Brownian fluctuations and heating of an optically aligned gold nanorod

We present the first quantitative measurements of the torque exerted on a single gold nanorod in a polarized three-dimensional optical trap. We determined the torque both by observing the time-averaged orientation distribution and by measuring the dynamics of the rotational brownian fluctuations. The measurements are in good agreement with calculations, where the temperature profile around the hot nanorod gives rise to a reduced, effective viscosity. The maximum torque on a 60 nm×25 nm nanorod was 100 pN·nm, large enough to address single-molecule processes in soft and biological matter.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

An integrable SU(3) spin chain

An integrable SU(3) soin chain equation is constructed. An explicit form of the Lax-pair representation is given and it is shown to be gauge equivalent to a set of nonlinear Schrödinger- type equations for three complex variables.     

A reaction-diffusion equation for a cyclic system with three components

The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.     

On the dynamics of a continuum spin system

For a one-dimensional system of classical spins with nearest neighbour Heisenberg interaction we derive the equation of motion for each three-dimensional spin vector. In the continuum limit where the spins lie dense on a line this set of equations reduces to a nonlinear partial differential equation. In addition to spin-wave solutions we obtain some other special solutions of this equation. In particular we find solitary waves having total energy localised in a finite region, with velocity of propagation inversely proportional to the width of this region. Solutions of still another type are shown to have a diffusive character. The stability of such solutions and the possibility of interaction of two or more solitary waves have not yet been studied.     

Renormalization group solution of the one-dimensional classical Heisenberg model

It is shown that the method of Van Leeuwen^1,2) and Nauenberg and Nienhuis³) in the application of the renormalization theory to Ising-like spin systems, can easily be extended to include all one-dimensional classical spin systems with nearest neighbor interactions. The series for the free energy converges very rapidly towards the known exact value (for Heisenberg interaction), provided that the temperature is not too close to the critical temperature T = 0.     

Quantum aspects of triangular billiards

The energy spectrum of a particle enclosed in a two-dimensional triangular box can in general not be calculated analytically. Therefore, in order to establish the degree of intergrability, using some well known criteria, this spectrum must be calculated numerically.

For more than 800 triangles these calculations were performed and then used to check a number of conjectures found in the literature. For almost all of them we find counter examples.

Our own suggestion is that in general acute triangles are more integrable than obtuse ones. However, also this rule has its exceptions, which cannot be explained away by some triangles being more rational than others.