采用正方元胞的Ising模型实空间重正化群解

在二维正方形晶格上,将元胞取为4格点正方形,采用3种不同的规则定义块自旋状态,进行了重正化群计算,得出了更为精确的结果;解决了元胞内格点数为偶数的重正化群计算问题.     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

在同位旋SU(2)不变耦合模型中研究 p pbar -> n nbar 核子反应的重整化无穷阶链图效应

本文采用描述中性及荷电 pion 介子（pion0,pion+,pion-）与核子-反核子强相互作用的同位旋SU(2)不变耦合模型,计算出在pion0 及 pion+, pion- 重整化链图传播下 p pbar -> n nbar 核子反应微分截面的“精确”解析结果;并且将此结果与在 pion0 及 pion+, pion- 树图传播下的微分截面作了对比分析,得到相应的辐射修正重要信息。本文完成的工作对进一步深入研究三种荷电状态 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型以及深入理论探讨质子-反质子对撞实验,都将提供某些理论研究的参考价值。     

On the predictivity of the non‐renormalizable quantum field theories

Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non‐renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological renormalization is introduced, which keeps a finite value for the parameters of the theory by trading the usual order‐by‐order renormalization procedure for an order‐by‐order redefinition of the perturbative vacuum. One additional measurement is then sufficient to systematically compute quantum corrections at any loop order, with no need of absorbing ultraviolet infinities in the Lagrangian.     

Kondo effect for electron transport through an artificial quantum dot

We have calculated the transport properties of electron through an artificial quantum dot by using the numerical renormalization group technique in this paper. We obtain the conductance for the system of a quantum dot which is embedded in a one-dimensional chain in zero and finite temperature cases. The external magnetic field gives rise to a negative magnetoconductance in the zero temperature case. It increases as the external magnetic field increases. We obtain the relation between the coupling coefficient and conductance. If the interaction is big enough to prevent conduction electrons from tunnelling through the dot, the dispersion effect is dominant in this case. In the Kondo temperature regime, we obtain the conductivity of a quantum dot system with Kondo correlation.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

Trees, Renormalization and Differential Equations

The Butcher group and its underlying Hopf algebra of rooted trees were originally formulated to describe Runge–Kutta methods in numerical analysis. In the past few years, these concepts turned out to have far-reaching applications in several areas of mathematics and physics: they were rediscovered in noncommutative geometry, they describe the combinatorics of renormalization in quantum field theory. The concept of Hopf algebra is introduced using a familiar example and the Hopf algebra of rooted trees is defined. Its role in Runge–Kutta methods, renormalization theory and noncommutative geometry is described.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度，在应用于二维或准二维问题时，要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略，可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分，实现了数据的分布式存储，并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例，测试了异构并行程序在不同DMRG保留状态数下的运行表现，并给出了相应的性能基准.应用于4腿梯子时，观测到了高温超导中常见的电荷密度条纹，此时保留状态数达到10⁴，使用的GPU显存小于12 GB.     

Electrophoretic evidence for a new type of counterion condensation

A systematic capillary electrophoresis study uncovered how polyelectrolyte effective charge density varies with backbone charge spacing and solvent dielectric constant. The study primarily focused on aliphatic ionenes, a special class of polyelectrolytes, which possess regularly spaced quaternary ammonium groups in the backbone. Complete ionization of functional units and good solvency in water or mixtures of water with lower dielectric constant solvents (methanol, acetonitrile) enabled continuous measurements of ionene effective charge density through the onset of counterion condensation. Ionenes with both uniform and alternating charge spacing were examined. As expected, effective charge density rose linearly with fixed charge density to a critical value, above which effective charge density remained constant. Deviating from expectation, the onset of condensation did not occur at a critical fixed charge density. Instead, condensation initiated at a constant critical Bjerrum length. The same onset condition was found for quaternized poly(vinyl pyridine)s. These experimental results suggest a new form of condensation, one driven by ion-pairing of polyelectrolyte with counterions. In support of this hypothesis, the onset of condensation appeared to correlate with counterion size. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3616–3627, 2004