Classical Aspects of Quantum Walls in One Dimension

We investigate the system of a particle moving on a half line x >= 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering with the quantum wall, and also by examining the WKB-exactness of the transition kernel based on the regularized potentials. It is shown that no classical counterpart exists for walls with L < 0, and that the WKB-exactness can hold only for L = 0 and L = infinity.Comment: TeX, 21 pages, 4 figures. v2: some parts of the text improved, new and improved figure

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page

Extensional rupture of model non-Newtonian fluid filaments

We present molecular dynamics computer simulations of filaments of model non-Newtonian liquid stretched in a uniaxial deformation to the point of breaking. The liquid consists of Lennard-Jones monomers bound into chains of 100 monomers by nonlinear springs, and several different constant velocity and constant strain rate deformations are considered. Generally we observe nonuniform extensions originating in an interplay between the stretching forces and elastic and capillary restoring mechanisms, leading to highly uneven shapes and alternating stretched and unstretched regions of liquid. Except at the fastest pulling speeds, the filaments continue to thin indefinitely and break only when depleted of molecules, rather than common viscoelastic rupture mechanisms.Comment: 7 pages text, 14 pages (eps) figure

Two fermion relativistic bound states: hyperfine shifts

We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suited for numerical computations, that allows to calculate the hyperfine shifts for any level, according to well established physical arguments that the Breit term must be treated at the first perturbative order. We discuss our results, comparing them with the corresponding values obtained from semi-classical expansions.Comment: 16 page

A Condensation-Ordering Mechanism in Nanoparticle-Catalyzed Peptide Aggregation

Nanoparticles introduced in living cells are capable of strongly promoting the aggregation of peptides and proteins. We use here molecular dynamics simulations to characterise in detail the process by which nanoparticle surfaces catalyse the self- assembly of peptides into fibrillar structures. The simulation of a system of hundreds of peptides over the millisecond timescale enables us to show that the mechanism of aggregation involves a first phase in which small structurally disordered oligomers assemble onto the nanoparticle and a second phase in which they evolve into highly ordered beta-sheets as their size increases

Microscopic calculations of medium effects for 200-MeV (p,p') reactions

We examine the quality of a G-matrix calculation of the effective nucleon-nucleon (NN) interaction for the prediction of the cross section and analyzing power for 200-MeV (p,p') reactions that populate natural parity states in $^{16}$O, $^{28}$Si, and $^{40}$Ca. This calculation is based on a one-boson-exchange model of the free NN force that reproduces NN observables well. The G-matrix includes the effects of Pauli blocking, nuclear binding, and strong relativistic mean-field potentials. The implications of adjustments to the effective mass ansatz to improve the quality of the approximation at momenta above the Fermi level will be discussed, along with the general quality of agreement to a variety of (p,p') transitions.Comment: 36 pages, TeX, 18 figure