Dynamical Casimir effect with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>δ</mml:mi><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>mirrors

Silva, Jeferson Danilo L.; Braga, Alessandra N.; Alves, Danilo T.

doi:10.1103/physrevd.94.105009

Cited by 15 publications

(14 citation statements)

References 52 publications

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“…The further generalization to the δ − δ potential was considered in [170]. In this model, the reflection and transmission coefficients have the form…”

Section: Partially Transparent Mirrors and General Boundary Conditionmentioning

confidence: 99%

Fifty Years of the Dynamical Casimir Effect

Dodonov

2020

Physics

150

105

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“…The further generalization to the δ − δ potential was considered in [170]. In this model, the reflection and transmission coefficients have the form…”

Section: Partially Transparent Mirrors and General Boundary Conditionmentioning

confidence: 99%

Fifty Years of the Dynamical Casimir Effect

Dodonov

2020

Physics

150

105

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“…Notably, Moore [41], DeWitt [42], and later on, Davies and Fulling [38,39] initiated a program using field theories with external conditions, which eventually demonstrated that quantities like the expectation values of the stress-energy tensor, and the localization of particles using wave packets, can be calculated in various physical problems and used to extract significant physical consequences of the quantum fields. Indeed, there has been renewed interest [23,24,[43][44][45][46][47][48][49][50][51][52][53][54] in the moving mirror model in recent years due, in part, to claims of experimental verification of the dynamical Casimir effect [55,56]. In many of these particle production scenarios, various systems that exploit the simple mathematical set up of the (1+1)-dimensional moving mirror model have led to novel experimental designs.…”

Section: Introduction: Some Puzzles With Moving Mirrors and Evaporatimentioning

confidence: 99%

On horizonless temperature with an accelerating mirror

Good

Yelshibekov

Ong

2017

J. High Energ. Phys.

111

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A new solution of a unitary moving mirror is found to produce finite energy and emit thermal radiation despite the absence of an acceleration horizon. In the limit that the mirror approaches the speed of light, the model corresponds to a black hole formed from the collapse of a null shell. For speeds less than light, the black hole correspondence, if it exists, is that of a remnant. 4 Note that there are two types of black hole remnant in the literature: the "long-lived" or "metastable" remnant, and the "eternal" remnant [31] . The former has lifetime much longer than that of a black hole, that is, proportional to M n where n > 3. An eternal remnant, on the other hand, lives forever. Our model corresponds to an eternal red-shifted scenario.5 Einstein's gravity is topological in (1+1)-dimensions, but with a suitable coupling to matter fields, gravity need not be trivial in (1+1)-dimensions. This allows one to study black hole evaporation. In our moving mirror model, of course, there is no gravity, only an accelerating mirror, so there is no complication either.

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“…In this manner it is consistent to take the 0-hit function to be the free space propagator, K 0 (y, x; T ). Through direct substitution we can now write the propagator (12) in a perturbative series that involves successive hit functions integrated over S K(y, x; T ) = K 0 (y, x; T ) − λ…”

Section: Quantum Propagation and The N-hit Functionmentioning

confidence: 99%

“…This is the case, for example, for many scattering problems and contact interactions [7][8][9] and varied models of lattice structure in condensed matter [10,11]. In the relativistic case, constrained path integrals arise in the context of the Casimir effect where one is interested in trajectories that touch the conducting plates [12][13][14][15], and for Dirichlet boundary conditions imposed in some spatial region [16][17][18][19][20][21][22][23][24][25] where the contributions from paths passing through this region should be removed. A fresh approach to calculating, either analytically, approximately or numerically, such path integrals will therefore find wide application.…”

Section: Introductionmentioning

confidence: 99%

Non-perturbative Quantum Propagators in Bounded Spaces

Edwards,

González-Domínguez,

Huet

et al. 2021

Preprint

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We outline a new approach to calculating the quantum mechanical propagator in the presence of geometrically non-trivial Dirichlet boundary conditions based upon a generalisation of an integral transform of the propagator studied in previous work (the so-called "hit function"), and a convergent sequence of Padé approximants. In this paper the generalised hit function is defined as a many-point propagator and we describe its relation to the sum over trajectories in the Feynman path integral.We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in D = 1 and D = 3 dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, nonlocalised potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials [1][2][3]. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.

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Dynamical Casimir effect withδ−δ′mirrors

Cited by 15 publications

References 52 publications

Fifty Years of the Dynamical Casimir Effect

Fifty Years of the Dynamical Casimir Effect

On horizonless temperature with an accelerating mirror

Non-perturbative Quantum Propagators in Bounded Spaces

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