A quantum violation of the second law?

An apparent violation of the second law of thermodynamics occurs when an atom coupled to a zero-temperature bath, being necessarily in an excited state, is used to extract work from the bath. Here the fallacy is that it takes work to couple the atom to the bath and this work must exceed that obtained from the atom. For the example of an oscillator coupled to a bath described by the single relaxation time model, the mean oscillator energy and the minimum work required to couple the oscillator to the bath are both calculated explicitly and in closed form. It is shown that the minimum work always exceeds the mean oscillator energy, so there is no violation of the second law

The Lorentz Force and the Radiation Pressure of Light

In order to make plausible the idea that light exerts a pressure on matter, some introductory physics texts consider the force exerted by an electromagnetic wave on an electron. The argument as presented is both mathematically incorrect and has several serious conceptual difficulties without obvious resolution at the classical, yet alone introductory, level. We discuss these difficulties and propose an alternate demonstration.Comment: More or less as in AJ

Planck 2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0:9603 _ 0:0073, ruling out exact scale invariance at over 5_: Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0:11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n _ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns=dln k = 0:0134 _ 0:0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by __2 e_ _ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the _2 e_ by approximately 4 as a result of slightly lowering the theoretical prediction for the ` <_ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions

Far-Infrared to Millimeter Astrophysical Dust Emission. II: Comparison of the Two-Level Systems (TLS) model with Astronomical Data

In a previous paper we proposed a new model for the emission by amorphous astronomical dust grains, based on solid-state physics. The model uses a description of the Disordered Charge Distribution (DCD) combined with the presence of Two-Level Systems (TLS) defects in the amorphous solid composing the grains. The goal of this paper is to confront this new model to astronomical observations of different Galactic environments in the FIR/submm, in order to derive a set of canonical model parameters to be used as a Galactic reference to be compared to in future Galactic and extragalactic studies. We confront the TLS model with existing astronomical data. We consider the average emission spectrum at high latitudes in our Galaxy as measured with FIRAS and WMAP, as well as the emission from Galactic compact sources observed with Archeops, for which an inverse relationship between the dust temperature and the emissivity spectral index has been evidenced. We show that, unlike models previously proposed which often invoke two dust components at different temperatures, the TLS model successfully reproduces both the shape of the Galactic SED and its evolution with temperature as observed in the Archeops data. The best TLS model parameters indicate a charge coherence length of \simeq 13 nm and other model parameters in broad agreement with expectations from laboratory studies of dust analogs. We conclude that the millimeter excess emission, which is often attributed to the presence of very cold dust in the diffuse ISM, is likely caused solely by TLS emission in disordered amorphous dust grains. We discuss the implications of the new model, in terms of mass determinations from millimeter continuum observations and the expected variations of the emissivity spectral index with wavelength and dust temperature. The implications for the analysis of the Herschel and Planck satellite data are discussed.Comment: Accepted for publication in A&A (16 pages, 9 figures, 6 tables

Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.Comment: 17 pages, 5 figure

Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures

Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year WMAP and the NVSS data for correlation induced by the integrated Sachs-Wolfe (ISW) effect. The steerable wavelet constructed from the second derivative of a Gaussian allows one to define three local morphological measures, namely the signed-intensity, orientation and elongation of local features. Detections of correlation between the WMAP and NVSS data are made with each of these morphological measures. The most significant detection is obtained in the correlation of the signed-intensity of local features at a significance of 99.9%. By inspecting signed-intensity sky maps, it is possible for the first time to see the correlation between the WMAP and NVSS data by eye. Foreground contamination and instrumental systematics in the WMAP data are ruled out as the source of all significant detections of correlation. Our results provide new insight on the ISW effect by probing the morphological nature of the correlation induced between the cosmic microwave background and large scale structure of the Universe. Given the current constraints on the flatness of the Universe, our detection of the ISW effect again provides direct and independent evidence for dark energy. Moreover, this new morphological analysis may be used in future to help us to better understand the nature of dark energy.Comment: 12 pages, 10 figures, replaced to match version accepted by MNRA

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

Planck 2015 results. XIV. Dark energy and modified gravity

We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories and coupled DE. In addition to the latest Planck data, for our main analyses we use baryonic acoustic oscillations, type-Ia supernovae and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations are in agreement with LCDM. When testing models that also change perturbations (even when the background is fixed to LCDM), some tensions appear in a few scenarios: the maximum one found is \sim 2 sigma for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to at most 3 sigma when external data sets are included. It however disappears when including CMB lensing

Radio to infrared spectra of late-type galaxies with Planck and WMAP data

We use the Planck Early Release Compact Source Catalogue combined with WMAP and other archival measurements to construct continuum spectra of three nearby dusty star-forming galaxies: Messier 82, NGC 253 and NGC 4945. We carry out a least-squares fit to the spectra using a combination of simple synchrotron, free-free and thermal dust models, and look for evidence of anomalous microwave emission (AME). We find that the radio spectra of all three galaxies are consistent with steep spectrum synchrotron emission, with a significant amount of free-free emission required to explain the Planck and WMAP data points in the frequency range 30-150 GHz. This brings the star-formation rate based on free-free emission into better agreement with that from the non-thermal emission. We place limits on the presence of AME in these galaxies, finding that it is lower than expectations based on the ratio of far infrared to AME from the Galaxy. Nevertheless, the shape of the spectrum of NGC 4945 hints at the presence of AME with a peak around 30 GHz. Future Planck data will let us look more closely at these galaxies, as well as to extend the analysis to many more galaxies.Comment: 5 pages, 1 figure (6 panels), 1 table. Submitted to MNRAS letter

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