We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The is obtained as interaction multipoles, generated by quantum current fluctuations. objects' shape and composition enter only through their scattering matrices. result when all multipoles are included, converges rapidly. A low frequency expansion yields a series in ratio of size to separation. As example, we obtain this two dielectric spheres full at...

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, any number objects, shapes, susceptibility functions, and separations. The technique is applicable objects immersed in media other than vacuum, nonzero temperatures, spatial arrangements which one object enclosed another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, convert between bases used calculate object, but...

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects arbitrary shape and separation. Here, we present details the for scalar field illustrate our approach in its most simple form; generalization electromagnetic fields is outlined Ref. [T. Emig, N. Graham, R. L. Jaffe, M. Kardar, Phys. Rev. Lett. 99, 170403 (2007).]. The interaction attributed quantum fluctuations source distributions on their surfaces, which decompose terms...

We investigate the rich nonlinear dynamics during end of hilltop inflation by numerically solving coupled Klein-Gordon-Friedmann equations in an expanding universe. In particular, we search for coherent, nonperturbative configurations that may emerge due to combination nontrivial couplings between fields and resonant effects from cosmological expansion. couple a massless field inflaton its effect on existence stability coherent effective equation state at reheating. For parameters consistent...

The averaged null energy condition (ANEC) requires that the integral over a complete geodesic of stress-energy tensor projected onto tangent vector is never negative. This sufficient to prove many important theorems in general relativity, but it violated by quantum fields curved spacetime. However there weaker condition, which free known violations, requiring only no self-consistent spacetime semiclassical gravity ANEC on complete, achronal geodesic. We indicate why such might be expected...

A numerical simulation of the full bosonic sector $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ electroweak standard model in $3+1$ dimensions demonstrates existence an oscillon---an extremely long-lived, localized, oscillatory solution to equations motion---when Higgs mass is equal twice ${W}^{\ifmmode\pm\else\textpm\fi{}}$ boson mass. The oscillon contains total energy 7 TeV localized a region radius 0.05 fm.

We investigate the nonlinear dynamics of hybrid inflation models, which are characterized by two real scalar fields interacting quadratically. start solving numerically coupled Klein-Gordon equations in static Minkowski spacetime, searching for possible coherent structures. find long-lived, localized configurations, we identify as a new kind oscillon. demonstrate that these two-field oscillons allow ``excited'' states with much longer lifetimes than those found previous studies single-field...

Arguments based on symmetry and thermodynamics may suggest the existence of a ratchetlike lateral Casimir force between two plates at different temperatures with broken inversion symmetry. We find that this is not sufficient, least one plate must be made nonreciprocal material. This setup operates as heat engine by transforming radiation into mechanical force. Although ratio to transfer in near field regime diverges inversely separation, $d$, an Onsager symmetry, which we extend plates,...

We consider a ($1+1$) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. study this in an expanding background and show oscillons now lose energy, but at rate is exponentially small when the expansion slow. also numerically universe starts with (almost) thermal initial conditions will cool final state where significant fraction energy universe---on order 50%---is stored oscillons. If phenomenon...

Casimir forces between conductors at the sub-micron scale cannot be ignored in design and operation of micro-electromechanical (MEM) devices. However, these depend non-trivially on geometry, existing formulae approximations deal with realistic micro-machinery components sharp edges tips. Here, we employ a novel approach to electromagnetic scattering, appropriate perfect tips, specifically wedges cones. The interaction objects metal plate (and among themselves) is then computed systematically...

Detrital petrochronology is a powerful method of characterizing sediment and potentially sources. The recently developed Tucker-1 decomposition holds promise using detrital to identify both sediment-source characteristics the proportions in which sources are present sink samples even when unknown or unavailable for sampling. However, correlation between endmember lithological sedimentary processes has not been established. Herein we case study multivariate geochemical data set from zircons...

We present a framework for the study of one–loop quantum corrections to extended field configurations in renormalizable theories. work continuum, transforming standard Casimir sum over modes into bound states and an integral scattering weighted by density states. express terms phase shifts, allowing us extract divergences identifying Born approximations shifts with low order Feynman diagrams. Once isolated diagrams, are canceled against counterterms. Thus regulated, is highly convergent...

We study classical dynamics in the spherical ansatz for $SU(2)$ gauge and Higgs fields of electroweak standard model absence fermions photon. With boson mass equal to twice mass, we numerically demonstrate existence oscillons, extremely long-lived localized configurations that undergo regular oscillations time. have only seen oscillons this reduced theory when masses are a two-to-one ratio. If similar phenomenon were persist full theory, it would suggest preferred value mass.

The Casimir interaction between two objects, or an object and a plane, depends on their relative orientations. We make these angular dependences explicit by considering prolate oblate spheroids. variation with orientation is calculated exactly at asymptotically large distances for the electromagnetic field arbitrary separations scalar field. For spheroid in front of mirror, leading term independent, we find optimal from computations higher order.

We review recent progress in the computation of leading quantum corrections to energies classical solitons with topological structure, including multi-soliton models one space dimension and string configurations three dimensions. Taking advantage analytic continuation techniques efficiently organize calculations, we show how affect stability Shifman-Voloshin model, stabilize charged electroweak strings coupled a heavy fermion doublet, bind Nielsen-Olesen vortices at transition between type I...

We consider a classical toy model of massive scalar field in 1+1 dimensions with constant exponential expansion rate space. The nonlinear theory under consideration supports approximate oscillon solutions, but they eventually decay due to their coupling the expanding background. Although all parameters and energies are order one units mass $m$, lifetime is exponentially large these natural units. For typical values parameters, we see lifetimes scaling approximately as $τ\propto \exp(k...

Through a detailed numerical investigation in three spatial dimensions, we demonstrate that long-lived time-dependent field configurations emerge dynamically during symmetry breaking an expanding de Sitter spacetime. We investigate two situations: single scalar with double-well potential and SU(2) non-Abelian Higgs model. For the scalar, show large-amplitude oscillon spontaneously persist to contribute about 1.2% of energy density Universe. also for range parameters, lifetimes are enhanced...

We present a general procedure for calculating one-loop ``Casimir'' energy densities scalar field coupled to fixed potential in renormalized quantum theory. implement direct subtraction of counterterms computed precisely dimensional regularization with definite renormalization scheme. Our allows us test theory conditions the presence background potentials spherically symmetric some dimensions and independent others. explicitly calculate density several examples. For square barrier, we find...

Numerical simulations of the bosonic sector $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ electroweak standard model in $3+1$ dimensions have demonstrated existence an oscillon---an extremely long-lived, localized, oscillatory solution to equations motion---when Higgs mass is equal twice ${W}^{\ifmmode\pm\else\textpm\fi{}}$ boson mass. It contains total energy roughly 30 TeV localized a region radius 0.05 fm. A detailed description these numerical results presented.