Exact boundary conditions at finite distance for the time-dependent Schrodinger equation

Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.Comment: Latex.tar.gz file, 20 pages, 9 figure

Driven Morse Oscillator: Model for Multi-photon Dissociation of Nitrogen Oxide

Within a one-dimensional semi-classical model with a Morse potential the possibility of infrared multi-photon dissociation of vibrationally excited nitrogen oxide was studied. The dissociation thresholds of typical driving forces and couplings were found to be similar, which indicates that the results were robust to variations of the potential and of the definition of dissociation rate. PACS: 42.50.Hz, 33.80.WzComment: old paper, 8 pages 6 eps file

Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution

The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wavepackets(WP). An open question is how time dependent expectation values can be calculated when the Hamiltonian is NH ? Using the F-product formalism, which was recently proposed, [J. Phys. Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of different observable quantities for a simple well known study test case model Hamiltonian. We carry out a comparison between these results with those obtained from conventional(i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in the NH-QM, unlike standard QM, there is no need to split the entire space into two regions; i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review

Quantum Dynamics of Spin Wave Propagation Through Domain Walls

Through numerical solution of the time-dependent Schrodinger equation, we demonstrate that magnetic chains with uniaxial anisotropy support stable structures, separating ferromagnetic domains of opposite magnetization. These structures, domain walls in a quantum system, are shown to remain stable if they interact with a spin wave. We find that a domain wall transmits the longitudinal component of the spin excitations only. Our results suggests that continuous, classical spin models described by LLG equation cannot be used to describe spin wave-domain wall interaction in microscopic magnetic systems

Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By constrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.Comment: 4 pages, 5 EPS figure

New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page

Inner ear tissue preservation by rapid freezing: improving fixation by high-pressure freezing and hybrid methods

In the preservation of tissues in as ‘close to life’ state as possible, rapid freeze fixation has many benefits over conventional chemical fixation. One technique by which rapid freeze-fixation can be achieved, high pressure freezing (HPF), has been shown to enable ice crystal artefact-free freezing and tissue preservation to greater depths (more than 40μm) than other quick-freezing methods. Despite increasingly becoming routine in electron microscopy, the use of HPF for the fixation of inner ear tissue has been limited. Assessment of the quality of preservation showed routine HPF techniques were suitable for preparation of inner ear tissues in a variety of species. Good preservation throughout the depth of sensory epithelia was achievable. Comparison to chemically fixed tissue indicated that fresh frozen preparations exhibited overall superior structural preservation of cells. However, HPF fixation caused characteristic artefacts in stereocilia that suggested poor quality freezing of the actin bundles. The hybrid technique of pre-fixation and high pressure freezing was shown to produce cellular preservation throughout the tissue, similar to that seen in HPF alone. Pre-fixation HPF produced consistent high quality preservation of stereociliary actin bundles. Optimising the preparation of samples with minimal artefact formation allows analysis of the links between ultrastructure and function in inner ear tissues

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure

A twist in chiral interaction between biological helices

Using an exact solution for the pair interaction potential, we show that long, rigid, chiral molecules with helical surface charge patterns have a preferential interaxial angle ~((RH)^1/2)/L, where L is the length of the molecules, R is the closest distance between their axes, and H is the helical pitch. Estimates based on this formula suggest a solution for the puzzle of small interaxial angles in a-helix bundles and in cholesteric phases of DNA.Comment: 7 pages, 2 figures, PDF file onl

Extended Gaussian wave packet dynamics

We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found, and relationships are explored between the squeezed system, Gaussian wave packet dynamics, the time dependent harmonic oscillator, and wave packet dynamics in a Gauss-Hermite basis. Expressions are given for the matrix elements of the potential in some simple cases. Several examples are given, including the propagation of a non-Gaussian initial state in a Morse potential