Casimir Forces Out of Thermal Equilibrium Near A Superconducting Transition

We present a comprehensive analysis of the out-of-equilibrium Casimir pressure between two high-T c superconducting plates, each kept at a different temperature. Two interaction regimes can be distinguished. While the zero-point energy dominates in the near field, thermal effects become important at large interplate separations causing a drop in the force’s magnitude compared with the usual thermal-equilibrium case. Our detailed calculations highlight the competing role played by propagating and evanescent modes. Moreover, as one of the plates undergoes the superconducting transition, we predict a sudden discontinuity in the force for any plate distance, which has not been previously observed in other systems. The sensitivity of the dielectric function of the high-T c superconductors makes them ideal systems for a possible direct measurement of the out-of-equilibrium Casimir pressure.

A Mathematical Analysis of Casimir Interactions I: The Scalar Field

Starting from the construction of the free quantum scalar field of mass $$m\ge 0$$ m ≥ 0 , we give mathematically precise and rigorous versions of three different approaches to computing the Casimir forces between compact obstacles. We then prove that they are equivalent.

Next Generation Design and Prospects for Cannex

The Casimir And Non-Newtonian force EXperiment (Cannex) implements the unique geometry of macroscopic plane parallel plates that guarantees an optimum sensitivity with respect to interfacial forces and their gradients. Based on experience from the recently completed proof-of-principle phase, we have started a re-design of the setup aiming to reduce systematic effects and maximize the achievable sensitivity. Several propositions have been made to measure Casimir forces in and out of thermal equilibrium, hypothetical axion and axion-like dark matter interactions, and forces originating from chameleon or symmetron dark energy interactions. In the present article, we give details on the design for the next implementation stage of Cannex and discuss the experimental opportunities, as well as limitations expected for this new setup.

Unifying Theory for Casimir Forces: Bulk and Surface Formulations

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class

We analyze the thermodynamic Casimir effect in strongly anisotropic systems from the vectorial N\to\inftyN→∞ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality dd in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion relation and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality d\in (\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dotsd∈(52,4)∪(6,8)∪(10,12)∪… and attractive for d\in (4,6)\cup (8,10)\cup \dotsd∈(4,6)∪(8,10)∪…. We argue, that for d\in\{4,6,8\dots\}d∈{4,6,8…} the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by 1/N>01/N>0 and possible realizations in the contexts of optical lattice systems and quantum phase transitions.

Revealing pseudorotation and ring-opening reactions in colloidal organic molecules

Colloids have a rich history of being used as ‘big atoms’ mimicking real atoms to study crystallization, gelation and the glass transition of condensed matter. Emulating the dynamics of molecules, however, has remained elusive. Recent advances in colloid chemistry allow patchy particles to be synthesized with accurate control over shape, functionality and coordination number. Here, we show that colloidal alkanes, specifically colloidal cyclopentane, assembled from tetrameric patchy particles by critical Casimir forces undergo the same chemical transformations as their atomic counterparts, allowing their dynamics to be studied in real time. We directly observe transitions between chair and twist conformations in colloidal cyclopentane, and we elucidate the interplay of bond bending strain and entropy in the molecular transition states and ring-opening reactions. These results open the door to investigate complex molecular kinetics and molecular reactions in the high-temperature classical limit, in which the colloidal analogue becomes a good model.

Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals

In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait analysis probed the occurrence of chaotic behavior leading to increased risk for stiction. It was found that the presence of the TI enhanced stable operation against chaotic behavior over a significantly wider range of operation conditions in comparison to typical metallic conductors. Therefore, the use of TIs can allow sufficient surface conductance to apply electrostatic compensation of residual contact potentials and, at the same time, to yield sufficiently weak Casimir forces favoring long-term stable actuation dynamics against chaotic behavior.