1,097 research outputs found
Casimir Forces: An Exact Approach for Periodically Deformed Objects
A novel approach for calculating Casimir forces between periodically deformed
objects is developed. This approach allows, for the first time, a rigorous
non-perturbative treatment of the Casimir effect for disconnected objects
beyond Casimir's original two-plate configuration. The approach takes into
account the collective nature of fluctuation induced forces, going beyond the
commonly used pairwise summation of two-body van der Waals forces. As an
application of the method, we exactly calculate the Casimir force due to scalar
field fluctuations between a flat and a rectangular corrugated plate. In the
latter case, the force is found to be always attractive.Comment: 4 pages, 3 figure
Ingredients of a Casimir analog computer
We present the basic ingredients of a technique to compute quantum Casimir
forces at micrometer scales using antenna measurements at tabletop, e.g.
centimeter, scales, forming a type of analog computer for the Casimir force.
This technique relies on a correspondence that we derive between the contour
integration of the Casimir force in the complex frequency plane and the
electromagnetic response of a physical dissipative medium in a finite, real
frequency bandwidth
Disorder induced rounding of the phase transition in the large q-state Potts model
The phase transition in the q-state Potts model with homogeneous
ferromagnetic couplings is strongly first order for large q, while is rounded
in the presence of quenched disorder. Here we study this phenomenon on
different two-dimensional lattices by using the fact that the partition
function of the model is dominated by a single diagram of the high-temperature
expansion, which is calculated by an efficient combinatorial optimization
algorithm. For a given finite sample with discrete randomness the free energy
is a pice-wise linear function of the temperature, which is rounded after
averaging, however the discontinuity of the internal energy at the transition
point (i.e. the latent heat) stays finite even in the thermodynamic limit. For
a continuous disorder, instead, the latent heat vanishes. At the phase
transition point the dominant diagram percolates and the total magnetic moment
is related to the size of the percolating cluster. Its fractal dimension is
found d_f=(5+\sqrt{5})/4 and it is independent of the type of the lattice and
the form of disorder. We argue that the critical behavior is exclusively
determined by disorder and the corresponding fixed point is the isotropic
version of the so called infinite randomness fixed point, which is realized in
random quantum spin chains. From this mapping we conjecture the values of the
critical exponents as \beta=2-d_f, \beta_s=1/2 and \nu=1.Comment: 12 pages, 12 figures, version as publishe
Fluctuation induced quantum interactions between compact objects and a plane mirror
The interaction of compact objects with an infinitely extended mirror plane
due to quantum fluctuations of a scalar or electromagnetic field that scatters
off the objects is studied. The mirror plane is assumed to obey either
Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using
the method of images, we generalize a recently developed approach for compact
objects in unbounded space [1,2] to show that the Casimir interaction between
the objects and the mirror plane can be accurately obtained over a wide range
of separations in terms of charge and current fluctuations of the objects and
their images. Our general result for the interaction depends only on the
scattering matrices of the compact objects. It applies to scalar fields with
arbitrary boundary conditions and to the electromagnetic field coupled to
dielectric objects. For the experimentally important electromagnetic Casimir
interaction between a perfectly conducting sphere and a plane mirror we present
the first results that apply at all separations. We obtain both an asymptotic
large distance expansion and the two lowest order correction terms to the
proximity force approximation. The asymptotic Casimir-Polder potential for an
atom and a mirror is generalized to describe the interaction between a
dielectric sphere and a mirror, involving higher order multipole
polarizabilities that are important at sub-asymptotic distances.Comment: 19 pages, 7 figure
Non-equilibrium Casimir forces: Spheres and sphere-plate
We discuss non-equilibrium extensions of the Casimir force (due to
electromagnetic fluctuations), where the objects as well as the environment are
held at different temperatures. While the formalism we develop is quite
general, we focus on a sphere in front of a plate, as well as two spheres, when
the radius is small compared to separation and thermal wavelengths. In this
limit the forces can be expressed analytically in terms of the lowest order
multipoles, and corroborated with results obtained by diluting parallel plates
of vanishing thickness. Non-equilibrium forces are generally stronger than
their equilibrium counterpart, and may oscillate with separation (at a scale
set by material resonances). For both geometries we obtain stable points of
zero net force, while two spheres may have equal forces in magnitude and
direction resulting in a self-propelling state.Comment: 6 pages, 6 figure
Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
We develop an exact method for computing the Casimir energy between arbitrary
