On the validity of constraints on light elementary particles and extra-dimensional physics from the Casimir effect

We discuss the constraints on the parameters of a Yukawa interaction obtained from the indirect measurements of the Casimir pressure between parallel plates using the sphere–plate configuration. Recently, it was claimed in the literature that the application of the proximity force approximation (PFA) to the calculation of a Yukawa interaction in the sphere–plate configuration could lead to a large error of order 100% in the constraints obtained. Here we re-calculate the constraints both exactly and using the PFA, and arrive at identical results. We elucidate the reasons why an incorrect conclusion was obtained suggesting that the PFA is inapplicable to calculate the Yukawa force.     

Demonstration of the lateral casimir force

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to 0.3 microm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.     

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Heisenberg representation of second-quantized fields in stationary external fields and nonlinear dielectric media

The Heisenberg formalism for the creation and annihilation operators of quantized fields in stationary external fields is developed. Fields with spin 0, 1/2, 1 are considered in external electromagnetic and scalar fields and in a field of stationary dielectric properties of a nonlinear medium. An elliptic operator that depends on the time as a parameter and whose eigenfunctions can be used to expand the field variables in the Heisenberg representation is constructed. The connection between the creation and annihilation Heisenberg operators and the operators found by diagonalizing the Hamiltonian by Bogolyubov transformations is established. Heisenberg equations of motion are obtained for external fields of arbitrary form. The phenomenological Hamiltonian that is widely used to describe parametric generation of light is derived in the framework of the quantum field theory, and the limits of applicability of the Hamiltonian are established.Technological Institute, St. Petersburg. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 3, pp. 431–451, December, 1993.