14,915 research outputs found
Regularized Born-Oppenheimer molecular dynamics
While the treatment of conical intersections in molecular dynamics generally
requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation
is still adopted as a valid alternative in certain circumstances. In the
context of Mead-Truhlar minimal coupling, this paper presents a new closure of
the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics
scheme capturing geometric phase effects. Specifically, a semiclassical closure
of the nuclear Ehrenfest dynamics is obtained through a convenient prescription
for the nuclear Bohmian trajectories. The conical intersections are suitably
regularized in the resulting nuclear particle motion and the associated Lorentz
force involves a smoothened Berry curvature identifying a loop-dependent
geometric phase. In turn, this geometric phase rapidly reaches the usual
topological index as the loop expands away from the original singularity. This
feature reproduces the phenomenology appearing in recent exact nonadiabatic
studies, as shown explicitly in the Jahn-Teller problem for linear vibronic
coupling. Likewise, a newly proposed regularization of the diagonal correction
term is also shown to reproduce quite faithfully the energy surface presented
in recent nonadiabatic studies.Comment: Third version with minor changes. To appear in Phys. Rev.
Adiabatically coupled systems and fractional monodromy
We present a 1-parameter family of systems with fractional monodromy and
adiabatic separation of motion. We relate the presence of monodromy to a
redistribution of states both in the quantum and semi-quantum spectrum. We show
how the fractional monodromy arises from the non diagonal action of the
dynamical symmetry of the system and manifests itself as a generic property of
an important subclass of adiabatically coupled systems
Controlling Quantum Rotation With Light
Semiclassical catastrophes in the dynamics of a quantum rotor (molecule)
driven by a strong time-varying field are considered. We show that for strong
enough fields, a sharp peak in the rotor angular distribution can be achieved
via time-domain focusing phenomenon, followed by the formation of angular
rainbows and glory-like angular structures. Several scenarios leading to the
enhanced angular squeezing are proposed that use specially designed and
optimized sequences of pulses. The predicted effects can be observed in many
processes, ranging from molecular alignment (orientation) by laser fields to
heavy-ion collisions, and the squeezing of cold atoms in a pulsed optical
lattice.Comment: 8 pages, Latex, 8 figures, based on the talk given at the Eighth
Rochester Conference on Coherence and Quantum Optics (June 13-16, 2001). To
appear in the proceedings of CQO8 (Plenum, 2002
Impact of Quantum Phase Transitions on Excited Level Dynamics
The influence of quantum phase transitions on the evolution of excited levels
in the critical parameter region is discussed. The analysis is performed for 1D
and 2D systems with first- and second-order ground-state transitions. Examples
include the cusp and nuclear collective Hamiltonians.Comment: 6 pages, 4 figure
A semiclassical study of the Jaynes-Cummings model
We consider the Jaynes-Cummings model of a single quantum spin coupled to
a harmonic oscillator in a parameter regime where the underlying classical
dynamics exhibits an unstable equilibrium point. This state of the model is
relevant to the physics of cold atom systems, in non-equilibrium situations
obtained by fast sweeping through a Feshbach resonance. We show that in this
integrable system with two degrees of freedom, for any initial condition close
to the unstable point, the classical dynamics is controlled by a singularity of
the focus-focus type. In particular, it displays the expected monodromy, which
forbids the existence of global action-angle coordinates. Explicit calculations
of the joint spectrum of conserved quantities reveal the monodromy at the
quantum level, as a dislocation in the lattice of eigenvalues. We perform a
detailed semi-classical analysis of the associated eigenstates. Whereas most of
the levels are well described by the usual Bohr-Sommerfeld quantization rules,
properly adapted to polar coordinates, we show how these rules are modified in
the vicinity of the critical level. The spectral decomposition of the
classically unstable state is computed, and is found to be dominated by the
critical WKB states. This provides a useful tool to analyze the quantum
dynamics starting from this particular state, which exhibits an aperiodic
sequence of solitonic pulses with a rather well defined characteristic
frequency.Comment: pdfLaTeX, 51 pages, 19 figures, references added and improved figure
captions. To appear in J. Stat. Mec
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
Non-adiabacity and large flucutations in a many particle Landau Zener problem
We consider the behavior of an interacting many particle system under slow
external driving -- a many body generalization of the Landau-Zener paradigm. We
find that a conspiracy of interactions and driving leads to physics profoundly
different from that of the single particle limit: for practically all values of
the driving rate the particle distributions in Hilbert space are very broad, a
phenomenon caused by a strong amplification of quantum fluctuations in the
driving process. These fluctuations are 'non-adiabatic' in that even at very
slow driving it is exceedingly difficult to push the center of the distribution
towards the limit of full ground state occupancy. We obtain these results by a
number of complementary theoretical approaches, including diagrammatic
perturbation theory, semiclassical analysis, and exact diagonalization.Comment: 25 pages, 16 figure
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