

Casimir theory of the relativistic composite string revisited, and a formally related problem in scalar QFT

The Casimir Force of Quantum Spring in the (D+1)-Dimensional Spacetime

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