On Casimir Pistons

In this paper we study the Casimir force for a piston configuration in $R^3$ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in $R^3$ and for possible modifications from extra dimensional manifolds.Comment: 20 pages, To be published in MPL

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections which we refer to as Bogoliubov corrections. The leading order term is identified as the Casimir energy of a massless scalar field moving with wave velocity equal to the speed of sound in the BEC. We then obtain the leading order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary lengths and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT v.3: references adde

Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston

Using a multidimensional cut-off technique, we obtain expressions for the cut-off dependent part of the vacuum energy for parallelepiped geometries in any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface divergences and we show explicitly that they cancel in the Casimir piston scenario in all dimensions. We obtain two different expressions for the d-dimensional Casimir force on the piston where one expression is more convenient to use when the plate separation a is large and the other when a is small (a useful $a \to 1/a$ duality). The Casimir force on the piston is found to be attractive (negative) for any dimension d. We apply the d-dimensional formulas (both expressions) to the two and three-dimensional Casimir piston with Neumann boundary conditions. The 3D Neumann results are in numerical agreement with those recently derived in arXiv:0705.0139 using an optical path technique providing an independent confirmation of our multidimensional approach. We limit our study to massless scalar fields.Comment: 29 pages; 3 figures; references added; to appear in JHE

Assaying locomotor activity to study circadian rhythms and sleep parameters in Drosophila.

Most life forms exhibit daily rhythms in cellular, physiological and behavioral phenomena that are driven by endogenous circadian (≡24 hr) pacemakers or clocks. Malfunctions in the human circadian system are associated with numerous diseases or disorders. Much progress towards our understanding of the mechanisms underlying circadian rhythms has emerged from genetic screens whereby an easily measured behavioral rhythm is used as a read-out of clock function. Studies using Drosophila have made seminal contributions to our understanding of the cellular and biochemical bases underlying circadian rhythms. The standard circadian behavioral read-out measured in Drosophila is locomotor activity. In general, the monitoring system involves specially designed devices that can measure the locomotor movement of Drosophila. These devices are housed in environmentally controlled incubators located in a darkroom and are based on using the interruption of a beam of infrared light to record the locomotor activity of individual flies contained inside small tubes. When measured over many days, Drosophila exhibit daily cycles of activity and inactivity, a behavioral rhythm that is governed by the animal's endogenous circadian system. The overall procedure has been simplified with the advent of commercially available locomotor activity monitoring devices and the development of software programs for data analysis. We use the system from Trikinetics Inc., which is the procedure described here and is currently the most popular system used worldwide. More recently, the same monitoring devices have been used to study sleep behavior in Drosophila. Because the daily wake-sleep cycles of many flies can be measured simultaneously and only 1 to 2 weeks worth of continuous locomotor activity data is usually sufficient, this system is ideal for large-scale screens to identify Drosophila manifesting altered circadian or sleep properties

The Catalytic and Non-catalytic Functions of the Brahma Chromatin-Remodeling Protein Collaborate to Fine-Tune Circadian Transcription in Drosophila.

Daily rhythms in gene expression play a critical role in the progression of circadian clocks, and are under regulation by transcription factor binding, histone modifications, RNA polymerase II (RNAPII) recruitment and elongation, and post-transcriptional mechanisms. Although previous studies have shown that clock-controlled genes exhibit rhythmic chromatin modifications, less is known about the functions performed by chromatin remodelers in animal clockwork. Here we have identified the Brahma (Brm) complex as a regulator of the Drosophila clock. In Drosophila, CLOCK (CLK) is the master transcriptional activator driving cyclical gene expression by participating in an auto-inhibitory feedback loop that involves stimulating the expression of the main negative regulators, period (per) and timeless (tim). BRM functions catalytically to increase nucleosome density at the promoters of per and tim, creating an overall restrictive chromatin landscape to limit transcriptional output during the active phase of cycling gene expression. In addition, the non-catalytic function of BRM regulates the level and binding of CLK to target promoters and maintains transient RNAPII stalling at the per promoter, likely by recruiting repressive and pausing factors. By disentangling its catalytic versus non-catalytic functions at the promoters of CLK target genes, we uncovered a multi-leveled mechanism in which BRM fine-tunes circadian transcription

The Bright Side of Dark Matter

We show that it is not possible in the absence of dark matter to construct a four-dimensional metric that explains galactic observations. In particular, by working with an effective potential it is shown that a metric which is constructed to fit flat rotation curves in spiral galaxies leads to the wrong sign for the bending of light i.e. repulsion instead of attraction. Hence, without dark matter the motion of particles on galactic scales cannot be explained in terms of geodesic motion on a four- dimensional metric. This reveals a new bright side to dark matter: it is indispensable if we wish to retain the cherished equivalence principle.Comment: 7 pages, latex, no figures. Received an honorable mention in the 1999 Gravity research Foundation Essay Competition. Submitted to Phys. Rev. Let

Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas

Considering the Casimir effect due to phononic excitations of a weakly interacting dilute {BEC}, we derive a re-normalized expression for the zero temperature Casimir energy $\mathcal{E}_c$ of a {BEC} confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, $\mathcal{E}_c$ smoothly describes the transition from the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}. For the weakly interacting case, $\mathcal{E}_c$ reduces to leading order to the Casimir energy due to zero-point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version with corrected typos and an additional appendi

The Casimir force on a piston in Randall-Sundrum models

The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall-Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force on the piston. We also discuss the Casimir force in the limit that one outer plate is moved to the remote place to show that the nature of the reduced force between the parallel plates left. In the Randall-Sundrum model involving two branes the two plates attract each other when they locate very close, but the reduced Casimir force turns to be repulsive as the plates separation is not extremely tiny, which is against the experimental phenomena. In the case of one brane model the shape of the reduced Casimir force is similar to that of the standard two-parallel-system in the four-dimensional flat spacetimes while the sign of force remains negative.Comment: 13 pages, 4 figure

Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions

Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and in addition an arbitrary number q of extra compacified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar 'refractive index' N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces we focus on the low temperature case, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q=1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to appear in Physica Script

Casimir interaction: pistons and cavity

The energy of a perfectly conducting rectangular cavity is studied by making use of pistons' interactions. The exact solution for a 3D perfectly conducting piston with an arbitrary cross section is being discussed.Comment: 10 pages, 2 figures, latex2