arXiv subjects

Kimball A. Milton

Publications and source records attributed to Kimball A. Milton.

At least 19 recordsLinked to original sources

arXiv2025

Perspectives on Quantum Friction, Self-Propulsion, and Self-Torque

This paper provides an overview of the nonequilibrium fluctuational forces and torques acting on a body either in motion or at rest relative to another body or to the thermal vacuum blackbody radiation. We consider forces and torques beyond the usual static Casimir-Polder and Casimir forces and torques. For a moving body, a retarding force emerges, called quantum or Casimir friction, which in vacuum was first predicted by Einstein and Hopf in 1910. Nonreciprocity may allow a stationary body, out of thermal equilibrium with its environment, to experience a torque. Moreover, if a stationary reciprocal body is not in thermal equilibrium with the blackbody vacuum, a self-propulsive force or torque can appear, resulting in a potentially observable linear or angular terminal velocity, even after thermalization.

quant-ph↗

arXiv2025

Spontaneous Torque on an Inhomogeneous Chiral Body out of Thermal Equilibrium

In a previous paper we showed that an inhomogeneous body in vacuum will experience a spontaneous force if it is not in thermal equilibrium with its environment. This is due to the asymmetric asymptotic radiation pattern such an object emits. We demonstrated this self-propulsive force by considering an expansion in powers of the electric susceptibility: A torque arises in first order, but only if the material constituting the body is nonreciprocal. No force arises in first order. A force does occur for bodies made of ordinary (reciprocal) materials in second order. Here we extend these considerations to the torque. As one would expect, a spontaneous torque will also appear on an inhomogeneous chiral object if it is out of thermal equilibrium with its environment. Once a chiral body starts to rotate, it will experience a small quantum frictional torque, but much more important, unless a mechanism is provided to maintain the nonequilibrium state, is thermalization: The body will rapidly reach thermal equilibrium with the vacuum, and the angular acceleration will essentially become zero. For a small, or even a large, inhomogeneous chiral body, a terminal angular velocity will result, which seems to be in the realm of observability.

quant-ph↗

arXiv2024

Quantum Vacuum Self-Propulsion and Torque

This article summarizes our recent efforts to understand spontaneous quantum vacuum forces and torques, which require that a stationary object be out of thermal equilibrium with the blackbody background radiation. We proceed by a systematic expansion in powers of the electric susceptibility. In first order, no spontaneous force can arise, although a torque can appear, but only if the body is composed of nonreciprocal material. In second order, both forces and torques can appear, with ordinary materials, but only if the body is inhomogeneous. In higher orders, this last requirement may be removed. We give a number of examples of bodies displaying second-order spontaneous forces and torques, some of which might be amenable to observation.

quant-ph↗

arXiv2024

Quantum Self-Propulsion of an Inhomogeneous Object out of Thermal Equilibrium

In an earlier paper, we explored how quantum vacuum torque can arise: a body or nanoparticle that is out of thermal equilibrium with its environment experiences a spontaneous torque. But this requires that the body be composed of nonreciprocal material, which seems to necessitate the presence of an external influence, such as a magnetic field. Then the electric polarizability of the particle has a real part that is nonsymmetric. This effect occurs to first order in the polarizability. To that order, no self-propulsive force can arise. Here, we consider second-order effects, and show that spontaneous forces can arise in vacuum, without requiring exotic electromagnetic properties. Thermal nonequilibrium is still necessary, but the electric susceptibility of the body need only be inhomogeneous. We investigate four examples of such a body: a needle composed of distinct halves; a sphere and a ball, each hemisphere being made of a different substance; and a thin slab, each face of which is different. The results found are consistent with previous numerical investigations. Here, we take into account the skin depth of metal surfaces. We also consider the frictional forces that would cause the body to acquire a terminal velocity, which might be observable. More likely to be important is relaxation to thermal equilibrium, which can still lead to a terminal velocity that might be experimentally verifiable. A general treatment of such forces on a moving body, expressed in momentum space, is provided, which incorporates both propulsive and frictional forces. The source of the propulsive force is the nonsymmetric pattern of radiation from different parts of the body, the higher reflectivity of the metal portion playing a crucial role.

quant-ph↗

arXiv2023

Thermal Casimir interactions in multi-particle systems: scattering channel approach

