6,929 research outputs found
Lorentz group theory and polarization of the light
Some facts of the theory of the Lorentz group are specified for looking at
the problems of light polarization optics in the frames of vector
Stokes-Mueller and spinor Jones formalism. In view of great differences between
properties of isotropic and time-like vectors in Special Relativity we should
expect principal differences in describing completely polarized and partly
polarized light. In particular, substantial differences are revealed when
turning to spinor techniques in the context of the polarized light. Because
Jones complex formalism has close relation to spinor objects of the Lorentz
group, within the field of the light polarization we could have physical
realizations on the optical desk of some subtle topological distinctions
between orthogonal L_{+}^{\uparrow} =SO_{0}(3.1) and spinor SL(2.C) groups.
These topological differences of the groups find their corollaries in the
problem of the so-called spinor structure of physical space-time, some new
points are considered.Comment: 17 pages. Talk given at 16 International Seminar: NCPS, May 19-22,
2009, Minsk. A shorter vertion published as a journal pape
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
Einstein's fluctuation formula. A historical overview
A historical overview is given on the basic results which appeared by the
year 1926 concerning Einstein's fluctuation formula of black-body radiation, in
the context of light-quanta and wave-particle duality. On the basis of the
original publications (from Planck's derivation of the black-body spectrum and
Einstein's introduction of the photons up to the results of Born, Heisenberg
and Jordan on the quantization of a continuum) a comparative study is presented
on the first line of thoughts that led to the concept of quanta. The nature of
the particle-like fluctuations and the wave-like fluctuations are analysed by
using several approaches. With the help of the classical probability theory, it
is shown that the infinite divisibility of the Bose distribution leads to the
new concept of classical poissonian photo-multiplets or to the binary
photo-multiplets of fermionic character. As an application, Einstein's
fluctuation formula is derived as a sum of fermion type fluctuations of the
binary photo-multiplets.Comment: 34 page
Dynamics of Einstein - de Haas Effect: Application to Magnetic Cantilever
Local time-dependent theory of Einstein - de Haas effect is developed. We
begin with microscopicinteractions and derive dynamical equations that couple
elastic deformations with internal twists due to spins. The theory is applied
to the description of the motion of a magnetic cantilever caused by the
oscillation of the domain wall. Theoretical results are compared with a recent
experiment on Einstein - de Haas effect in a microcantilever.Comment: 7 PR pages, 5 figures, submitted to PR
The Maxwell Lagrangian in purely affine gravity
The purely affine Lagrangian for linear electrodynamics, that has the form of
the Maxwell Lagrangian in which the metric tensor is replaced by the
symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of
homothetic curvature, is dynamically equivalent to the Einstein-Maxwell
equations in the metric-affine and metric formulation. We show that this
equivalence is related to the invariance of the Maxwell Lagrangian under
conformal transformations of the metric tensor. We also apply to a purely
affine Lagrangian the Legendre transformation with respect to the tensor of
homothetic curvature to show that the corresponding Legendre term and the new
Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the
electromagnetic field. Therefore the purely affine picture, in addition to
generating the gravitational Lagrangian that is linear in the curvature,
justifies why the electromagnetic Lagrangian is quadratic in the
electromagnetic field.Comment: 9 pages; published versio
Vortices in fermion droplets with repulsive dipole-dipole interactions
Vortices are found in a fermion system with repulsive dipole-dipole
interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator
potential. Such systems have much in common with electrons in quantum dots,
where rotation is induced via an external magnetic field. In contrast to the
Coulomb interactions between electrons, the (externally tunable) anisotropy of
the dipole-dipole interaction breaks the rotational symmetry of the
Hamiltonian. This may cause the otherwise rotationally symmetric exact
wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
Cities in American federalism: evidence on state-local government conflict from a survey of mayors
Previous scholarship on American federalism has largely focused on the national government's increasingly conflictual relationship with the states. While some studies have explored the rise of mandates at the state level, there has been comparatively less attention on stateâlocal relationships. Using a new survey of mayors, we explore variations in local government attitudes towards their state governments. We find some evidence that, regardless of partisanship, mayors in more conservative states are unhappy about state funding andâespeciallyâregulations. More strikingly, we also uncover a partisan mismatch in which Democratic mayors provide especially negative ratings of their stateâs funding andâeven more stronglyâregulations. These findings have important implications for stateâlocal relations as cities continue to become more Democratic and Republicans increasingly dominate state-level contests
On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
The quantum field theoretic prediction for the vacuum energy density leads to
a value for the effective cosmological constant that is incorrect by between 60
to 120 orders of magnitude. We review an old proposal of replacing Einstein's
Field Equations by their trace-free part (the Trace-Free Einstein Equations),
together with an independent assumption of energy--momentum conservation by
matter fields. While this does not solve the fundamental issue of why the
cosmological constant has the value that is observed cosmologically, it is
indeed a viable theory that resolves the problem of the discrepancy between the
vacuum energy density and the observed value of the cosmological constant.
However, one has to check that, as well as preserving the standard cosmological
equations, this does not destroy other predictions, such as the junction
conditions that underlie the use of standard stellar models. We confirm that no
problems arise here: hence, the Trace-Free Einstein Equations are indeed viable
for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title
and emphasis of the paper although all original results of v1. remai
Dualities in fractional statistics
We first reobtain in a simpler way the Haldane fractional statistics at
thermal equilibrium using an interpolation argument. We then show that the mean
occupation number for fractional statistics is invariant to a group of duality
transformations, a nonabelian subgroup of the fractional linear groupComment: 7 pages, no figur
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