Sahand Jamal Rahi

Scattering theory approach to electrodynamic Casimir forces

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each objects classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Casimir forces between cylinders and plates

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the objects separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.

The CDK-APC/C Oscillator Predominantly Entrains Periodic Cell-Cycle Transcription

Throughout cell-cycle progression, the expression of multiple transcripts oscillate, and whether these are under the centralized control of the CDK-APC/C proteins or can be driven by a de-centralized transcription factor (TF) cascade is a fundamental question for understanding cell-cycle regulation. In budding yeast, we find that the transcription of nearly all genes, as assessed by RNA-seq or fluorescence microscopy in single cells, is dictated by CDK-APC/C. Three exceptional genes are transcribed in a pulsatile pattern in a variety of CDK-APC/C arrests. Pursuing one of these transcripts, the SIC1 inhibitor of B-type cyclins, we use a combination of mathematical modeling and experimentation to provide evidence that, counter-intuitively, Sic1 provides a failsafe mechanism promoting nuclear division when levels of mitotic cyclins are low.

Constraints on Stable Equilibria with Fluctuation-Induced (Casimir) Forces

We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaws theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir or van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium, the former being the generic case for ordinary materials in vacuum.

Analytical results on Casimir forces for conductors with edges and tips

Casimir forces between conductors at the submicron scale are paramount to the design and operation of microelectromechanical devices. However, these forces depend nontrivially on geometry, and existing analytical formulae and approximations cannot deal with realistic micromachinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically wedges and cones. The Casimir interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of microelectromechanical devices. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe. We find an unexpectedly large temperature dependence of the force in the cone tip which is of immediate relevance to experiments.Mohammad F. Maghrebi, 2 Sahand Jamal Rahi∗,2 Thorsten Emig, Noah Graham, Robert L. Jaffe, and Mehran Kardar Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, 91405 Orsay, France Department of Physics, Middlebury College, Middlebury, VT 05753, USA (Dated: August 24, 2012)

Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

We analyze the Casimir force between two parallel infinite metal cylinders with nearby metal plates using two methods. Surprisingly, the attractive force between cylinders depends nonmonotonically on the separation from the plate(s), and the cylinder-plate force depends nonmonotonically on the separation of the cylinders. These multibody phenomenona do not follow from simple two-body force descriptions. We can explain the nonmonotonicity with the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders and their images on the nearby plate(s).

Casimir force at a knife’s edge

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 a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination,

Predicting transcription factor specificity with all-atom models

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Casimir interactions of an object inside a spherical metal shell

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Three-body Casimir effects and nonmonotonic forces

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