Contact value relations and density functional theory for the electrical double layer

The recently developed contact-corrected density functional theory is applied to an electric double layer containing a valence and size symmetric electrolyte. The restricted primitive model is used to describe the electrolyte, and a non-polarisable, smooth, planar, uniformly charged hard surface is used to model the electrode. Comparison with Monte Carlo simulation results for this system shows that the theory satisfies the first contact value relation in line with the premise of the approach. Additionally, the theory is found to satisfy the semi-empirical second contact value relation quite closely. This is a welcome result, since no reference is made to this second relation nor is the relation used in the theoretical development. The second contact relation is closely related to the anomalous positive temperature derivative of the double layer capacitance at low temperature, low ion concentration, and low electrode charge, and indeed, the contact-corrected density functional theory predicts this effect.     

An extinction theorem for optical scattering

From a many-body theory of optical scattering we derive a relation for the collective behaviour of incoherently scattered light emerging from a molecular fluid. The relation involves a surface integral and has precisely the mathematical form of the Ewald-Oseen extinction theorem; it is exact in the sense of that theorem. We prove from the relation that scattered radiation is refracted and reflected at the surface of the scattering medium according to rules inferred from macroscopic optics. The relation provides a construction of contributions to the scattering with any number of internal reflections; it applies also to scattering restricted by stops. Explicit expressions for the surface dependent scattering in terms of a Fresnel transmissivity correct a previously reported theory of bulk scattering.     

等离子体重整化准线性理论中的渐近传播函数与色散关系

本文引入了系统中六维相空间的表象理论。利用这一理论分析了Misguich-Balescu所给出的单位子渐近传播算子和Dupree的平均格林函数之间的关系,发现在平稳过程中两者是一致的。从而解决了MB所给出非线性色散关系中共振函数的发散困难。指出产生发散困难的原因在于M-B在子动力学中引入的涨落产生算子的概念对多重时间尺度的摄动理论是不适用的。 关键词：     

Tree-level recursion relation and dual superconformal symmetry of the ABJM theory

We propose a recursion relation for tree-level scattering amplitudes in three-dimensional Chern-Simons-matter theories. The recursion relation involves a complex deformation of momenta which generalizes the BCFW-deformation used in higher dimensions. Using background field methods, we show that all tree-level superamplitudes of the ABJM theory vanish for large deformations, establishing the validity of the recursion formula. Furthermore, we use the recursion relation to compute six-point and eight-point component amplitudes and match them with independent computations based on Feynman diagrams or the Grassmannian integral formula. As an application of the recursion relation, we prove that all tree-level amplitudes of the ABJM theory have dual superconformal symmetry. Using generalized unitarity methods, we extend this symmetry to the cut-constructible parts of the loop amplitudes.     

Commutator of gauge generators in non-abelian chiral theory

Commutators among non-abelian fermion currents are calculated using the BJL limit. The relation between the covariant seagull and the gauge dependence of the fermion current is derived for a canonical non-abelian theory using the path integral formulation. We observe that in a non-abelian theory with coupling to chiral fermions this relation is violated and this produces a non-trivial commutator of gauge group generators.     

Planar amplitudes in maximally supersymmetric Yang-Mills theory

The collinear factorization properties of two-loop scattering amplitudes in dimensionally regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the anti-de Sitter/conformal field theory correspondence that the form of the large-N(c) L-loop amplitudes should be simple enough to allow a resummation to all orders.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

The Optimal Uncertainty Relation

Employing the lattice theory on majorization, the universal quantum uncertainty relation for any number of observables and general measurement is investigated. It is found that 1) the least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2) contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; and 3) the lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society.     

The properties of conformal blocks,the AGT hypothesis,and knot polynomials

Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern–Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.     

WDVV equation and triple-product relation

We study the relation between the WDVV equations and the τ-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the nontrivial equation for τ-function of the NC KP hierarchy, while the prepotential in the Seiberg–Witten (SW) theory has been identified to the τ-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show explicitly that Whitham hierarchy includes commutative Toda/KP hierarchy. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory.     

