Small-scale properties of the KPZ equation and dynamical symmetry breaking

A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.Comment: V2 --- 6 pages, LaTeX 209, ReV_TeX 3.2. Title changed, presentation clarified, additional discussion added, references updated. No significant changes in physics conclusions. This version to appear in Physics Letters

Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation--SPDE) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy vorticity-free Burgers equation), and analyze its behaviour in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for lambda phi^4 QFT. In particular we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman-Weinberg mechanism) in 1 and 2 space dimensions, and that this behaviour does not persist in 3 space dimensions.Comment: 13 pages, LaTeX 209, ReV_TeX 3.2, three *.eps figures, epsf.st

Effort vs. Concentration: The Asymmetric Impact of Pressure on NBA Performance

Abstract How and why does performance change under pressure? Psychologists have argued that pressure can both distract, motivate and generate too much self-focus (thinking about the details of how one should accomplish a goal, as opposed to "just doing it"). Studies have implicated self-focus as the key factor in pressure-associated performance declines. To understand if these results extend to highly trained experts, we examine two fundamentally different actions within the context of the same professional sport, basketball. The first action, free throw shooting, requires quiet concentration, while the second, offensive rebounding, is based on effort exerted in the heat of the moment. Home vs. Away variation allows us to understand how a supportive audience moderates the impact of pressure. Using a dataset over 1.3 million possessions and 300,000 free-throws, we find that home free throw shooters do significantly worse in clutch situations, with the effect being larger for poor shooters. Road players show no change in behavior under pressure, indicating distraction plays a limited role in this task. In stark contrast, the home team gets significantly better at offensive rebounding in pressure packed moments, while again the road team shows no relationship between performance and pressure. The results show a clear asymmetric impact of a supportive audience-it can both inspire effort and lead to detrimental self-focus, even for experienced agents. From a sports perspective, it shows how the traditional notion of home-court advantage is not inconsistent with some pressure-related disadvantages ("home choke"). 1 We thank Douglas J. Brown for detailed comments on the manuscript. Ned Augenblick provided many helpful comments

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version of the pape

Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.Comment: 20 pages, 13 figures, RevTeX, accepted for publication in PR

HOW THE GROWING GAP IN LIFE EXPECTANCY MAY AFFECT RETIREMENT BENEFITS AND REFORMS.

Older Americans have experienced dramatic gains in life expectancy in recent decades, but an emerging literature reveals that these gains are accumulating mostly to those at the top of the income distribution. We explore how growing inequality in life expectancy affects lifetime benefits from Social Security, Medicare, and other programs and how this phenomenon interacts with possible program reforms. We first project that life expectancy at age 50 for males in the two highest income quintiles will rise by 7 to 8 years between the 1930 and 1960 birth cohorts, but that the two lowest income quintiles will experience little to no increase over that time period. This divergence in life expectancy will cause the gap between average lifetime program benefits received by men in the highest and lowest quintiles to widen by $130,000 (in$2009) over this period. Finally we simulate the effect of Social Security reforms such as raising the normal retirement age and changing the benefit formula to see whether they mitigate or enhance the reduced progressivity resulting from the widening gap in life expectancy

Dynamics and transport near quantum-critical points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N=1 d=1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N=3, d=1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N=3, d=2,3 models describe Heisenberg antiferromagnets with collinear N\'{e}el correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N=2, d=2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical properties of unconventional magnetic systems", Geilo, Norway, April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be published. 46 page

Body Temperature Patterns and Rhythmicity in Free-Ranging Subterranean Damaraland Mole-Rats, Fukomys damarensis

Body temperature (Tb) is an important physiological component that affects endotherms from the cellular to whole organism level, but measurements of Tb in the field have been noticeably skewed towards heterothermic species and seasonal comparisons are largely lacking. Thus, we investigated patterns of Tb patterns in a homeothermic, free-ranging small mammal, the Damaraland mole-rat (Fukomys damarensis) during both the summer and winter. Variation in Tb was significantly greater during winter than summer, and greater among males than females. Interestingly, body mass had only a small effect on variation in Tb and there was no consistent pattern relating ambient temperature to variation in Tb. Generally speaking, it appears that variation in Tb patterns varies between seasons in much the same way as in heterothermic species, just to a lesser degree. Both cosinor analysis and Fast Fourier Transform analysis revealed substantial individual variation in Tb rhythms, even within a single colony. Some individuals had no Tb rhythms, while others appeared to exhibit multiple rhythms. These data corroborate previous laboratory work showing multiplicity of rhythms in mole-rats and suggest the variation seen in the laboratory is a true indicator of the variation seen in the wild

Disentangling the numbers behind agriculture-driven tropical deforestation

Tropical deforestation continues at alarming rates with profound impacts on ecosystems, climate, and livelihoods, prompting renewed commitments to halt its continuation. Although it is well established that agriculture is a dominant driver of deforestation, rates and mechanisms remain disputed and often lack a clear evidence base. We synthesize the best available pantropical evidence to provide clarity on how agriculture drives deforestation. Although most (90 to 99%) deforestation across the tropics 2011 to 2015 was driven by agriculture, only 45 to 65% of deforested land became productive agriculture within a few years. Therefore, ending deforestation likely requires combining measures to create deforestation-free supply chains with landscape governance interventions. We highlight key remaining evidence gaps including deforestation trends, commodity-specific land-use dynamics, and data from tropical dry forests and forests across Africa