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The first part of this paper is a brief survey of the approaches to economic inequality based on ideas from statistical physics and kinetic theory. These include the Boltzmann kinetic equation, the time-reversal symmetry, the ergodicity hypothesis, entropy maximization and the Fokker–Planck equation. The origins of the exponential Boltzmann–Gibbs distribution and the Pareto power law are discussed in relation to additive and multiplicative stochastic processes. The second part of the paper analyses income distribution data in the USA for the time period 1983–2018 using a two-class decomposition. We present overwhelming evidence that the lower class (more than 90% of the population) is described by the exponential distribution, whereas the upper class (about 4% of the population in 2018) by the power law. We show that the significant growth of inequality during this time period is due to the sharp increase in the upper-class income share, whereas relative inequality within the lower class remains constant. We speculate that the expansion of the upper-class population and income shares may be due to increasing digitization and non-locality of the economy in the last 40 years. This article is part of the theme issue 'Kinetic exchange models of societies and economies'. [ABSTRACT FROM AUTHOR]

We propose an explanation for the experiment by Schemm et al. (2015) where the polar Kerr effect (PKE), indicating time-reversal symmetry (TRS) breaking, was observed in the hidden-order (HO) phase of URu 2 Si 2 . The PKE signal on warmup was seen only if a training magnetic field was present on cool-down. Using a Ginzburg–Landau model for a complex order parameter, we show that the system can have a metastable ferromagnetic state producing the PKE, even if the HO ground state respects TRS. We predict that a strong reversed magnetic field should reset the PKE to zero. [ABSTRACT FROM AUTHOR]

We study how the energy dispersion of bosonic atoms loaded into an optical lattice becomes modified due to periodic circular stirring of the lattice to the second order in the strength of stirring. If the lattice breaks mirror symmetry, the bosonic atoms may acquire a nonzero group velocity at the center of the Brillouin zone and produce a nonzero direct current. This effect is similar to the circular photogalvanic effect in solid-state physics. It can be used to transport neutral bosonic atoms in an optical lattice over a given distance in an arbitrary direction. However, when the drive frequency is detuned to avoid resonant transitions with energy absorption, we argue that the induced current is not persistent, but transient. An experimental study of the relaxation of the induced current can provide insight about equilibrization in driven systems. • Circular stirring of a 2D optical lattice causes renormalization of energy dispersion. • As a result, bosonic atoms in the lattice may acquire a nonzero group velocity at k=0. • Like in photogalvanic effect, the induced current can transport neutral atoms. [ABSTRACT FROM AUTHOR]

We study how the energy dispersion of bosonic atoms loaded into an optical lattice becomes modified due to periodic circular stirring of the lattice to the second order in the strength of stirring. If the lattice breaks mirror symmetry, the bosonic atoms may acquire a nonzero group velocity at the center of the Brillouin zone and produce a nonzero direct current. This effect is similar to the circular photogalvanic effect in solid-state physics. It can be used to transport neutral bosonic atoms in an optical lattice over a given distance in an arbitrary direction. However, when the drive frequency is detuned to avoid resonant transitions with energy absorption, we argue that the induced current is not persistent, but transient. An experimental study of the relaxation of the induced current can provide insight about equilibrization in driven systems. • Circular stirring of a 2D optical lattice causes renormalization of energy dispersion. • As a result, bosonic atoms in the lattice may acquire a nonzero group velocity at k=0. • Like in photogalvanic effect, the induced current can transport neutral atoms. [ABSTRACT FROM AUTHOR]

We calculate the tunneling conductance between the surface states on the opposite sides of an ultrathin film of a topological insulator in a parallel magnetic field. The parallel magnetic field produces a relative shift of the in-plane momenta of the two surfaces states. An overlap between the shifted Fermi circles and the spinor wave functions results in an unusual dependence of the tunneling conductance on the magnetic field. Because the spin orientation of the electronic surface states in topological insulators is locked to momentum, the spin polarization of the tunneling current can be controlled by the magnetic field. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel principle for photovoltaic (PV) energy conversion using surface acoustic waves (SAWs) in piezoelectric semiconductors. A SAW produces a periodically modulated electric potential, which spatially segregates photoexcited electrons and holes to the maxima and minima of the SAW potential. The moving SAW collectively transports the carriers with the speed of sound to the electrodes made of different materials, which extract electrons and holes separately and generate dc output. The proposed active design is expected to have higher efficiency than passive designs of the existing PV devices and to produce enough energy to sustain the SAW. [Copyright &y& Elsevier]

