453 research outputs found
The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of Statistical Mechanics
In 1916 Einstein introduced the first rules for a quantum theory of
electromagnetic radiation, and he applied them to a model of matter in thermal
equilibrium with radiation to derive Planck's black-body formula. Einstein's
treatment is extended here to time-dependent stochastic variables, which leads
to a master equation for the probability distribution that describes the
irreversible approach of Einstein's model towards thermal equilibrium, and
elucidates aspects of the foundation of statistical mechanics. An analytic
solution of this equation is obtained in the Fokker-Planck approximation which
is in excellent agreement with numerical results. At equilibrium, it is shown
that the probability distribution is proportional to the total number of
microstates for a given configuration, in accordance with Boltzmann's
fundamental postulate of equal a priori probabilities for these states. While
the counting of these configurations depends on particle statistics- Boltzmann,
Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined
here by the dynamics which are embodied in the form of Einstein's quantum
transition probabilities for the emission and absorption of radiation. In a
special limit, it is shown that the photons in Einstein's model can act as a
thermal bath for the evolution of the atoms towards the canonical equilibrium
distribution of Gibbs. In this limit, the present model is mathematically
equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which
has been discussed recently by Ambegaokar and Clerk
Energy conservation and equivalence principle in General Relativity
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4)
is formulated in a curved space-time in terms of paths in Minkowski space
(forming Path Group). A covariant integral form of the conservation law for the
energy-momentum of matter is then derived in General Relativity. It extends
Einstein's equivalence principle on the energy conservation, since it
formulates the conservation law for the energy-momentum of matter without
explicit including the gravitational field in the formulation.Comment: 9 pages, Latex, one figur
EPR effect in gravitational field: nature of non-locality
The realization of the Einstein-Podolsky-Rosen effect by the correlation of
spin projections of two particles created in the decay of a single scalar
particle is considered for particles propagating in gravitational field. The
absence of a global definition of spatial directions makes it unclear whether
the correlation may exist in this case and, if yes, what directions in distant
regions must be correlated. It is shown that in a gravitational field an
approximate correlation may exist and the correlated directions are connected
with each other by the parallel transport along the world lines of the
particles. The reason for this is that the actual origin of the quantum
non-locality is founded in local processes.Comment: 12 pages, LATE
Princess and the Pea at the nanoscale: Wrinkling and delamination of graphene on nanoparticles
Thin membranes exhibit complex responses to external forces or geometrical
constraints. A familiar example is the wrinkling, exhibited by human skin,
plant leaves, and fabrics, resulting from the relative ease of bending versus
stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest
known membrane, deposited on a silica substrate decorated with silica
nanoparticles. At small nanoparticle density monolayer graphene adheres to the
substrate, detached only in small regions around the nanoparticles. With
increasing nanoparticle density, we observe the formation of wrinkles which
connect nanoparticles. Above a critical nanoparticle density, the wrinkles form
a percolating network through the sample. As the graphene membrane is made
thicker, global delamination from the substrate is observed. The observations
can be well understood within a continuum elastic model and have important
implications for strain-engineering the electronic properties of graphene.Comment: 11 pages, 8 figures. Accepted for publication in Physical Review
Bounds on the nonminimal coupling of the Higgs Boson to gravity
We derive the first bound on the value of the Higgs boson nonminimal coupling to the Ricci scalar. We show that the recent discovery of the Higgs boson at the Large Hadron Collider at CERN implies that the nonminimal coupling is smaller than 2.6×10^15
The influence of modified gravitational fields on motions of Keplerian objects at the far-edge of the Solar System
We investigated the impact of three different modifications of Newtonian
gravity on motions of Keplerian objects within the Solar System. These objects
are located at distances of the order of the distance to the Oort cloud. With
these three modifications we took into account a heliocentric Dark-Matter halo
as was indicated by Diemand et al, Modified Newtonian Dynamics (MOND) and a
vacuum-induced force due to a locally negative cosmological constant
derived by Fahr & Siewert. In gravitationally bound systems it
turns out that all three modifications deliver the same qualitative results:
Initially circular orbits for the pure Newtonian case are forced to convert
into ellipses with perihelion migrations. The quantitative consideration,
however, of the orbital parameters showed strong differences between MOND on
the one side, and Dark-Matter and effects on the other side.Comment: 9 pages, 16 figures, MNRAS accepte
Cluster-state quantum computation
This article is a short introduction to and review of the cluster-state model
of quantum computation, in which coherent quantum information processing is
accomplished via a sequence of single-qubit measurements applied to a fixed
quantum state known as a cluster state. We also discuss a few novel properties
of the model, including a proof that the cluster state cannot occur as the
exact ground state of any naturally occurring physical system, and a proof that
measurements on any quantum state which is linearly prepared in one dimension
can be efficiently simulated on a classical computer, and thus are not
candidates for use as a substrate for quantum computation.Comment: 15 pages, resubmitted version accepted to Rev. Math. Phy
Bose-Einstein condensation of stationary-light polaritons
We propose and analyze a mechanism for Bose-Einstein condensation of
stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in
the interaction of light with laser-driven 3-level Lambda-type atoms and are
the basis of phenomena such as electromagnetically induced transparency (EIT),
ultra-slow and stored light. They have long intrinsic lifetimes and in a
stationary set-up with two counterpropagating control fields of equal intensity
have a 3D quadratic dispersion profile with variable effective mass. Since DSPs
are bosons they can undergo a Bose-Einstein condensation at a critical
temperature which can be many orders of magnitude larger than that of atoms. We
show that thermalization of polaritons can occur via elastic collisions
mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale
short compared to the decay time. Finally condensation can be observed by
turning stationary into propagating polaritons and monitoring the emitted
light.Comment: 4 pages, 3 figure
Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric
The total momentum of a thermodynamically closed system is unique, as is the
total energy. Nevertheless, there is continuing confusion concerning the
correct form of the momentum and the energy-momentum tensor for an
electromagnetic field interacting with a linear dielectric medium. Here we
investigate the energy and momentum in a closed system composed of a
propagating electromagnetic field and a negligibly reflecting dielectric. The
Gordon momentum is easily identified as the total momentum by the fact that it
is, by virtue of being invariant in time, conserved. We construct continuity
equations for the energy and the Gordon momentum and use the continuity
equations to construct an array that has the properties of a traceless,
diagonally symmetric energy-momentum tensor. Then the century-old
Abraham-Minkowski momentum controversy can be viewed as a consequence of
attempting to construct an energy-momentum tensor from continuity equations
that contain densities that correspond to nonconserved quantities.Comment: added publication informatio
Fluctuations of an Atomic Ledge Bordering a Crystalline Facet
When a high symmetry facet joins the rounded part of a crystal, the step line
density vanishes as sqrt(r) with r denoting the distance from the facet edge.
This means that the ledge bordering the facet has a lot of space to meander as
caused by thermal activation. We investigate the statistical properties of the
border ledge fluctuations. In the scaling regime they turn out to be
non-Gaussian and related to the edge statistics of GUE multi-matrix models.Comment: Version with major revisions -- RevTeX, 4 pages, 2 figure
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