The Reality of Casimir Friction

For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with phenomena, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.Comment: 12 pages, 2 figure

Electrodynamic friction of a charged particle passing a conducting plate

The classical electromagnetic friction of a charged particle moving with prescribed constant velocity parallel to a planar imperfectly conducting surface is reinvestigated. As a concrete example, the Drude model is used to describe the conductor. The transverse electric and transverse magnetic contributions have very different character both in the low velocity (nonrelativistic) and high velocity (ultrarelativistic) regimes. Both numerical and analytical results are given. Most remarkably, the transverse magnetic contribution to the friction has a maximum for $|\mathbf{v}|<c$, and persists in the limit of vanishing resistivity for sufficiently high velocities. We also show how Vavilov-\v{C}erenkov radiation can be treated in the same formalism.Comment: 13 pages, 7 figures. This is the extensively revised version accepted by Physical Review Researc

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini [9,10,51] have considered some configurations involving delta-type potentials concentrated at points of $\mathbb{R}^3$; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on $\mathbb{R}^3\setminus \{\mathbf{0}\}$, with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of $\mathbb{R}^3\setminus \{\mathbf{0}\}$; to this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours (see [29-31] and references therein).Comment: 20 pages, 6 figures; the final version accepted for publication. In the initial part of the paper, possible text overlaps with our previous works arXiv:1104.4330, arXiv:1505.00711, arXiv:1505.01044, arXiv:1505.01651, arXiv:1505.03276. These overlaps aim to make the present paper self-contained, and do not involve the main result

Vacuum torque, propulsive forces, and anomalous tangential forces: Effects of nonreciprocal media out of thermal equilibrium

From the generalized fluctuation-dissipation theorem, it is known that a body at rest made of nonreciprocal material may experience a torque, even in vacuum, if it is not in thermal equilibrium with its environment. However, it does not experience self-propulsion in such circumstances, except in higher order. Nevertheless, such a body may experience both a normal torque and a lateral force when adjacent to an ordinary surface with transverse translational symmetry. We explore how these phenomena arise, discuss what terminal velocities might be achieved, and point out some of the limitations of applying our results to observations, including the Lorenz-Lorentz correction, and the cooling due to radiation. In spite of these limitations, the effects discussed would seem to be observable.Comment: 20 pages, 8 figure

Some aspects of nonlinearity and self-organization in biosystems on examples of localized excitations in the DNA molecule and generalized Fisher-KPP model

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed