Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

Nonlinear Dynamics of a Three‐Wave CO2 Laser with Loss Modulation

The nonlinear dynamics of a CO₂ laser having continuous electrical discharge pumping and loss modulation and generating in three vibrationalpm333325601150/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">rotational lines of the same vibrational band is investigated theoretically. It is shown that it is possible to monitor the time and energy parameters of radiation in rather wide ranges by changing the depth and frequency of modulation and also the relationship between the constant components of losses. The character of the response of the threepm333325601150/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">wave laser in loss modulation in one or two channels at certain parameters is similar to the response of a system with two degrees of freedom. In loss modulation simultaneously in three channels the response is equivalent to the response of a system with one degree of freedom.     

Microscopic interactions in CuGeO 3 and organic Spin-Peierls systems deduced from their pretransitional lattice fluctuations

CuGeO₃ exhibits a Spin-Peierls (SP) transition, at T _SP = 14.3 K, which is announced above 19 K by an important regime of one-dimensional (1D) pretransitional lattice fluctuations which can be detected until about 40 K using X-ray diffuse scattering investigations. A quantitative analysis of this scattering shows that in this 1D direction the correlation length follows the “universal” behaviour expected for the thermal fluctuations of a real order parameter which characterizes the lattice dimerization. This allows to define a 1D mean-field temperature, T _SP ^MF , of about 60 K and invalidates any mean field scenario for the SP transition of CuGeO₃. As T _SP ^MF is as high as 4 T _SP we propose that the 3D-SP order is achieved by the interchain coupling between 1D solitons which form below about 16-20 K. CuGeO₃ being in the non-adiabatic regime, it is also suggested that the observed pretransitional fluctuations of CuGeO₃ originate from the X-ray scattering on a very broad damped critical response of lower frequency than the “critical” phonon modes. From the quantitative analysis of the 1D fluctuations we also estimate the microscopic parameters of the SP chain. These parameters allow to locate CuGeO₃ close to the quantum critical boundary separating the gapped SP ground state to the ungapped anti-ferromagnetic ground state. The vicinity of a quantum critical point emphasizes the role of the quantum and non-adiabatic fluctuations and the importance of the interchain coupling in the physics of CuGeO₃. Finally we compare these findings with those obtained for the organic SP systems (BCPTTF)₂PF₆, (TMTTF)₂PF₆ and MEM(TCNQ)₂. From a similar analysis of the pretransitional lattice fluctuations it is found that (BCPTTF)₂PF₆ and (TMTTF)₂PF₆ are located on the SP gapped classical-quantum boundary and are in the adiabatic regime where the fluctuations lead to the formation of a pseudo-gap in the spin degrees of freedom. Differently, we place MEM(TCNQ)₂ inside the SP quantum phase around the crossover line between the adiabatic and non-adiabatic regimes. Received 13 September 2000 and Received in final form 6 February 2001     

A model dielectric response function for metallic nanotube ropes

We propose a model dielectric function for ropes of single-walled nanotubes distributed in a glassy graphite host medium. We study the significance of the bosonic charge excitations arising in interacting quasi-one-dimensional systems in the screening processes. We also pay special attention to the role of the intertube Coulomb interactions. In order to compare with experiments, weak relaxation processes are also considered in the relaxation-time approximation.     

Global Solutions of Multidimensional Approximate Navier–Stokes Equations of a Viscous Gas

Considering the simplified Navier–Stokes equations for the motion of a viscous gas under the adherence condition, we define a weak solution and prove an existence theorem by means of a priori estimates.     

Dielectric and conductivity relaxation in mixtures of glycerol with LiCl

We report a thorough dielectric characterization of the α relaxation of glass-forming glycerol with varying additions of LiCl. Nine salt concentrations from 0.1 to 20mol% are investigated in a frequency range of 20Hz-3GHz and analyzed in the dielectric loss and modulus representation. Information on the dc conductivity, the dielectric relaxation time (from the loss) and the conductivity relaxation time (from the modulus) is provided. Overall, with increasing ion concentration, a transition from reorientationally to translationally dominated behavior is observed and the translational ion dynamics and the dipolar reorientational dynamics become successively coupled. This gives rise to the prospect that, by adding ions to dipolar glass formers, dielectric spectroscopy may directly couple to the translational degrees of freedom determining the glass transition, even in frequency regimes where usually strong decoupling is observed.     

Asymptotics of the reduced logarithmic capacity of a narrow cylinder

We consider the Dirichlet problem for the Laplace operator in the exterior of a narrow infinite cylinder with periodically varying directrix. The solution is sought in the class of functions logarithmically increasing as the distance from the cylinder is increased. The reduced logarithmic capacity is defined as a generalization of the logarithmic capacity (of the outer conformal radius).We construct and justify the asymptotics of the solution of the problem as the ratio of the diameter of the cross-section of the cylinder to its period tends to zero.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 16–27.Original Russian Text Copyright © 2005 by I. I. Argatov.This revised version was published online in April 2005 with a corrected issue number.     

The local index and the Swan conductor

In this paper we study local indices of systems of p-adic linearly differential equations which arise from p-adic representations of the absolute Galois group of local field of characteristic p with finite monodromy. We show the induction formula of the local index of p-adic differential equations and prove the equality between the local index of differential equations and the Swan conductor of p-adic Galois representations by inductive methods.     

基于覆盖模型的pm2.5监测站点布局优化方法研究

科学的监测站点选址与布局优化是pm2.5等空气污染监测面临的重要问题.针对pm2.5重点监测城市哈尔滨,分析了影响pm2.5浓度及分布的主要因素,构建了以区域地理邻接关系及覆盖水平为基础的监测设施覆盖模型.模型综合了人口、地域面积以pm2.5关注度等因素,实现了重点监测区域覆盖指数及总体覆盖水平最大化目标.实证分析说明了模型的有效性和实用性,为相关环境监测网点选址和优化问题提供了科学的依据和参考.     

An extremal property of Fekete polynomials

The Fekete polynomials are defined as

where is the Legendre symbol. These polynomials arise in a number of contexts in analysis and number theory. For example, after cyclic permutation they provide sequences with smallest known norm out of the polynomials with pm 1$"> coefficients.

The main purpose of this paper is to prove the following extremal property that characterizes the Fekete polynomials by their size at roots of unity.

Theorem 0.1. Let with odd and pm 1$">. If

then must be an odd prime and is pm F_q(x)$">. Here

This result also gives a partial answer to a problem of Harvey Cohn on character sums.