3,785 research outputs found
WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction
WavePacket is an open-source program package for numeric simulations in
quantum dynamics. It can solve time-independent or time-dependent linear
Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions.
Also coupled equations can be treated, which allows, e.g., to simulate
molecular quantum dynamics beyond the Born-Oppenheimer approximation.
Optionally accounting for the interaction with external electric fields within
the semi-classical dipole approximation, WavePacket can be used to simulate
experiments involving tailored light pulses in photo-induced physics or
chemistry. Being highly versatile and offering visualization of quantum
dynamics 'on the fly', WavePacket is well suited for teaching or research
projects in atomic, molecular and optical physics as well as in physical or
theoretical chemistry. Building on the previous Part I which dealt with closed
quantum systems and discrete variable representations, the present Part II
focuses on the dynamics of open quantum systems, with Lindblad operators
modeling dissipation and dephasing. This part also describes the WavePacket
function for optimal control of quantum dynamics, building on rapid
monotonically convergent iteration methods. Furthermore, two different
approaches to dimension reduction implemented in WavePacket are documented
here. In the first one, a balancing transformation based on the concepts of
controllability and observability Gramians is used to identify states that are
neither well controllable nor well observable. Those states are either
truncated or averaged out. In the other approach, the H2-error for a given
reduced dimensionality is minimized by H2 optimal model reduction techniques,
utilizing a bilinear iterative rational Krylov algorithm
Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching
We theoretically and numerically studied ordering of "colloidal ionic
clusters" on periodic substrate potentials as those generated by optical
trapping. Each cluster consists of three charged spherical colloids: two
negatively and one positively charged. The substrate is a square or rectangular
array of traps, each confining one such cluster. By varying the lattice
constant from large to small, the observed clusters are first rod-like and form
ferro- and antiferro-like phases, then they bend into a banana-like shape and
finally condense into a percolated structure. Remarkably, in a broad parameter
range between single-cluster and percolated structures, we have found stable
supercomplexes composed of six colloids forming grape-like or rocket-like
structures. We investigated the possibility of macroscopic pattern switching by
applying external electrical fields.Comment: 14 pages, 13 figure
Real Time Animation of Virtual Humans: A Trade-off Between Naturalness and Control
Virtual humans are employed in many interactive applications using 3D virtual environments, including (serious) games. The motion of such virtual humans should look realistic (or ‘natural’) and allow interaction with the surroundings and other (virtual) humans. Current animation techniques differ in the trade-off they offer between motion naturalness and the control that can be exerted over the motion. We show mechanisms to parametrize, combine (on different body parts) and concatenate motions generated by different animation techniques. We discuss several aspects of motion naturalness and show how it can be evaluated. We conclude by showing the promise of combinations of different animation paradigms to enhance both naturalness and control
Hill crossing during preheating after hilltop inflation
In 'hilltop inflation', inflation takes place when the inflaton field slowly
rolls from close to a maximum of its potential (i.e. the 'hilltop') towards its
minimum. When the inflaton potential is associated with a phase transition,
possible topological defects produced during this phase transition, such as
domain walls, are efficiently diluted during inflation. It is typically assumed
that they also do not reform after inflation, i.e. that the inflaton field
stays on its side of the 'hill', finally performing damped oscillations around
the minimum of the potential. In this paper we study the linear and the
non-linear phases of preheating after hilltop inflation. We find that the
fluctuations of the inflaton field during the tachyonic oscillation phase grow
strong enough to allow the inflaton field to form regions in position space
where it crosses 'over the top of the hill' towards the 'wrong vacuum'. We
investigate the formation and behaviour of these overshooting regions using
lattice simulations: Rather than durable domain walls, these regions form
oscillon-like structures (i.e. localized bubbles that oscillate between the two
vacua) which should be included in a careful study of preheating in hilltop
inflation.Comment: 22 pages, 10 figures, v2 matches publication in JCAP. Animated movies
of our simulations are available online at
https://particlesandcosmology.unibas.ch/files/hilltop_preheating.htm
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