Boundary reduction formula

Bajnok, Zoltán; Böhm, Gabriella; Takács, Gábor

doi:10.1088/0305-4470/35/44/304

Cited by 18 publications

(21 citation statements)

References 11 publications

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“…one can see that this result is in a complete agreement with the formula obtained form the boundary state formalism previously (6). (The results in (A6, A7) should be multiplied by (−1) in case of computing the Casimir energy of fermionic fields, since their vacuum energy is − 1 2 ω(k)).…”

Section: Discussionsupporting

confidence: 88%

“…The striking fact about the general formulae (5,6) is that they are manifestly finite, and only depend on physical quantities, such as the dispersion relation of asymptotic particles and their reflection amplitudes on the boundaries. This is even more emphasized in the boundary state formalism, where the bulk and boundary divergences appearing in usual derivations of the Casimir effect are manifestly absent, and the whole derivation is performed in terms of finite (renormalized) physical objects.…”

Section: Discussionmentioning

confidence: 99%

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Casimir force between planes as a boundary finite size effect

2006

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The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.Comment: 10 pages, 2 eps figures, LaTeX2e file. v2: A reference is added, some minor modifications made to clarify the text. v3: 9 pages, 3 eps figures, LaTeX2e file, revtex style. Paper throughly restructured and rewritten. Much more details are given, but essential results and conclusions are unchanged. Version accepted for publicatio

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Section: Discussionsupporting

confidence: 88%

Section: Discussionmentioning

confidence: 99%

Casimir force between planes as a boundary finite size effect

2006

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“…This corresponds to a particle propagating between the space time points (x 1 , t 1 ) and (x 2 , t 2 ). The second integral corresponds to a particle propagating between the same two points via the boundary where it is reflected and picks up the momentum dependent amplitude R(p), which is the equivalent to the R-matrix found using any other commonly used definitions, see [16]. The third term on the right of (12) arises from any boundary bound states of the system, such contributions will fall off to zero as x 1 → −∞ and x 2 → −∞ due to the localization of the boundary bound state particles close to the boundary.…”

Section: The Massive Klein-gordon Field With a Robin Boundarymentioning

confidence: 99%

The massive Klein–Gordon field coupled to a harmonic oscillator at the boundary

George¹

2005

J. Phys. A: Math. Gen.

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We consider the massive Klein-Gordon field on the half line with and without a Robin boundary potential. The field is coupled at the boundary to a harmonic oscillator. We solve the system classically and observe the existence of classical boundary bound states in some regions of the parameter space. The system is then quantized, the quantum reflection matrix and reflection cross section are calculated. Resonances and Ramsauer-Townsend effects are observed in the cross section. The pole structure of the reflection matrix is discussed.ag160@garfield.elte.hu

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“…This variation of pole can be shown to be given by the particle-antiparticle FF F 1 ÿ 2 , and the change of the particles mass is given by [19] It is possible to argue in general that the time evolution of expectation values of some local observable operator in an initial state formed by a sudden quench will provide the information about the spectrum of the theory after this transition. One can indeed show [20] that the boundary reflection amplitude R k is related to the bulk Green function G x; x 0 ; t ÿ t 0 as G x; x 0 ; t ÿ t 0 R d! e ÿi!…”

mentioning

confidence: 92%

Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

et al. 2007

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We study the problem of rapid change of the interaction parameter (quench) in a many-body lowdimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.

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Boundary reduction formula

Cited by 18 publications

References 11 publications

Casimir force between planes as a boundary finite size effect

Casimir force between planes as a boundary finite size effect

The massive Klein–Gordon field coupled to a harmonic oscillator at the boundary

Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

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