Nonequilibrium fluctuations in a resistor

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation constant in the system, exploiting the Fluctuation-Dissipation Theorem (FDT). In non-equilibrium steady systems, Fluctuations Theorems (FT) additionally describe symmetry properties of the probability density functions (PDFs) of the fluctuations of injected and dissipated energies. We experimentally probe a model system: an electrical dipole driven out of equilibrium by a small constant current $I$, and show that FT are experimentally accessible and valid. Furthermore, we stress that FT can be used to measure the dissipated power $\bar{\cal P}=RI^2$ in the system by just studying the PDFs symmetries.Comment: Juillet 200

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

Nothing but Relativity, Redux

Here we show how spacetime transformations consistent with the principle of relativity can be derived without an explicit assumption of the constancy of the speed of light, without gedanken experiments involving light rays, and without an assumption of differentiability, or even continuity, for the spacetime mapping. Hence, these historic results could have been derived centuries ago, even before the advent of calculus. This raises an interesting question: Could Galileo have derived Einsteinian relativity

Apparent superluminal advancement of a single photon far beyond its coherence length

We present experimental results relative to superluminal propagation based on a single photon traversing an optical system, called 4f-system, which acts singularly on the photon's spectral component phases. A single photon is created by a CW laser light down{conversion process. The introduction of a linear spectral phase function will lead to the shift of the photon peak far beyond the coherence length of the photon itself (an apparent superluminal propagation of the photon). Superluminal group velocity detection is done by interferometric measurement of the temporal shifted photon with its correlated untouched reference. The observed superluminal photon propagation complies with causality. The operation of the optical system allows to enlighten the origin of the apparent superluminal photon velocity. The experiment foresees a superluminal effect with single photon wavepackets.Comment: 11 pages, 2 figure

Anomalous low temperature ambipolar diffusion and Einstein relation

Regular Einstein relation, connecting the coefficient of ambipolar diffusion and the Dember field with mobilities, is generalized for the case of interacting electron-hole plasma. The calculations are presented for a non-degenerate plasma injected by light in semiconductors of silicon and germanium type. The Debye-Huckel correlation and the Wigner-Seitz exchange terms are considered. The corrections to the mobilities of carriers due to difference between average and acting electric fields within the electron-hole plasma is taken into account. The deviation of the generalized relation from the regular Einstein relation is pronounced at low temperatures and can explain anomaly of the coefficient of ambipolar diffusion, recently discovered experimentally.Comment: 4 pages, 2 eps figure

Brownian Simulations and Uni-Directional Flux in Diffusion

Brownian dynamics simulations require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages. The continuum baths are connected to the simulation through interfaces, located in the baths sufficiently far from the channel. Average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the interfaces. The particles injected into the simulation volume represent a unidirectional diffusion flux, while the outgoing particles represent the unidirectional flux in the opposite direction. The classical diffusion equation defines net diffusion flux, but not unidirectional fluxes. The stochastic formulation of classical diffusion in terms of the Wiener process leads to a Wiener path integral, which can split the net flux into unidirectional fluxes. These unidirectional fluxes are infinite, though the net flux is finite and agrees with classical theory. We find that the infinite unidirectional flux is an artifact caused by replacing the Langevin dynamics with its Smoluchowski approximation, which is classical diffusion. The Smoluchowski approximation fails on time scales shorter than the relaxation time $1/\gamma$ of the Langevin equation. We find the unidirectional flux (source strength) needed to maintain average boundary concentrations in a manner consistent with the physics of Brownian particles. This unidirectional flux is proportional to the concentration and inversely proportional to $\sqrt{\Delta t}$ to leading order. We develop a BD simulation that maintains fixed average boundary concentrations in a manner consistent with the actual physics of the interface and without creating spurious boundary layers

Deforming the Maxwell-Sim Algebra

The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde

Einstein energy associated with the Friedmann -Robertson -Walker metric

Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general formula for the total matter plus gravitational field energy ($P_0$) of an arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C., {\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962)); Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in quasi-Cartesian coordinates, this formula leads to the well known result $P_0 = \int \sqrt{-g} (T_0^0 - T_1^1 -T_2^2 -T_3^3) ~d^3 x$, where $g$ is the determinant of the metric tensor and $T^a_b$ is the energy momentum tensor of the {\em matter}. Though in the literature, this is known as "Tolman Mass", it must be realized that this is essentially "Einstein Mass" because the underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz obtained the same expression for the "inertial mass" of a static isolated system without using any pseudo-tensor at all and which points to physical significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz, E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed., 1962)! For the first time we apply this general formula to find an expression for $P_0$ for the Friedmann- Robertson -Walker (FRW) metric by using the same quasi-Cartesian basis. As we analyze this new result, physically, a spatially flat model having no cosmological constant is suggested. Eventually, it is seen that conservation of $P_0$ is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the journal version is uploade

Multi-particle structure in the Z_n-chiral Potts models

We calculate the lowest translationally invariant levels of the Z_3- and Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating N to infinity. In the high-temperature massive phase we find that the pattern of the low-lying zero momentum levels can be explained assuming the existence of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m_Q = Q m_1. Exponential convergence in N is observed for the single particle gaps, while power convergence is seen for the scattering levels. We also verify that qualitatively the same pattern appears for the self-dual and integrable cases. For general Z_n we show that the energy-momentum relations of the particles show a parity non-conservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi, where \phi is the chiral angle and Q is the Z_n-charge of the respective particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript), BONN-HE-92-3

The Measurement Process in Local Quantum Theory and the EPR Paradox

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic part of the measurement apparatus; 2. the finite space size R of that apparatus; 3. the fact that the macroscopic part of the measurement apparatus, having the role of amplifying the effect of that interaction to a macroscopic scale, is composed by a very large but finite number N of particles. The conventional picture of the measurement, as an instantaneous action turning a pure state into a mixture, arises only in the limit in which N and R tend to infinity, and T tends to 0. We sketch here a proposed scheme, which still ought to be made mathematically precise in order to analyse its implications and to test it in specific models, where we argue that in Quantum Field Theory this picture should apply to the unique time evolution expressing the dynamics of a given theory, and should comply with the Principle of Locality. We comment on the Einstein Podolski Rosen thought experiment (partly modifying the discussion on this point in an earlier version of this note), reformulated here only in terms of local observables (rather than global ones, as one particle or polarisation observables). The local picture of the measurement process helps to make it clear that there is no conflict with the Principle of Locality.Comment: 18 page