compact objects, both with boundary conditions for a scalar field and
dielectrics or perfect conductors for the electromagnetic field. The energy is
obtained as an interaction between multipoles, generated by quantum source or
current fluctuations. The objects' shape and composition enter only through
their scattering matrices. The result is exact when all multipoles are
included, and converges rapidly. A low frequency expansion yields the energy as
a series in the ratio of the objects' size to their separation. As examples, we
obtain this series for two spheres with Robin boundary conditions for a scalar
field and dielectric spheres for the electromagnetic field. The full
interaction at all separations is obtained for spheres with Robin boundary
conditions and for perfectly conducting spheres.Comment: 24 pages, 3 figures, contribution to QFEXT07 proceeding
Delocalization in Coupled Luttinger Liquids with Impurities
We study effects of quenched disorder on coupled two-dimensional arrays of
Luttinger liquids (LL) as a model for stripes in high-T_c compounds. In the
framework of a renormalization-group analysis, we find that weak inter-LL
charge-density-wave couplings are always irrelevant as opposed to the pure
system. By varying either disorder strength, intra- or inter-LL interactions,
the system can undergo a delocalization transition between an insulator and a
novel strongly anisotropic metallic state with LL-like transport. This state is
characterized by short-ranged charge-density-wave order, the superconducting
order is quasi long-ranged along the stripes and short-ranged in the
transversal direction.Comment: 6 pages, 5 figures, substantially extended and revised versio
On the accuracy of the PFA: analogies between Casimir and electrostatic forces
We present an overview of the validity of the Proximity Force Approximation
(PFA) in the calculation of Casimir forces between perfect conductors for
different geometries, with particular emphasis for the configuration of a
cylinder in front of a plane. In all cases we compare the exact numerical
results with those of PFA, and with asymptotic expansions that include the next
to leading order corrections. We also discuss the similarities and differences
between the results for Casimir and electrostatic forces.Comment: 17 pages, 5 figures, Proceedings of the meeting "60 years of Casimir
effect", Brasilia, 200
Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects
We present a detailed derivation of heat radiation, heat transfer and
(Casimir) interactions for N arbitrary objects in the framework of
fluctuational electrodynamics in thermal non-equilibrium. The results can be
expressed as basis-independent trace formulae in terms of the scattering
operators of the individual objects. We prove that heat radiation of a single
object is positive, and that heat transfer (for two arbitrary passive objects)
is from the hotter to a colder body. The heat transferred is also symmetric,
exactly reversed if the two temperatures are exchanged. Introducing partial
wave-expansions, we transform the results for radiation, transfer and forces
into traces of matrices that can be evaluated in any basis, analogous to the
equilibrium Casimir force. The method is illustrated by (re)deriving the heat
radiation of a plate, a sphere and a cylinder. We analyze the radiation of a
sphere for different materials, emphasizing that a simplification often
employed for metallic nano-spheres is typically invalid. We derive asymptotic
formulae for heat transfer and non-equilibrium interactions for the cases of a
sphere in front a plate and for two spheres, extending previous results. As an
example, we show that a hot nano-sphere can levitate above a plate with the
repulsive non-equilibrium force overcoming gravity -- an effect that is not due
to radiation pressure.Comment: 29 pages, 6 figures (v2: Sentence added in Sec. 1
Geometry and material effects in Casimir physics - Scattering theory
We give a comprehensive presentation of methods for calculating the Casimir
force to arbitrary accuracy, for any number of objects, arbitrary shapes,
susceptibility functions, and separations. The technique is applicable to
objects immersed in media other than vacuum, to nonzero temperatures, and to
spatial arrangements in which one object is enclosed in another. Our method
combines each object's classical electromagnetic scattering amplitude with
universal translation matrices, which convert between the bases used to
calculate scattering for each object, but are otherwise independent of the
details of the individual objects. This approach, which combines methods of
statistical physics and scattering theory, is well suited to analyze many
diverse phenomena. We illustrate its power and versatility by a number of
examples, which show how the interplay of geometry and material properties
helps to understand and control Casimir forces. We also examine whether
electrodynamic Casimir forces can lead to stable levitation. Neglecting
permeabilities, we prove that any equilibrium position of objects subject to
such forces is unstable if the permittivities of all objects are higher or
lower than that of the enveloping medium; the former being the generic case for
ordinary materials in vacuum.Comment: 44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics
volume in Casimir physic
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