Multi-particle thermal Casimir interactions are investigated, mostly in terms of the Casimir entropy, from the point of view based on multiple-scattering processes. The geometry of the scattering path is depicted in detail, and the contributions from different types of channels, namely the transverse, longitudinal and mixing channels, are demonstrated. The geometry of the path can strongly influence the weight of each channel in the path. Negativity and nonmonotonicity are commonly seen in the multi-particle Casimir entropy, the sources of which are diverse, including the geometry of the path, the types of polarization mixing, the polarizability of each particle, etc. Thermal contributions from multi-particle scatterings can be significant in the system, while the zero-temperature multi-particle scattering effects are insignificant. Limiting behaviors from a multi-particle configuration to a continuum are briefly explored.

hep-th↗

arXiv2023

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.

quant-ph↗

arXiv2023

Quantum friction in the presence of a perfectly conducting plate

A neutral but polarizable particle at rest near a perfectly conducting plate feels a force normal to the surface of the plate, which tends to pull the particle towards the plate. This is the well-known Casimir-Polder force, which has long been theoretically proposed and experimentally observed. In this paper, we explore the transverse frictional force on an atom moving uniformly parallel to a perfectly conducting plate. Although many theoretical predictions can be found for the quantum friction on a particle moving above an imperfect surface, the extreme situation with a perfectly conducting plate seems to have been largely ignored by the theoretical community. We investigate this ideal case as a natural extension of our previous works on quantum vacuum friction (blackbody friction), and conclude that there does exist a quantum frictional force on an atom moving above a perfectly conducting plate. Very interestingly, the distance dependence, the temperature dependence and even the sign of the frictional force can depend on the polarization state of the atom. For an isotropic atom with a static polarizability, the resultant frictional force is found to be negative definite and therefore remains a true drag. Just above the surface of the plate, the magnitude of the frictional force is twice that of the quantum vacuum friction in the absence of the plate.

quant-ph↗

arXiv2022

Casimir Self-Entropy of Nanoparticles with Classical Polarizabilities: Electromagnetic Field Fluctuations

Not only are Casimir interaction entropies not guaranteed to be positive, but also, more strikingly, Casimir self-entropies of bodies can be negative. Here, we attempt to interpret the physical origin and meaning of these negative self-entropies by investigating the Casimir self-entropy of a neutral spherical nanoparticle. After extracting the polarizabilities of such a particle by examining the asymptotic behavior of the scattering Green's function, we compute the corresponding free energy and entropy. Two models for the nanoparticle, namely a spherical plasma $δ$-function shell and a homogeneous dielectric/diamagnetic ball, are considered at low temperature, because that is all that can be revealed from a nanoparticle perspective. The second model includes a contribution to the entropy from the bulk free energy, referring to the situation where the medium inside or outside the ball fills all space, which must be subtracted on physical grounds in order to maintain consistency with van der Waals interactions, corresponding to the self-entropy of each bulk. (The van der Waals calculation is described in Appendix A.) The entropies so calculated agree with known results in the low-temperature limit, appropriate for a small particle, and are negative. But we suggest that the negative self-entropy is simply an interaction entropy, the difference between the total entropy and the blackbody entropy of the two bulks, outside or inside of the nanosphere. The vacuum entropy is always positive and overwhelms the interaction entropy. Thus the interaction entropy can be negative, without contradicting the principles of statistical thermodynamics. Because the entropy of blackbody radiation by itself plays an important role, it is also discussed, including dispersive effects, in detail.

hep-th↗

arXiv2022

Energetics of quantum vacuum friction. II: Dipole fluctuations and field fluctuations

As a second paper in series with arXiv:2108.01539, we discuss here quantum vacuum friction on an intrinsically dissipative particle. The friction arises not only from the field fluctuations but also from the dipole fluctuations intrinsic to the particle. As a result, the dissipative particle can be out of the nonequilibrium steady state (NESS), where it loses or gains internal energy. Only if the temperature of the particle equals a special NESS temperature will the particle be in NESS. We first derive the NESS conditions which give the NESS temperature of the particle as a function of the radiation temperature and the velocity of the particle. Imposing the NESS conditions, we then obtain an expression for the quantum vacuum friction in NESS. The NESS quantum vacuum friction is shown to be always negative definite, therefore a true drag. The NESS temperature and quantum vacuum friction are calculated numerically for various models. Out of NESS, even though the quantum vacuum frictional force no longer has a definite sign in the rest frame of the radiation, we find the external force needed to keep the particle moving must be in the same direction as the motion of the particle. This then excludes the possibility of making a perpetual motion machine, which could convert the vacuum energy into useful mechanical work. In addition, we find that the deviation of the temperature of the particle from its NESS temperature causes the particle to lose or gain internal energy in such a way that the particle would return to NESS after deviating from it. This enables experimental measurements of the NESS temperature of the particle to serve as a feasible signature for these quantum vacuum frictional effects.

