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

The ROSAT-ESO Flux Limited X-ray Galaxy Cluster Survey (REFLEX II) I. Newly identified X-ray luminous clusters at z>=0.2

We report 19 intermediate redshift clusters newly detected in the ROSAT All-Sky survey that are spectroscopically confirmed. They form a part of 911 objects in the REFLEX II cluster catalogue with a limiting flux of 1.8\times10^12 erg/s/cm2 in the 0.1-2.4 keV ROSAT band at redshift z >= 0.2. In addition we report three clusters from the REFLEX III supplementary catalogue, which contains objects below the REFLEX II flux limit but satisfies the redshift constraint above. These clusters are spectroscopically followed-up by our ESO NTT-EFOSC2 campaigns for the redshift measurement. We describe our observing and data reduction methods. We show how X-ray properties such as spectral hardness ratio and source extent can be used as important diagnostics in selecting galaxy cluster candidates. Physical properties of the clusters are subsequently calculated from the X-ray observations. This sample contains the high mass and intermediate-redshift galaxy clusters for astrophysical and cosmological applications.Comment: Astronomy and Astrophysics (in press

A Note on Polarization Vectors in Quantum Electrodynamics

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors epsilon_\lambda(k) with lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.Comment: 6 pages late

Energy average formula of photon gas rederived by using the generalized Hermann-Feynman theorem

By virtue of the generalized Hermann-Feynmam theorem and the method of characteristics we rederive energy average formula of photon gas, this is another useful application of the theorem.Comment: 2 page

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

High density culturing of porcine hepatocytes immobilized on nonwoven polyurethane-based biomatrices

Objective: Hepatocytes are increasingly used as functional units in bioartificial liver devices. The objective of the present study was to investigate the feasibility of culturing porcine hepatocytes in high density on a novel polyurethane-based nonwoven three-dimensional matrix. We investigated (1) the optimal cell density within this culture configuration, (2) the maintenance of liver-specific morphology and cell functions over long-term periods and (3) the necessity to apply an additional extracellular matrix component (collagen gel). Methods: Nonwoven polyurethane matrices were manufactured by a specially developed fiber extrusion technology. Pig hepatocytes were cultured at various cell densities of 0.1, 0.25, 0.5, 0.75, 1 and 2 x 10(6) cells/cm(2) on three-dimensional networks of nonwoven polyurethane matrices and cell adhesion as well as functional parameters (DNA of nonattached/attached cells, lactate dehydrogenase release and cytochrome P450 activity) were determined. To assess the performance of cells within this configuration albumin and urea excretion was measured over 8 days. The potentially beneficial effect of an additional extracellular matrix configuration was evaluated by comparing the average albumin synthesis in groups of identical cell numbers. Results: The optimal cell density in this three-dimensional culture configuration was 1 x 10(6) cells/cm(2). The functional capacity of hepatocytes was stable for 8 days at an average level of 53.7 +/- 5.6 ng/h/mug DNA and of 1.8 +/- 0.14 mug/h/mug DNA for albumin and urea excretion, respectively. The supplementation of an extracellular matrix configuration did not improve functional activity of cells. Average albumin synthesis was 35.6 ng/h/mug DNA (28.7, 42.8) and 32.7 ng/h/mug DNA (23.4, 49.2) for collagen-immobilized and control cultures, respectively, Conclusion: The results of the study indicate that nonwoven polyurethane sheets supply a biocompatible support structure for functionally active high density cultures. Thus, nonwoven polyurethane matrices should be further investigated on with respect to their role in the development, optimization and design of bioartificial liver systems. Copyright (C) 2001 S.Karger AG, Basel

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 $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu)$ follows from a special modular transformation in a massless relativistic theor

Einstein's "Zur Elektrodynamik..." (1905) Revisited, with Some Consequences

Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But with regard to "place" in describing motion, he assumed without analysis the concept of a system of co-ordinates. In the present paper, we propose a way of giving physical (operational) meaning to the concepts of "place" and "co-ordinate system", and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system "in uniform motion of translation relatively to the former". Without assuming "the properties of homogeneity which we attribute to space and time", we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, "one-way" and "two-way" velocities of light, symmetry, the "group property" of inertial reference frames, length contraction and time dilatation, and the "twin paradox". Finally, we point out a flaw in Einstein's argument in the "Electrodynamical Part" of his paper and show that the Lorentz force formula and Einstein's formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck's formula for mass suffices. (Except for the reference to Planck's formula, we restrict ourselves to Physics of 1905.)Comment: 55 pages, 4 figures, accepted for publication in "Foundations of Physics

Constraints on Deflation from the Equation of State of Dark Energy

In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/\rho = -1 - \phi$ with $\phi > 0$. More accurate measurement of $\phi$ will constrain $N_{\rm cp}$. The critical density $\rho_c$ in the model has a lower bound $\rho_c \ge (10^9 {\rm GeV})^4$ or $\rho_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.Comment: 23 pages, 3 figures, typos fixe