The Politics of Memory: Otto Hahn and the Third Reich

As President of the Kaiser Wilhelm Society and its successor, the Max Planck Society, from 1946 until 1960, Otto Hahn (1879–1968) sought to portray science under the Third Reich as a purely intellectual endeavor untainted by National Socialism. I outline Hahn’s activities from 1933 into the postwar years, focusing on the contrast between his personal stance during the National Socialist period, when he distinguished himself as an upright non-Nazi, and his postwar attitude, which was characterized by suppression and denial of Germany’s recent past. Particular examples include Hahn’s efforts to help Jewish friends; his testimony for colleagues involved in denazification and on trial in Nuremberg; his postwar relationships with émigré colleagues, including Lise Meitner; and his misrepresentation of his wartime work in the Kaiser Wilhelm Institute for Chemistry.     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Local coexistence of different phases

Under intuitively reasonable assumptions it is shown that in two dimensions different phases cannot exist locally. In three dimensions we discuss the possibility of local coexistence of districts with different magnetization for the Heisenberg ferromagnet and show that an interaction that breaks rotational invariance is necessary for this phenomenon.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

单的完备Lie代数

给出了一个Ｈｅｉｓｅｎｂｅｒｇ代数与一个交换Ｌｉｅ代数的直和ｇ０的全形ｈ（ｇ０）和ｈ（ｇ０）的导子代数Ｄｅｒｈ（ｇ０）．证明了ｈ（ｇ０）不是一个完备Ｌｉｅ代数，但Ｄｅｒｈ（ｇ０）是一个单完备Ｌｉｅ代数．     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N1-A以及单个正常位与其余部分间的纠缠NL-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J1和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对NL-A,量子位L为奇数时,纠缠随杂质参数J1的变化与L=3类似,而L为偶数时纠缠随杂质参数|J1|的增加而增加.     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N_1-A以及单个正常位与其余部分间的纠缠N_L-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J₁和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N_1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对N_L-A, 量子位L为奇数时,纠缠随杂质参数J₁的变化与L=3类似,而L为偶数时纠缠随杂质参数|J₁|的增加而增加.     

Reciprocal Relativity of Noninertial Frames and the Quaplectic Group

The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds² = d t². Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest frame by making velocities relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements and . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group.     

Effects of Different Spin-Spin Couplings and Magnetic Fields on Thermal Entanglement in Heisenberg XYZ Chain

The effects of spin-spin interaction on thermed entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the Ji （i-axis spin-spin interaction）, the higher critical value the Bi （i-axis uniform magnetic field） has. Moreover, in the weak-field regime, the larger Ji corresponds to more entanglement, while in the strong-field regime, different Ji correspond to the same entanglement. In addition, it is found that with the increase of Ji, the concurrence can approach the maximum value more rapidly for the smaller Bi, and can reach a larger value for the smaller bi （i-axis nonuniform magnetic field）. So we can get more entanglement by increasing the spin-spin interaction Ji, or by decreasing the uniform magnetic field Bi and the nonuniform magnetic field hi.