2,303 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
Bubble size statistics during reionization from 21-cm tomography
The upcoming SKA1-Low radio interferometer will be sensitive enough to produce tomographic imaging data of the redshifted 21-cm signal from the Epoch of Reionization. Due to the non-Gaussian distribution of the signal, a power spectrum analysis alone will not provide a complete description of its properties. Here, we consider an additional metric which could be derived from tomographic imaging data, namely the bubble size distribution of ionized regions. We study three methods that have previously been used to characterize bubble size distributions in simulation data for the hydrogen ionization fraction â the spherical-average (SPA), mean-free-path (MFP) and friends-of-friends (FOF) methods â and apply them to simulated 21-cm data cubes. Our simulated data cubes have the (sensitivity-dictated) resolution expected for the SKA1-Low reionization experiment and we study the impact of both the light-cone (LC) and redshift space distortion (RSD) effects. To identify ionized regions in the 21-cm data we introduce a new, self-adjusting thresholding approach based on the K-Means algorithm. We find that the fraction of ionized cells identified in this way consistently falls below the mean volume-averaged ionized fraction. From a comparison of the three bubble size methods, we conclude that all three methods are useful, but that the MFP method performs best in terms of tracking the progress of reionization and separating different reionization scenarios. The LC effect is found to affect data spanning more than about 10 MHz in frequency (Îz ⌠0.5). We find that RSDs only marginally affect the bubble size distributions
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
Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
We illustrate recent results concerning the validity of the work fluctuation
theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi,
Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable
model of an open quantum system. The central role played by the thermodynamic
partition function of the open quantum system, -- a two level fluctuator with a
strong quantum nondemolition coupling to a harmonic oscillator --, is
elucidated. The corresponding quantum Hamiltonian of mean force is evaluated
explicitly. We study the thermodynamic entropy and the corresponding specific
heat of this open system as a function of temperature and coupling strength and
show that both may assume negative values at nonzero low temperatures.Comment: 8 pages, 6 figure
Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis
We apply the S-matrix based finite temperature formalism to non-relativistic
Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case,
the free energy is given in terms of Roger's dilogarithm in a way analagous to
the relativistic 1+1 dimensional case. The 1d fermionic case with a
quasi-periodic 2-body potential provides a physical framework for understanding
the Riemann hypothesis.Comment: version 3: additional appendix explains how the to
duality of Riemann's follows from a special modular
transformation in a massless relativistic theor
The ideal energy of classical lattice dynamics
We define, as local quantities, the least energy and momentum allowed by
quantum mechanics and special relativity for physical realizations of some
classical lattice dynamics. These definitions depend on local rates of
finite-state change. In two example dynamics, we see that these rates evolve
like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335
Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
We study the stability of three-dimensional numerical evolutions of the
Einstein equations, comparing the standard ADM formulation to variations on a
family of formulations that separate out the conformal and traceless parts of
the system. We develop an implementation of the conformal-traceless (CT)
approach that has improved stability properties in evolving weak and strong
gravitational fields, and for both vacuum and spacetimes with active coupling
to matter sources. Cases studied include weak and strong gravitational wave
packets, black holes, boson stars and neutron stars. We show under what
conditions the CT approach gives better results in 3D numerical evolutions
compared to the ADM formulation. In particular, we show that our implementation
of the CT approach gives more long term stable evolutions than ADM in all the
cases studied, but is less accurate in the short term for the range of
resolutions used in our 3D simulations.Comment: 17 pages, 15 figures. Small changes in the text, and a change in the
list of authors. One new reference adde
Dark gas in the solar neighnorhood from extinction data
When modeling infrared or gamma-ray data as a linear combination of observed
gas tracers, excess emission has been detected compared to expectations from
known neutral and atomic gas as traced by HI and CO measurements, respectively.
This excess might correspond to an additional gas component. This so-called
"dark gas" (DG) has been observed in our Galaxy, as well as the Magellanic
Clouds. For the first time, we investigate the correlation between visible
extinction (Av) data and gas tracers on large scales in the solar neighborhood.
Our work focuses on both the solar neighborhood (|b|>10\degr), and the inner
and outer Galaxy, as well as on four individual regions: Taurus, Orion,
Cepheus-Polaris and Aquila-Ophiuchus. Thanks to the recent production of an
all-sky Av map, we first perform the correlation between Av and both HI and CO
emission over the most diffuse regions, to derive the optimal (Av/NH)^(ref)
ratio. We then iterate the analysis over the entire regions to estimate the
CO-to-H2 conversion factor as well as the DG mass fraction. The average
extinction to gas column-density ratio in the solar neighborhood is found to be
(Av/NH)^(ref)=6.53 10^(-22) mag. cm^2, with significant differences between the
inner and outer Galaxy. We derive an average XCO value of 1.67 10^(20) H2
cm^(-2)/(K km s^(-1)). In the solar neighborhood, the gas mass in the dark
component is found to be 19% relative to that in the atomic component and
164 relative to the one traced by CO. These results are compatible with the
recent analysis using Planck data within the uncertainties of our measurements.
We estimate the ratio of dark gas to total molecular gas to be 0.62 in the
solar neighborhood. The HI-to-H2 and H2-to-CO transitions appear for Av
0.2 mag and Av mag, respectively, in agreement with
theoretical models of dark-H2 gas.Comment: 9 pages, 4 figures, 1 table. Accepted for publication in A&A (in
press
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