Abstract: We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a non-trivial distribution of log-returns for a given time interval , which has exponential tails and a Gaussian central part, in agreement with empirical observations. [Copyright &y& Elsevier]

Abstract: We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution. [Copyright &y& Elsevier]

Abstract: Angular magnetoresistance oscillations (AMRO) were originally discovered in organic conductors and then found in many other layered metals. It should be possible to observe AMRO to semiconducting bilayers as well. Here we present an intuitive geometrical interpretation of AMRO as the Aharonov–Bohm interference effect, both in real and momentum spaces, for balanced and imbalanced bilayers. Applications to the experiments with bilayers in tilted magnetic fields in the metallic state are discussed. We speculate that AMRO may be also observed when each layer of the bilayer is in the composite-fermion state. [Copyright &y& Elsevier]

We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dra˘gulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982–1999, we find a very good agreement between the theory and the data for a wide range of time lags from 1 to 250 days. On the other hand, deviations start to appear when the data for 2000–2002 are included. We interpret this as a statistical evidence of the major change in the market from a positive growth rate in 1980s and 1990s to a negative rate in 2000s. [Copyright &y& Elsevier]

We discuss a number of experiments that could detect the electron edge states in the organic quasi-one-dimensional conductors (TMTSF)2X and the inorganic quasi-two-dimensional perovskites Sr2RuO4. We consider the chiral edges states in the magnetic-field-induced spin-density-wave (FISDW) phase of (TMTSF)2X and in the time-reversal-symmetry-breaking triplet superconducting phase of Sr2RuO4, as well as the nonchiral midgap edge states in the triplet superconducting phase of (TMTSF)2X. The most realistic experiment appears to be an observation of spontaneous magnetic flux at the edges of Sr2RuO4 by a scanning SQUID microscope. [Copyright &y& Elsevier]

We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow-Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data for 1982-2001 follow the scaling function for seven orders of magnitude. [ABSTRACT FROM AUTHOR]

Ambitious scenarios of carbon emission redistribution for mitigating climate change in line with the Paris Agreement and reaching the sustainable development goal of eradicating poverty have been proposed recently. They imply a strong reduction in carbon footprint inequality by 2030 that effectively halves the Gini coefficient to about 0.25. This paper examines feasibility of these scenarios by analyzing the historical evolution of both weighted international inequality in CO 2 emissions attributed territorially and global inequality in carbon footprints attributed to end consumers. For the latter, a new dataset is constructed that is more comprehensive than existing ones, and footprints are found to be more unequal than territorial emissions. In both cases, we find a decreasing trend in global inequality, partially attributed to the move of China from the lower to the middle part of the distributio. Still, realization of the redistributive scenarios would require an unprecedented reduction in global inequality far below historical levels. Moreover, the territorial emissions data, available for more recent years up to 2017, show a saturation of the decreasing Gini coefficient at a level of 0.5. This observation confirms an earlier prediction based on maximal entropy reasoning that the Lorenz curve converges to the exponential distribution. This saturation further undermines feasibility of the redistributive scenarios, which are also hindered by structural tendencies that reinforce carbon footprint inequality under global capitalism. One way out of this conundrum is a fast decarbonization of the global energy supply in order to decrease global carbon emissions without relying crucially on carbon inequality reduction. [ABSTRACT FROM AUTHOR]

Surface states in topological insulators can be understood based on the well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case representing a sequence of layers connected via tunneling amplitudes t, which depend on the in-plane momentum p=(px,py). The Hamiltonian of the model is a 2×2 matrix with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the existence of the surface states depends on the complex function t(k,p). The surface states exist for those in-plane momenta p where the winding number of the function t(k,p) is nonzero when k is changed from 0 to 2π. The sign of the winding number determines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. Projection of the vortex line onto the space of the two-dimensional momentum p encircles the domain where the surface states exist. We illustrate how this approach works for a well-known model of a topological insulator on the diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. A topological transition occurs when the vortex lines reconnect from spiral to circular form. We apply the Shockley model to Bi2Se3 and discuss applicability of a continuous approximation for the description of the surface states. We conclude that the tight-binding model gives a better description of the surface states. [ABSTRACT FROM AUTHOR]

