There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Physical Review B

Tables of integrals

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.

/pdf/casimir-forces-between-arbitrary-compact-objects-4d7vs7cg9w.pdf

Casimir forces between arbitrary compact objects.

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

/pdf/scattering-theory-approach-to-electrodynamic-casimir-forces-4fowlblwlj.pdf

Scattering theory approach to electrodynamic Casimir forces

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay $\ensuremath{\sim}L/[{H}^{3}\mathrm{ln}﻿(H/R)]$ at large plate-cylinder separations $H$ ($L$ and $R$ are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

/pdf/casimir-interaction-between-a-plate-and-a-cylinder-wqyw931dsc.pdf

Casimir Interaction between a Plate and a Cylinder

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy dE in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for dE as a function of the ratio of the mean plate distance H, to the corrugation length l :F orl o H we find a slower decay H 24 , compared to the H 25 behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for l ? H.

/pdf/probing-the-strong-boundary-shape-dependence-of-the-casimir-11fryyi4vo.pdf

Thorsten Emig

Papers

Casimir forces between arbitrary compact objects.

Scattering theory approach to electrodynamic Casimir forces

Casimir Interaction between a Plate and a Cylinder

Scattering theory approach to electrodynamic Casimir forces

Probing the Strong Boundary Shape Dependence of the Casimir Force