530 research outputs found
Interference in Bohmian Mechanics with Complex Action
In recent years, intensive effort has gone into developing numerical tools
for exact quantum mechanical calculations that are based on Bohmian mechanics.
As part of this effort we have recently developed as alternative formulation of
Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP
{125}, 231103 (2006)]. In the alternative formulation there is a significant
reduction in the magnitude of the quantum force as compared with the
conventional Bohmian formulation, at the price of propagating complex
trajectories. In this paper we show that Bohmian mechanics with complex action
is able to overcome the main computational limitation of conventional Bohmian
methods -- the propagation of wavefunctions once nodes set in. In the vicinity
of nodes, the quantum force in conventional Bohmian formulations exhibits rapid
oscillations that pose severe difficulties for existing numerical schemes. We
show that within complex Bohmian mechanics, multiple complex initial conditions
can lead to the same real final position, allowing for the description of nodes
as a sum of the contribution from two or more crossing trajectories. The idea
is illustrated on the reflection amplitude from a one-dimensional Eckart
barrier. We believe that trajectory crossing, although in contradiction to the
conventional Bohmian trajectory interpretation, provides an important new tool
for dealing with the nodal problem in Bohmian methods
Tailoring many-body entanglement through local control
We construct optimal time-local control pulses based on a multipartite
entanglement measure as target functional. The underlying control Hamiltonians
are derived in a purely algebraic fashion, and the resulting pulses drive a
composite quantum system rapidly into that highly entangled state which can be
created most efficiently for a given interaction mechanism, and which bears
entanglement that is robust against decoherence. Moreover, it is shown that the
control scheme is insensitive to experimental imperfections in first order.Comment: 12 pages, 11 figure
Phase Space Approach to Solving the Time-independent Schr\"odinger Equation
We propose a method for solving the time independent Schr\"odinger equation
based on the von Neumann (vN) lattice of phase space Gaussians. By
incorporating periodic boundary conditions into the vN lattice [F. Dimler et
al., New J. Phys. 11, 105052 (2009)] we solve a longstanding problem of
convergence of the vN method. This opens the door to tailoring quantum
calculations to the underlying classical phase space structure while retaining
the accuracy of the Fourier grid basis. The method has the potential to provide
enormous numerical savings as the dimensionality increases. In the classical
limit the method reaches the remarkable efficiency of 1 basis function per 1
eigenstate. We illustrate the method for a challenging two-dimensional
potential where the FGH method breaks down.Comment: 5 figures. Includes supplementary material. arXiv admin note:
substantial text overlap with arXiv:1010.258
WavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories
WavePacket is an open-source program package for numerical simulations in
quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213,
223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt
with quantum dynamics of closed and open systems, respectively, the present
Part III adds fully classical and mixed quantum-classical propagations to
WavePacket. In those simulations classical phase-space densities are sampled by
trajectories which follow (diabatic or adiabatic) potential energy surfaces. In
the vicinity of (genuine or avoided) intersections of those surfaces
trajectories may switch between surfaces. To model these transitions, two
classes of stochastic algorithms have been implemented: (1) J. C. Tully's
fewest switches surface hopping and (2) Landau-Zener based single switch
surface hopping. The latter one offers the advantage of being based on
adiabatic energy gaps only, thus not requiring non-adiabatic coupling
information any more.
The present work describes the MATLAB version of WavePacket 6.0.2 which is
essentially an object-oriented rewrite of previous versions, allowing to
perform fully classical, quantum-classical and quantum-mechanical simulations
on an equal footing, i.e., for the same physical system described by the same
WavePacket input. The software package is hosted and further developed at the
Sourceforge platform, where also extensive Wiki-documentation as well as
numerous worked-out demonstration examples with animated graphics are
available
Non-adiabatic dynamics of molecules in optical cavities
Strong coupling of molecules to the vacuum field of micro cavities can modify
the potential energy surfaces opening new photophysical and photochemical
reaction pathways. While the influence of laser fields is usually described in
terms of classical field, coupling to the vacuum state of a cavity has to be
described in terms of dressed photon-matter states (polaritons) which require
quantized fields. We present a derivation of the non-adiabatic couplings for
single molecules in the strong coupling regime suitable for the calculation of
the dressed state dynamics. The formalism allows to use quantities readily
accessible from quantum chemistry codes like the adiabatic potential energy
surfaces and dipole moments to carry out wave packet simulations in the dressed
basis. The implications for photochemistry are demonstrated for a set of model
systems representing typical situations found in molecules
- …