We calculate the energy spectrum of a Dirac double layer, where each layer has the Dirac electronic dispersion, in the presence of a tilted magnetic field and small interlayer tunneling. We show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic held. Using a semiclassical analysis, we show that these special tilt angles are determined by the Berry phase of the Dirac Hamiltonian. The interlayer tunneling conductance also exhibits an oscillatory dependence on the magnetic held tilt angle, known as the angular magnetoresistance oscillations (AMRO). Our results are applicable to graphene double layers and thin films of topological insulators. [ABSTRACT FROM AUTHOR]

We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient, G, has decreased from 0.66 in 1980 to 0.55 in 2010, indicating a decrease in inequality. The global probability distribution of energy consumption per capita in 2010 is close to the exponential distribution withG = 0:5. We attribute this result to the globalization of the world economy, which mixes the world and brings it closer to the state of maximal entropy. We argue that global energy production is a limited resource that is partitioned among the world population. The most probable partition is the one that maximizes entropy, thus resulting in the exponential distribution function. A consequence of the latter is the law of 1/3: the top 1/3 of the world population consumes 2/3 of produced energy. We also find similar results for the global probability distribution of CO2 emissions per capita. [ABSTRACT FROM AUTHOR]

We propose a novel chiral order parameter to explain the unusual polar Kerr effect in underdoped cuprates. It is based on the loop-current model by Varma, which is characterized by the in-plane anapole moment N and exhibits the magnetoelectric effect. We propose a helical structure where the vector N(n) in the layer n is twisted by the angle π/2 relative to N(n-1), thus breaking inversion symmetry. We show that coupling between magnetoelectric terms in the neighboring layers for this structure produces optical gyrotropy, which results in circular dichroism and the polar Kerr effect. [ABSTRACT FROM AUTHOR]

Abstract: We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility. [Copyright &y& Elsevier]

Over the last two centuries, the impact of the Human System has grown dramatically, becoming strongly dominant within the Earth System in many different ways. Consumption, inequality, and population have increased extremely fast, especially since about 1950, threatening to overwhelm the many critical functions and ecosystems of the Earth System. Changes in the Earth System, in turn, have important feedback effects on the Human System, with costly and potentially serious consequences. However, current models do not incorporate these critical feedbacks. We argue that in order to understand the dynamics of either system, Earth SystemModels must be coupled with Human SystemModels through bidirectional couplings representing the positive, negative, and delayed feedbacks that exist in the real systems. In particular, key Human System variables, such as demographics, inequality, economic growth, and migration, are not coupled with the Earth System but are instead driven by exogenous estimates, such as United Nations population projections.This makes current models likely to miss important feedbacks in the real Earth-Human system, especially those that may result in unexpected or counterintuitive outcomes, and thus requiring different policy interventions from current models.The importance and imminence of sustainability challenges, the dominant role of the Human System in the Earth System, and the essential roles the Earth System plays for the Human System, all call for collaboration of natural scientists, social scientists, and engineers in multidisciplinary research and modeling to develop coupled Earth-Human system models for devising effective science-based policies and measures to benefit current and future generations. [ABSTRACT FROM AUTHOR]

We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe2 nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature T, the increasing critical current Ic exhibits a sharp upturn at a temperature T* around 20% of the junction critical temperature for several different samples and various gate voltages. The Ic vs T demonstrates a short junction behavior for T>T*, but crosses over to a long junction behavior for T

A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high-temperature superconductors: the signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is nonexistent. The mechanism does not break global time-reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBa2Cu3O6+δ, in which intrabilayer tunneling nucleates a chiral d-density wave such that the individual layers have opposite chirality. Although specific to the chiral d-density wave, the mechanism may be more general to any quasi-two-dimensional orbital antiferromagnet in which time-reversal symmetry is broken in each plane, but not when averaged macroscopically. [ABSTRACT FROM AUTHOR]