The physics of swarms and some basic questions of kinetic theory

This report provides an introduction to the physics of swarms to those interested in kinetic theory. After a brief historical sketch the principles of experiments and their phenomenological analysis are discussed. The relation of this analysis to kinetic theory and the potential of the experiments for studying the nature of hydrodynamic regime and the nonhydrodynamic effects is pointed out. Recent advances in the kinetic theory of swarms in free space are surveyed. They include results such as the generalised Einstein relations and others from the momentum transfer theory, which point to some interesting properties of the many averages that occur in kinetic theory and their relation to thermodynamics, as well as the more technical advances in analysing the structure of the collision operator and solutions of kinetic equations which have lead to very precise calculations of the transport coefficients. The use of theory and experiment in precise determination of cross-sections, potentials and reaction rates is illustrated. Observations showing the effects of finite enclosures are summarised and a theory of swarms in a finite enclosure is outlined. The implications of the subject for kinetic theory are discussed.     

Fourier analysis of wave turbulence in a thin elastic plate

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.     

The real gauge hierarchy problem

We discuss the problem of generating two vastly different mass scales through spontaneous symmetry breaking. We find that to all orders in perturbation theory this can only be achieved if there is a non-trivial relation between the couplings of the theory. While this relation may come from a higher symmetry we find that this symmetry can only be broken at the low mass scale.     

Measurements of the shear Alfvén wave dispersion for finite perpendicular wave number

Measurements of the dispersion relation for shear Alfvén waves as a function of the perpendicular wave number are reported for the regime in which V(A) approximately V(Te). By measuring the parallel phase velocity of the waves, the measurements can be compared directly to theoretical predictions of the dispersion relation for a parameter regime in which particle kinetic effects become important. The comparison shows that the best agreement between theory and experiment is achieved when a fully complex, warm plasma dispersion relation is used.     

Polarization processes in the ice lattice

The theory of electrical properties of ice by Jaccard is reviewed. Using a matrix notation it is shown that the theory can be extended to a larger class of defects and some discrepancies with an earlier formulation are explained. A universal relation between the electrical parameters is derived and allows a quantitative verification of the theory. Experimental data from ice doped with HF and NH₃, spreading over several decades in conductivity, can be collapsed on this relation.     

通过计算氢原子的玻尔半径,加深对量子力学的理解

通过玻尔理论基本假设、不确定关系、薛定谔方程以及波函数性质4种方法求氢原子的玻尔半径,理解了玻尔理论基本假设的半经典、半量子;不确定关系正是微观粒子波动性的必然结果;氢原子中电子遵从薛定谔方程,方程的解析即为波函数,是概率波.     

The influence of the second harmonic in the current-phase relation on the voltage-current characteristic of high TC DC SQUID

A theory for the voltage-current characteristic in high TC DC SQUIDs (Superconducting Quantum Interference Devices), which accounts for a second harmonic in the junction current-phase relation, is developed. It is shown that the small inductance DC SQUIDs can be used for the investigation of the second harmonic via its influence on the voltage-flux curve. If the second harmonic is perceptible, then for large inductance DC SQUIDs the theory can explain the substantial deviations of the experimental voltage modulation from theoretical predictions and computer simulations based on conventional sinusoidal current-phase relation. The detail comparison with the experiment is performed.     

Matone's Relation ofN =2 Super Yang-Mills and Spectrum of Toda Chain

InN=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation <
Trφ²>. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.     

Stokes-Einstein relation in supercooled aqueous solutions of glycerol

The diffusion of glycerol molecules decreases with decreasing temperature as its viscosity increases in a manner simply described by the Stokes-Einstein relation. Approaching the glass transition, this relation breaks down as it does with a number of other pure liquid glass formers. We have measured the diffusion coefficient for binary mixtures of glycerol and water and find that the Stokes-Einstein relation is restored with increasing water concentration. Our comparison with theory suggests that adding water postpones the formation of frustration domains.