The Szego-Widom theorem provides an expression for the determinant of block Toeplitz matrices in the asymptotic limit of large matrix dimension n. We show that the presence of zero modes, i.e, eigenvalues that vanish as n, ||<1, when n, requires a modification of the Szego-Widom theorem. A new asymptotic expression for the determinant of a certain class of block Toeplitz matrices with one pair of zero modes is derived. The result is inspired by one-dimensional topological superconductors, and the relation with the latter systems is discussed.

VL - 174 UR - http://link.springer.com/10.1007/s10955-018-2177-8 JO - J Stat Phys ER - TY - JOUR T1 - A minimal power model for human running performance JF - PLOS ONE Y1 - 2018 A1 - Mulligan, Matthew A1 - Adam, Guillaume A1 - Emig, Thorsten ED - Piknova, Barbora KW - ENERGY-COST; OXYGEN-UPTAKE; ATHLETIC RECORDS; ECONOMY; RUNNERS; RUN; ENDURANCE; MARATHON; EXERCISE; EXHAUSTION AB -Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. The purpose of this work is to develop a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Our hypothesis is that various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model. Indeed, we confirm this hypothesis with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.

VL - 13 UR - http://dx.plos.org/10.1371/journal.pone.0206645 IS - 11 JO - PLoS ONE ER - TY - JOUR T1 - Role of City Texture in Urban Heat Islands at Nighttime JF - Physical Review Letters Y1 - 2018 A1 - Sobstyl, Jake M. A1 - Emig, Thorsten A1 - Qomi, M. J. Abdolhosseini A1 - Franz-Josef Ulm A1 - Roland Jean-Marc Pellenq KW - IDEAL CONDITIONS; CLIMATE-CHANGE; CITIES; SIMULATION; GEOMETRY; ENERGY; HEALTH; IMPACT; MODEL AB -An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture-measured by a building distribution function and the sky view factor-explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

Despite decades of research seeking to derive the urban energy budget, the dynamics of thermal exchange in the densely constructed environment is not yet well understood. Using New York City as a study site, we present a novel hybrid experimental-computational approach for a better understanding of the radiative heat transfer in complex urban environments. The aim of this work is to contribute to the calculation of the urban energy budget, particularly the stored energy. We will focus our attention on surface thermal radiation. Improved understanding of urban thermodynamics incorporating the interaction of various bodies, particularly in high rise cities, will have implications on energy conservation at the building scale, and for human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, in addition to a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. Despite assumptions in surface emissivity and thermal conductivity of buildings walls, the close comparison of temperatures derived from measurements and computations is promising. Results imply that the presented geospatial thermodynamic model of urban structures can enable accurate and high resolution analysis of instantaneous urban surface temperatures.

VL - 8 UR - http://www.nature.com/articles/s41598-018-19846-5 JO - Sci Rep ER - TY - JOUR T1 - Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions JF - Journal of Statistical Mechanics: Theory and Experiment Y1 - 2017 A1 - Dubail, Jerome A1 - Santachiara, Raoul A1 - Emig, Thorsten KW - Casimir effect; conformal field theory; critical exponents and amplitudes AB -Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szego formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.

UR - http://stacks.iop.org/1742-5468/2017/i=3/a=033201?key=crossref.e58e04fb8593248b573c53589bed0f1d JO - J. Stat. Mech. ER - TY - JOUR T1 - Many-body heat radiation and heat transfer in the presence of a nonabsorbing background medium JF - Physical Review B Y1 - 2017 A1 - Müller, Boris A1 - Incardone, Roberta A1 - Antezza, Mauro A1 - Emig, Thorsten A1 - Krüger, Matthias AB -Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically, these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of N arbitrary objects embedded in a passive nonabsorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

VL - 95 UR - https://link.aps.org/doi/10.1103/PhysRevB.95.085413 IS - 8 JO - Phys. Rev. B ER - TY - JOUR T1 - Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow JF - Physical Review E Y1 - 2017 A1 - Bette, Henrik M. A1 - Habel, Lars A1 - Emig, Thorsten A1 - Schreckenberg, Michael AB -We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P(v=0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P(v∈{0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.

VL - 95 UR - https://link.aps.org/doi/10.1103/PhysRevE.95.012311 IS - 1 JO - Phys. Rev. E ER - TY - JOUR T1 - Nonequilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force JF - Annual Review of Condensed Matter Physics Y1 - 2017 A1 - Bimonte, Giuseppe A1 - Emig, Thorsten A1 - Kardar, Mehran A1 - Krüger, Matthias AB -Quantum-thermal fluctuations of electromagnetic waves are the cornerstone of quantum statistics and inherent to phenomena such as thermal radiation and van der Waals forces. Although the principles are found in elementary texts, recent experimental and technological advances make it necessary to come to terms with counterintuitive consequences at short scales—the so-called near-field regime. We focus on three manifestations: (*a*) The Stefan–Boltzmann law describes radiation from macroscopic bodies but fails for small objects. (*b*) The heat transfer between two bodies at close proximity is dominated by evanescent waves and can be orders of magnitude larger than the classical (propagating) contribution. (*c*) Casimir forces, dominant at submicron separation, are not sufficiently explored for objects at different temperatures (at least experimentally). We explore these phenomena using fluctuational quantum electrodynamics (QED), introduced by Rytov in the 1950s, combined with scattering formalisms. This enables investigation of different material properties, shapes, separations, and arrangements.

