The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction

We consider relativistic many-particle operators which - according to Brown and Ravenhall - describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas-Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev-Gagliardo-Nirenberg-type inequality is established for the critical atomic Brown-Ravenhall operator. Moreover, we prove sharp upper and lower bound on the eigenvalues of the hydrogenic Brown-Ravenhall operator up to and including the critical coupling constant.Comment: 42 page

Integral Fluctuation Relations for Entropy Production at Stopping Times

A stopping time $T$ is the first time when a trajectory of a stochastic process satisfies a specific criterion. In this paper, we use martingale theory to derive the integral fluctuation relation $\langle e^{-S_{\rm tot}(T)}\rangle=1$ for the stochastic entropy production $S_{\rm tot}$ in a stationary physical system at stochastic stopping times $T$. This fluctuation relation implies the law $\langle S_{\rm tot}(T)\rangle\geq 0$, which states that it is not possible to reduce entropy on average, even by stopping a stochastic process at a stopping time, and which we call the second law of thermodynamics at stopping times. This law implies bounds on the average amount of heat and work a system can extract from its environment when stopped at a random time. Furthermore, the integral fluctuation relation implies that certain fluctuations of entropy production are universal or are bounded by universal functions. These universal properties descend from the integral fluctuation relation by selecting appropriate stopping times: for example, when $T$ is a first-passage time for entropy production, then we obtain a bound on the statistics of negative records of entropy production. We illustrate these results on simple models of nonequilibrium systems described by Langevin equations and reveal two interesting phenomena. First, we demonstrate that isothermal mesoscopic systems can extract on average heat from their environment when stopped at a cleverly chosen moment and the second law at stopping times provides a bound on the average extracted heat. Second, we demonstrate that the average efficiency at stopping times of an autonomous stochastic heat engines, such as Feymann's ratchet, can be larger than the Carnot efficiency and the second law of thermodynamics at stopping times provides a bound on the average efficiency at stopping times.Comment: 37 pages, 6 figure

Generic Properties of Stochastic Entropy Production

We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non steady-state conditions.Comment: 5 pages, 5 figures (contains Supplemental Material, 7 pages

Underlying event sensitive observables in Drell-Yan production using GENEVA

We present an extension of the GENEVA Monte Carlo framework to include multiple parton interactions (MPI) provided by PYTHIA8. This allows us to obtain predictions for underlying-event sensitive measurements in Drell-Yan production, in conjunction with GENEVA's fully-differential NNLO calculation, NNLL' resummation for the 0-jet resolution variable (beam thrust), and NLL resummation for the 1-jet resolution variable. We describe the interface with the parton shower algorithm and MPI model of PYTHIA8, which preserves both the precision of partonic N-jet cross sections in GENEVA as well as the shower accuracy and good description of soft hadronic physics of PYTHIA8. We present results for several underlying-event sensitive observables and compare to data from ATLAS and CMS as well as to standalone PYTHIA8 predictions. This includes a comparison with the recent ATLAS measurement of the beam thrust spectrum, which provides a potential avenue to fully disentangle the physical effects from the primary hard interaction, primary soft radiation, multiple parton interactions, and nonperturbative hadronization.Comment: 23 pages, 11 figures. v3: version accepted by EPJ

Ocean acidification in the aftermath of the Marinoan glaciation

Boron isotope patterns preserved in cap carbonates deposited in the aftermath of the younger Cryogenian (Marinoan, ca. 635 Ma) glaciation confirm a temporary ocean acidification event on the continental margin of the southern Congo craton, Namibia. To test the significance of this acidification event and reconstruct Earth’s global seawater pH states at the Cryogenian-Ediacaran transition, we present a new boron isotope data set recorded in cap carbonates deposited on the Yangtze Platform in south China and on the Karatau microcontinent in Kazakhstan. Our compiled δ11B data reveal similar ocean pH patterns for all investigated cratons and confirm the presence of a global and synchronous ocean acidification event during the Marinoan deglacial period, compatible with elevated postglacial pCO2 concentrations. Differences in the details of the ocean acidification event point to regional distinctions in the buffering capacity of Ediacaran seawater

Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED 2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field

Properties of Galaxy Groups in the SDSS: I.-- The Dependence of Colour, Star Formation, and Morphology on Halo Mass

Using a large galaxy group catalogue constructed from the SDSS, we investigate the correlation between various galaxy properties and halo mass. We split the population of galaxies in early types, late types, and intermediate types, based on their colour and specific star formation rate. At fixed luminosity, the early type fraction increases with increasing halo mass. Most importantly, this mass dependence is smooth and persists over the entire mass range probed, without any break or feature at any mass scale. We argue that the previous claim of a characteristic feature on galaxy group scales is an artefact of the environment estimators used. At fixed halo mass, the luminosity dependence of the type fractions is surprisingly weak: galaxy type depends more strongly on halo mass than on luminosity. We also find that the early type fraction decreases with increasing halo-centric radius. Contrary to previous studies, we find that this radial dependence is also present in low mass haloes. The properties of satellite galaxies are strongly correlated with those of their central galaxy. In particular, the early type fraction of satellites is significantly higher in a halo with an early type central galaxy than in a halo of the same mass but with a late type central galaxy. This phenomenon, which we call `galactic conformity', is present in haloes of all masses and for satellites of all luminosities. Finally, the fraction of intermediate type galaxies is always ~20 percent, independent of luminosity, independent of halo mass, independent of halo-centric radius, and independent of whether the galaxy is a central galaxy or a satellite galaxy. We discuss the implications of all these findings for galaxy formation and evolution.Comment: 28 pages, 15 figures. Submitted for publication in MNRA

Drell-Yan Production at NNLL'+NNLO Matched to Parton Showers

We present results for Drell-Yan production from the GENEVA Monte-Carlo framework. We combine the fully-differential NNLO calculation with higher-order resummation in the 0-jettiness resolution variable. The resulting parton-level events are further combined with parton showering and hadronization provided by PYTHIA8. The 0-jettiness resummation is carried out to NNLL', which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment of perturbative uncertainties. In this way, inclusive observables are correct to NNLO, up to small power corrections in the resolution cutoff. Furthermore, the perturbative accuracy of 0-jet-like resummation variables is significantly improved beyond the parton shower approximation. We provide comparisons with LHC measurements of Drell-Yan production at 7 TeV from ATLAS, CMS, and LHCb. As already observed in $e^+e^-$ collisions, for resummation-sensitive observables, the agreement with data is noticeably improved by using a lower value of $\alpha_s(M_Z) = 0.1135$.Comment: 26 pages, 20 figure

Hydrodynamics for the partial exclusion process in random environment

In this paper, we introduce a random environment for the exclusion process in $\Z^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in \cite{nagy_symmetric_2002} and \cite{faggionato_bulk_2007}. To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in \cite{redig_symmetric_2018}

Spatial planning and territorial governance in Southern Europe between economic crisis and austerity policies

This article examines how spatial planning systems have changed in Portugal, Spain, Italy and Greece in times of economic recession and austerity politics, in amid pressures of external actors and local conditions and traditions. We analyse the round of reforms of spatial planning and territorial governance implemented by national governments under pressures by European institutions, as well as local responses to them. On the one hand, we highlight how European institutions have used the conditionalities attached to bailout packages and other instrument of pressure to frame what can be considered an implicit Southern European spatial planning policy developed by the European Union. On the other, we suggest that Southern European planning amid crisis and austerity should be understood, together, as field that problematizes the idea of Europeanization of planning; a space used as ‘prototype’ for new rounds of neoliberalization; and a political space that continuously develops through top-down/bottom-up dialectic conflicts.info:eu-repo/semantics/publishedVersio