4,236 research outputs found
Real-time propagator eigenstates
Obtaining a numerical solution of the time-dependent Schrödinger equation requires an initial state for the time evolution. If the system Hamiltonian can be split into a time-independent part and a time-dependent perturbation, the initial state is typically chosen as an eigenstate of the former. For propagation using approximate methods such as operator splitting, we show that both imaginary-time evolution and diagonalization of the time-independent Hamiltonian produce states that are not exactly stationary in absence of the perturbation. In order to avoid artifacts from these non-stationary initial states, we propose an iterative method for calculating eigenstates of the real-time propagator. We compare the performance of different initial states by simulating ionization of a model atom in a short laser pulse and we demonstrate that much lower noise levels can be achieved with the real-time propagator eigenstates
Fourth order real space solver for the time-dependent Schr\"odinger equation with singular Coulomb potential
We present a novel numerical method and algorithm for the solution of the 3D
axially symmetric time-dependent Schr\"odinger equation in cylindrical
coordinates, involving singular Coulomb potential terms besides a smooth
time-dependent potential. We use fourth order finite difference real space
discretization, with special formulae for the arising Neumann and Robin
boundary conditions along the symmetry axis. Our propagation algorithm is based
on merging the method of the split-operator approximation of the exponential
operator with the implicit equations of second order cylindrical 2D
Crank-Nicolson scheme. We call this method hybrid splitting scheme because it
inherits both the speed of the split step finite difference schemes and the
robustness of the full Crank-Nicolson scheme. Based on a thorough error
analysis, we verified both the fourth order accuracy of the spatial
discretization in the optimal spatial step size range, and the fourth order
scaling with the time step in the case of proper high order expressions of the
split-operator. We demonstrate the performance and high accuracy of our hybrid
splitting scheme by simulating optical tunneling from a hydrogen atom due to a
few-cycle laser pulse with linear polarization
Lifshitz quasinormal modes and relaxation from holography
We obtain relaxation times for field theories with Lifshitz scaling and with
holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by
computing quasinormal modes of a bulk scalar field in the presence of Lifshitz
black branes. We determine the relation between relaxation time and dynamical
exponent z, for various values of boundary dimension d and operator scaling
dimension. It is found that for d>z+1, at zero momenta, the modes are
non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1
and zero momenta, we present analytical results.Comment: 16 pages and 5 figure
From Classical to Wave-Mechanical Dynamics
The time-independent Schroedinger and Klein-Gordon equations - as well as any
other Helmholtz-like equation - were recently shown to be associated with exact
sets of ray-trajectories (coupled by a "Wave Potential" function encoded in
their structure itself) describing any kind of wave-like features, such as
diffraction and interference. This property suggests to view Wave Mechanics as
a direct, causal and realistic, extension of Classical Mechanics, based on
exact trajectories and motion laws of point-like particles "piloted" by de
Broglie's matter waves and avoiding the probabilistic content and the
wave-packets both of the standard Copenhagen interpretation and of Bohm's
theory.Comment: 15 pages, 1 figure. Substantial updates. arXiv admin note: text
overlap with arXiv:1310.807
Sub-barrier Coulomb effects on the interference pattern in tunneling ionization photoelectron spectra
We use a quantum trajectory-based semi-classical method to account for
Coulomb interaction between the photoelectron and the parent ion in the
classically forbidden, sub-barrier region during strong-field tunneling
ionization processes. We show that---besides the well-known modification of the
tunneling ionization probability---there is also an influence on the
interference pattern in the photoelectron spectra. In the long-wavelength
limit, the shift of the intra-cycle interference fringes caused by sub-barrier
Coulomb effects in the laser polarization direction can be derived
analytically. We compare our results with \emph{ab initio} solutions of the
time-dependent Schr\"odinger equation and find good agreement in the
long-wavelength regime, whereas the standard strong field approximation fails.
We show that the nodal structure along low-order above-threshold ionization
rings is also affected by sub-barrier Coulomb effects.Comment: 10 pages, 4 figures, RevTe
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