We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across the surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.

VL - 95 UR - http://link.aps.org/doi/10.1103/PhysRevE.95.052104 IS - 5 JO - Phys. Rev. E ER - TY - JOUR T1 - Electromagnetic Casimir energy of a disk opposite a plane JF - Physical Review A Y1 - 2016 A1 - Emig, Thorsten A1 - Graham, Noah AB -Building on work by J. Meixner [Z. Naturforschung **3a**, 506 (1948)], we show how to compute the exact scattering amplitude (or T-matrix) for electromagnetic scattering from a perfectly conducting disk. This calculation is a rare example of a nondiagonal T-matrix that can nonetheless be obtained in a semianalytic form. We then use this result to compute the electromagnetic Casimir interaction energy for a disk opposite a plane, for arbitrary orientation angle of the disk, for separations greater than the disk radius. We find that the proximity force approximation (PFA) significantly overestimates the Casimir energy, in the case of both the ordinary PFA, which applies when the disk is parallel to the plane, and the “edge PFA”, which applies when the disk is perpendicular to the plane.

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals interaction with a gently curved dielectric surface at temperature T, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of T, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural linewidths and thermal broadening.

VL - 94 UR - https://link.aps.org/doi/10.1103/PhysRevA.94.022509 IS - 2 JO - Phys. Rev. A ER - TY - JOUR T1 - Velocity statistics of the Nagel-Schreckenberg model JF - Physical Review E Y1 - 2016 A1 - Bain, Nicolas A1 - Emig, Thorsten A1 - Franz-Josef Ulm A1 - Schreckenberg, Michael AB -The statistics of velocities in the cellular automaton model of Nagel and Schreckenberg for traffic are studied. From numerical simulations, we obtain the probability distribution function (PDF) for vehicle velocities and the velocity-velocity (vv) correlation function. We identify the probability to find a standing vehicle as a potential order parameter that signals nicely the transition between free congested flow for sufficiently large number of velocity states. Our results for the vv correlation function resemble features of a second order phase transition. We develop a 3-body approximation that allows us to relate the PDFs for velocities and headways. Using this relation, an approximation to the velocity PDF is obtained from the headway PDF observed in simulations. We find a remarkable agreement between this approximation and the velocity PDF obtained from simulations.

VL - 93 IS - 2 JO - Phys. Rev. E ER - TY - JOUR T1 - Casimir-Polder force between anisotropic nanoparticles and gently curved surfaces JF - Physical Review D Y1 - 2015 A1 - Bimonte, Giuseppe A1 - Emig, Thorsten A1 - Kardar, Mehran AB -The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO2 and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

VL - 92 IS - 2 JO - Phys. Rev. D ER - TY - JOUR T1 - Critical Casimir force between inhomogeneous boundaries JF - EPL (Europhysics Letters) Y1 - 2015 A1 - Dubail, Jerome A1 - Santachiara, Raoul A1 - Emig, Thorsten AB -To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.

VL - 112 IS - 6 JO - EPL ER - TY - JOUR T1 - Effect of curvature and confinement on the Casimir-Polder interaction JF - Physical Review A Y1 - 2015 A1 - Rodriguez-Lopez, Pablo A1 - Emig, Thorsten A1 - Noruzifar, Ehsan A1 - Zandi, Roya AB -Modifications of Casimir-Polder interactions due to confinement inside a cylindrical cavity and due to curvature in- and outside the cavity are studied. We consider a perfectly conducting cylindrical shell with a single particle (atom or macroscopic sphere) located next to its interior or exterior surface, or two atoms placed inside the shell. By employing the scattering approach, we obtain the particle-cavity interaction and the modification of the two-particle interaction due to the cavity. We consider both retardation and thermal effects. While for the atoms a dipole description is sufficient, for the macroscopic sphere we sum (numerically) over many multipole fluctuations to compute the interaction at short separations. In the latter limit we compare to the proximity approximation and a gradient expansion and find agreement. Our results indicate an confinement induced suppression of the force between atoms. General criteria for suppression and enhancement of Casimir interactions due to confinement are discussed.

VL - 91 IS - 1 JO - Phys. Rev. A ER - TY - JOUR T1 - Interplay of curvature and temperature in the Casimir–Polder interaction JF - Journal of Physics: Condensed Matter Y1 - 2015 A1 - Bimonte, Giuseppe A1 - Emig, Thorsten AB -We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.

VL - 27 IS - 21 JO - J. Phys.: Condens. Matter ER - TY - JOUR T1 - Reversing the critical Casimir force by shape deformation JF - Physics Letters B Y1 - 2015 A1 - Bimonte, Giuseppe A1 - Emig, Thorsten A1 - Kardar, Mehran AB -The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium points, is demonstrated for certain conformally invariant models, including the tricritical Ising model.

VL - 743 JO - Physics Letters B ER - TY - JOUR T1 - Casimir-Polder interaction for gently curved surfaces JF - Physical Review D Y1 - 2014 A1 - Bimonte, Giuseppe A1 - Emig, Thorsten A1 - Kardar, Mehran AB -We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a nonplanar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, nonretarded and classical high-temperature limits.

VL - 90 ER -