Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.Comment: 4 pages, plain tex, UMTG-16

Numerical Methods for the 3-dimensional 2-body Problem in the Action-at-a-Distance Electrodynamics

We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes that a step of integration can be taken as a step of light ladder, which limits its use to shallow energies. The second method is an improvement of pre-existing iterative schemes, designed for stronger convergence and can be used at high-energies.Comment: 17 pages, 11 figure

Single-Sweep Methods for Free Energy Calculations

A simple, efficient, and accurate method is proposed to map multi-dimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [Maragliano & Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)] with a variational reconstruction method using radial-basis functions for the representation of the free energy. TAMD is used to rapidly sweep through the important regions of the free energy landscape and compute the gradient of the free energy locally at points in these regions. The variational method is then used to reconstruct the free energy globally from the mean force at these points. The algorithmic aspects of the single-sweep method are explained in detail, and the method is tested on simple examples, compared to metadynamics, and finally used to compute the free energy of the solvated alanine dipeptide in two and four dihedral angles

Boundary S Matrix for the XXZ Chain

We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-1/2 chain with diagonal boundary magnetic fields in the noncritical regime (Delta > 1). Our result, which is formulated in terms of q-gamma functions, agrees with the vertex-operator result of Jimbo et al.Comment: 9 pages, LaTeX, no figure

Direct Calculation of the Boundary SS Matrix for the Open Heisenberg Chain

We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions.Comment: 29 pages, plain TEX, UMTG-17