2010

Casimir potential of a compact object enclosed by a spherical cavity

Saad Zaheer 1, Sahand Jamal Rahi 1, Thorsten Emig 2, 3, Robert L. Jaffe 4 Physical Review A: Atomic, Molecular and Optical Physics 82 (2010) 052507 We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects’ scattering matrices and translation matrices that relate the coordinate […]

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Casimir Force at a Knife’s Edge

Noah Graham 1, Alexander Shpunt 2, Thorsten Emig 2, 3, 4, Sahand Jamal Rahi 2, Robert L. Jaffe 2, 5, Mehran Kardar 2 Physical Review D 81 (2010) 061701 The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such

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$\zeta$-regularised spectral determinants on metric graphs

Christophe Texier 1, 2 Journal of Physics A Mathematical and Theoretical 43 (2010) 425203 Several general results for the spectral determinant of the Schrödinger operator on metric graphs are reviewed. Then, a simple derivation for the $\zeta$-regularised spectral determinant is proposed, based on the Roth trace formula. Two types of boundary conditions are studied: functions continuous at the

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