hep-th↗

arXiv2021

Premelting and formation of ice due to Casimir-Lifshitz interactions: Impact of improved parameterization for materials

Recently, the premelting and formation of ice due to the Casimir-Lifshitz interaction, proposed in early 1990s by Elbaum and Schick [Phys. Rev. Lett. 66, 1713-1716 (1991)], have been generalized to diverse practical scenarios, yielding novel physical intuitions and possibilities of application for those phenomena. The properties of materials, in particular, the electrical permittivity and permeability, exert significant influences on the Casimir-Cifshitz energies and forces, and hence on the corresponding premelting and formation of ice. To address these influences in detail and explore the resulting physics, here we revisit and extend the analyses of previous work, with both the dielectric data utilized there and the latest dielectric functions for ice and cold water. While our previous results are rederived, an error there has also been spotted. For the four-layer cases considered by some of us, the existence of stable configurations depending on the initial conditions has been confirmed, and different types of stability corresponding to minima of the Casimir-Lifshitz free energy are demonstrated. As the new dielectric functions for ice and cold water deviate considerably from those used by Elbaum and Schick, their vital impacts on three- and four-layer configurations are therefore being reconsidered.

cond-mat.mtrl-sci↗

arXiv2021

The energetics of quantum vacuum friction: Field fluctuations

Quantum fluctuations can induce a friction on a neutral but polarizable particle and cause it to radiate energy even if the particle is moving in free space filled with blackbody radiation, and is not in contact with or close to any surface or other object. We explore the energetics of such a particle moving uniformly in vacuum, continuing our previous investigations of quantum friction. The intrinsic polarizability of the particle is considered to be purely real before it is dressed by radiation. The particle is then guaranteed to be in the nonequilibrium steady state (NESS), where it absorbs and emits energy at the same rate. We first calculate the quantum frictional power and force on the particle in the rest frame of the blackbody radiation from first principles, namely the Maxwell-Heaviside equations and the Lorentz force law. Then we provide a simpler method of obtaining the same quantities in the rest frame of the particle by using the principle of virtual work. The equivalence of the two approaches is illustrated. The formulas we derive for quantum vacuum frictional power and force are fully relativistic and applicable to finite temperature. In NESS, the quantum vacuum frictional force on the particle is shown to be a true drag, independent of the model for polarizability and the polarization state of the particle. Finally, we give an estimate of the quantum vacuum friction on a gold atom and comment on the feasibility of detecting such quantum vacuum frictional effects.

hep-th↗

arXiv2021

Negativity of the Casimir self-entropy in spherical geometries

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self-entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

quant-ph↗

arXiv2020

Self-force on moving electric and magnetic dipoles: dipole radiation, Vavilov-Čerenkov radiation, friction with a conducting surface, and the Einstein-Hopf effect

The classical electromagnetic self-force on an arbitrary time-dependent electric or magnetic dipole moving with constant velocity in vacuum, and in a medium, is considered. Of course, in vacuum there is no net force on such a particle. Rather, because of loss of mass by the particle due to radiation, the self-force precisely cancels this inertial effect, and thus the spectral distribution of the energy radiated by dipole radiation is deduced without any consideration of radiation fields or of radiation reaction, in both the nonrelativistic and relativistic regimes. If the particle is moving in a homogeneous medium faster than the speed of light in the medium, Vavilov-Čerenkov radiation results. This is derived for the different polarization states, in agreement with the earlier results of Frank. The friction experienced by a point (time-independent) dipole moving parallel to an imperfectly conducting surface is examined. Finally, the quantum/thermal Einstein-Hopf effect is rederived. We obtain a closed form for the spectral distribution of the force, and demonstrate that, even if the atom and the blackbody background have independent temperatures, the force is indeed a drag in the case that the imaginary part of the polarizability is proportional to a power of the frequency.

