Pre-acceleration from Landau-Lifshitz Series

The Landau-Lifshitz equation is considered as an approximation of the Abraham-Lorentz-Dirac equation. It is derived from the Abraham-Lorentz-Dirac equation by treating radiation reaction terms as a perturbation. However, while the Abraham-Lorentz-Dirac equation has pathological solutions of pre-acceleration and runaway, the Landau-Lifshitz equation and its finite higher order extensions are free of these problems. So it seems mysterious that the property of solutions of these two equations is so different. In this paper we show that the problems of pre-acceleration and runaway appear when one consider a series of all-order perturbation which we call it the Landau-Lifshitz series. We show that the Landau-Lifshitz series diverges in general. Hence a resummation is necessary to obtain a well-defined solution from the Landau-Lifshitz series. This resummation leads the pre-accelerating and the runaway solutions. The analysis is focusing on the non-relativistic case, but we can extend the results obtained here to relativistic case at least in one dimension.Comment: 16 page

Uniform-Price Mechanism Design for a Large Population of Dynamic Agents

This paper focuses on the coordination of a large population of dynamic agents with private information over multiple periods. Each agent maximizes the individual utility, while the coordinator determines the market rule to achieve group objectives. The coordination problem is formulated as a dynamic mechanism design problem. A mechanism is proposed based on the competitive equilibrium of the large population game. We derive the conditions for the general nonlinear dynamic systems under which the proposed mechanism is incentive compatible and can implement the social choice function in $\epsilon$-Nash equilibrium. In addition, we show that for linear quadratic problems with bounded parameters, the proposed mechanism can maximize the social welfare subject to a total resource constraint in $\epsilon$-dominant strategy equilibrium

Dynamic range maximization in excitable networks

We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which the critical state is reached when the largest eigenvalue of the weighted non-backtracking (WNB) matrix is exactly one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintain the largest size of the giant connected component.Comment: 10 pages, 8 figure

Quiver Chern-Simons Theories, D3-branes and Lorentzian Lie 3-algebras

We show that the Bagger-Lambert-Gustavsson (BLG) theory with two pairs of negative norm generators is derived from the scaling limit of an orbifolded Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The BLG theory with many Lorentzian pairs is known to be reduced to the Dp-brane theory via Higgs mechanism, so our scaling procedure can be used to derive Dp-branes directly from M2-branes in the field theory language. In this paper, we focus on the D3-brane case and investigate the scaling limits of various quiver Chern-Simons theories obtained from different orbifolding actions. Remarkably, in the case of N=2 quiver CS theories, the resulting D3-brane action covers a larger region in the parameter space of the complex structure moduli than the N=4 quiver CS theories. We also investigate how the SL(2,Z) duality transformation is realized in the resultant D3-brane theory.Comment: 27 pages, 5 figures. v2: minor corrections, references added, published versio

Can we detect "Unruh radiation" in the high intensity lasers?

An accelerated particle sees the Minkowski vacuum as thermally excited, which is called the Unruh effect. Due to an interaction with the thermal bath, the particle moves stochastically like the Brownian motion in a heat bath. It has been discussed that the accelerated charged particle may emit extra radiation (the Unruh radiation) besides the Larmor radiation, and experiments are under planning to detect such radiation by using ultrahigh intensity lasers. There are, however, counterarguments that the radiation is canceled by an interference effect between the vacuum fluctuation and the radiation from the fluctuating motion. In this reports, we review our recent analysis on the issue of the Unruh radiation. In this report, we particularly consider the thermalization of an accelerated particle in the scalar QED, and derive the relaxation time of the thermalization.Comment: A contribution to the proceeding of PIF201

On Social Optima of Non-Cooperative Mean Field Games

This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean field term that depends on the mean of the population states. We show that under some mild conditions any $\epsilon$-Nash equilibrium of the mean field game coincides with the optimal solution to a convex social welfare optimization problem. The results are proved based on a general formulation in the functional spaces and can be applied to a variety of mean field games studied in the literature. Our result also implies that the computation of the mean field equilibrium can be cast as a convex optimization problem, which can be efficiently solved by a decentralized primal dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach

Unruh radiation and Interference effect

A uniformly accelerated charged particle feels the vacuum as thermally excited and fluctuates around the classical trajectory. Then we may expect additional radiation besides the Larmor radiation. It is called Unruh radiation. In this report, we review the calculation of the Unruh radiation with an emphasis on the interference effect between the vacuum fluctuation and the radiation from the fluctuating motion. Our calculation is based on a stochastic treatment of the particle under a uniform acceleration. The basics of the stochastic equation are reviewed in another report in the same proceeding. In this report, we mainly discuss the radiation and the interference effect.Comment: A contribution to the proceeding of PIF201

Quantum radiation produced by a uniformly accelerating charged particle in thermal random motion

We investigate the properties of quantum radiation produced by a uniformly accelerating charged particle undergoing thermal random motions, which originates from the coupling to the vacuum fluctuations of the electromagnetic field. Because the thermal random motions are regarded to result from the Unruh effect, this quantum radiation is termed Unruh radiation. The energy flux of Unruh radiation is negative and smaller than that of Larmor radiation by one order in a/m, where a is the constant acceleration and m is the mass of the particle. Thus, the Unruh radiation appears to be a suppression of the classical Larmor radiation. The quantum interference effect plays an important role in this unique signature. The results is consistent with the predictions of a model consisting of a particle coupled to a massless scalar field as well as those of the previous studies on the quantum effect on the Larmor radiation.Comment: 6 pages, 4 figures, Physical Review D, in pres

Connections between Mean-Field Game and Social Welfare Optimization

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the $\epsilon$-Nash equilibrium of the mean-field game coincides with the optimal solution to a social welfare optimization problem, and this is true even when the individual cost functions are non-convex. The connection enables us to evaluate and promote the efficiency of the mean-field equilibrium. In addition, it also leads to several important implications on the existence, uniqueness, and computation of the mean-field equilibrium. Numerical results are presented to validate the solution, and examples are provided to show the applicability of the proposed approach

Quantum radiation from a particle in an accelerated motion coupled to vacuum fluctuations

A particle in a uniformly accelerated motion exhibits Brownian random motions around the classical trajectory due to the coupling to the field vacuum fluctuations. Previous works show that the Brownian random motions satisfy the energy equipartition relation. This thermal property is understood as the consequence of the Unruh effect. In the present work, we investigate the radiation from the thermal random motions of an accelerated particle coupled to vacuum fluctuations. The energy flux of this radiation is negative of the order smaller than the classical radiation by the factor a/m, where a is the acceleration constant and m is the mass of a particle. The results could be understood as a suppression of the classical radiation by the quantum effect.Comment: 14 pages, typos correcte