188 research outputs found
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 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
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