hep-th↗

arXiv2020

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-Čerenkov radiation can be treated in the same formalism.

physics.class-ph↗

arXiv2020

Role of zero point energy in promoting ice formation in a spherical drop of water

We demonstrate that the Lifshitz interaction energy (excluding the self-energies of the inner and outer spherical regions) for three concentric spherical dielectric media can be evaluated easily using the immense computation power in recent processors relative to those of a few decades ago. As a prototype, we compute the Lifshitz interaction energy for a spherical shell of water immersed in water vapor of infinite extent while enclosing a spherical ball of ice inside the shell, such that two concentric spherical interfaces are formed: one between solid ice and liquid water and the other between liquid water and gaseous vapor. We evaluate the Lifshitz interaction energy for the above configuration at the triple point of water when the solid, liquid, and gaseous states of water coexist, and, thus, extend the analysis of Elbaum and Schick in Phys. Rev. Lett. 66 (1991) 1713 to spherical configurations. We find that, when the Lifshitz energy contributes dominantly to the total energy of this system, which is often the case when electrostatic interactions are absent, a drop of water surrounded by vapor of infinite extent is not stable at the triple point. This instability, that is a manifestation of the quantum fluctuations in the medium, will promote formation of ice in water, which will then grow in size indefinitely. This is a consequence of the finding here that the Lifshitz energy is minimized for large (micrometer size) radius of the ice ball and small (nanometer size) thickness of the water shell surrounding the ice. These results might be relevant to the formation of hail in thunderclouds. These results are tentative in that the self-energies are omitted; surface tension and nucleation energy are not considered.

cond-mat.mes-hall↗

arXiv2019

Self-Stress on a Dielectric Ball and Casimir-Polder Forces

It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir-Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt [Ann.\ Phys.\ {\bf 395}, 326 (2018)], who find that the energy or self-stress of a homogeneous dielectric ball with permittivity $\varepsilon$ begins with a term of order $\varepsilon-1$. Here we demonstrate that this cannot be correct. The only possible origin of a term linear in $\varepsilon-1$ lies in the bulk energy, that energy which would be present if either the material of the body, or of its surroundings, filled all space. Since Avni and Leonhardt correctly subtract the bulk terms, the linear term they find likely arises from their omission of an integral over the transverse stress tensor.

hep-th↗

arXiv2019

Remarks on the Casimir Self-Entropy of a Spherical Electromagnetic $δ$-Function Shell

Recently the Casimir self-entropy of an electromagnetic $δ$-function shell was considered by two different groups, with apparently discordant conclusions, although both had concluded that a region of negative entropy existed for sufficiently weak coupling. We had found that the entropy contained an infrared divergence, which we argued should be discarded on physical grounds. On the contrary, Bordag and Kirsten recently found a completely finite self-entropy, although they, in fact, have to remove an infrared divergence. Apart from this, the high- and low-temperature results for finite coupling agree precisely for the transverse electric mode, but there are significant discrepancies in the transverse magnetic mode. We resolve those discrepancies here. In particular, it is shown that coupling-independent terms do not occur in a consistent regulated calculation, they likely being an artefact of the omission of pole terms. The results of our previous analysis, especially, the existence of a negative entropy region for sufficiently weak coupling, are therefore confirmed. Finally, we offer some analogous remarks concerning the Casimir entropy of a thin electromagnetic sheet, where the total entropy is always positive. In that case, the origin of the analogous discrepancy can be explicitly isolated.

hep-th↗

arXiv2019

Casimir forces in inhomogeneous media: renormalization and the principle of virtual work

We calculate the Casimir forces in two configurations, namely, three parallel dielectric slabs and a dielectric slab between two perfectly conducting plates, where the dielectric materials are dispersive and inhomogeneous in the direction perpendicular to the interfaces. A renormalization scheme is proposed consisting of subtracting the effect of one interface with a single inhomogeneous medium. Some examples are worked out to illustrate this scheme. Our method always gives finite results and is consistent with the principle of virtual work; it extends the Dzyaloshinskii-Lifshitz-Pitaeveskii force to inhomogeneous media.

hep-th↗