<span class=strong>Reception and Poster Session</span><br><b><br/><br/><b>Poster submissions welcome from all participants</b>
Tuesday, March 3, 2009 - 5:00pm - 6:30pm
- Landscape of unitary Transformation in controlled
Tak-San Ho (Princeton University)
The control problem of generating unitary transformations is especially relevant to current research in quantum information
processing and computing. Control dynamical landscapes for unitary transformations is analyzed in the inﬁnite dimensional
function space of the time-dependent external ﬁeld. The dynamical analysis reveals many essential geometric features of optimal control landscapes for unitary transformations, including bounds on the local landscape slope and curvature. Close examination of the curvatures at the critical points shows that the unitary transformation control landscapes are free of local traps and proper choices of the adaptation matrix may facilitate the search for optimal control ﬁelds producing desired unitary transformations, in particular, in the neighborhood of the global extrema.
- Universal families and quantum control in infinite dimensions
Rui Vilela Mendes (Instituto Superior Tecnico)
In a topological space, a family of continuous mappings is called universal
if its action, in at least one element of the space, is dense. If the
mappings are unitary or trace-preserving completely positive, the notion of
universality is closely related to the notion of controllability in either
closed or open quantum systems. Quantum controllability in infinite
dimensions is discussed in this setting and minimal generators are found for
full control universal families. Some of the requirements of the operators
needed for control in infinite dimensions follow from the properties of the
infinite unitary group. Hence, a brief discussed of this group and their
appropriate mathematical spaces is also included.
- Lyapunov control of Schrödinger equations: beyond the dipole
Andreea Grigoriu (Université de Paris IX (Paris-Dauphine))Catalin Lefter (University Al. I. Cuza of Iaşi)
In this joint work with Gabriel Turinici, we analyse the Lyapunov
trajectory tracking of the Schrödinger equation for a second order
coupling operator. We present a theoretical convergence result; for
situations not covered by the first theorem we propose a numerical
approach and complement it with a second theoretical result.
- Laser-induced currents along molecular wire junctions: control in
the presence of decoherence due to vibronic couplings
Ignacio Franco (Northwestern University)
The effect of electron-vibrational interactions on the electronic
transport induced by femtosecond omega + 2omega laser fields along
unbiased molecular nanojunctions is investigated. For this, the
photoinduced vibronic dynamics of trans-polyacetylene oligomers coupled
to macroscopic metallic leads is followed in a mean-field mixed quantum-
classical approximation. A reduced description of the dynamics is
obtained by introducing projective lead-molecule couplings and deriving
an effective Schrödinger equation satisfied by the orbitals in the
molecular region. Two possible rectification mechanisms are identified
and investigated. The first one relies on near-resonance photon
absorption and is shown to be fragile to the ultrafast electronic
decoherence processes introduced by the wire's vibrations. The second
one employs the dynamic Stark effect and is demonstrated to be highly
efficient and robust to electron-vibrational interactions.
- Fast and accurate computational techniques for the
optimal control of quantum systems
Gregory von Winckel (Karl-Franzens-Universität Graz)
The manipulation and control of quantum systems is fundamental to a host
applications from the design of qubits and novel nanoscale devices, to
the control of photochemical reactions as well as atomic and molecular
dynamics. Although there are established techniques to simulate the
evolution of a quantum system, the problem of finding the control
potential which results in a desired evolution is considerably more
challenging. Recent contributions to the development of new quantum
control methodologies and optimal control formulation are discussed. In
particular, the investigation of theoretical issues such as the
appropriate choice of function spaces for the control and the non-convex
structure of the optimization problems as well as the interplay between
discretization and optimization are considered. Accurate and
computationally efficient algorithms for computing the optimal controls
which take advantage of the underlying physics are introduced with a
focus on Krylov-Newton methods for solving controls for fast state
transitions in a system.
- Canards, black swans and control of chemical reactions
Vladimir Sobolev (Samara State University)
In this joint work with Elena Shchepakina we consider a canard trajectory (in the case of scalar slow variable) and a black swan (in the case of vector slow variable) as the result of gluing attractive and repulsive slow integral manifolds, due to the availability of an additional parameter (function in the case of vector slow variable) in the differential system. As a result we obtain the continuous attractive/repulsive slow invariant surface. It is possible to consider the gluing parameter (function) as a special kind of partial feedback control, which guarantees the safety of chemical regimes, even with perturbations, during a chemical process.
- Density matrix treatment of optical response with
combined instantaneous and delayed dissipations:
Adsorbates on solid surfaces
David Micha (University of Florida)
Joint work with Andrew S. Leathers (Quantum Theory Project, Departments of Chemistry and of Physics,
University of Florida, Gainesville, Florida 32611, U.S.A.).
The interaction of light with a localized (primary) region in a
many atom system undergoing electronic and vibrational transitions
energy dissipation and
uctuations through both nearly instantaneous
and delayed processes. A fast dissipation typically occurs due
to electronic energy relaxation in the medium, while a delayed
arises from vibrational energy relaxation. A theoretical and
computational treatment of these phenomena has been done in terms of
a reduced density matrix (RDM) satisfying a generalized
Liouville-von Neumann equation. Instantaneous dissipation is described by
a Lindblad term containing electronic transition rates, while the
dissipation is given by a time integral derived from the
function (TCF) of atomic displacements in the medium. We
consider cases where the TCF decays exponentially (fast) or as an
power (slowly). An initial thermal equilibrium can not be
there are long lasting interactions between the primary region
medium. We describe a general procedure that provides the
optical response in this case by calculating the difference between
solutions for the RDM with and without excitation by a light pulse. We
present examples for slow relaxation of optical excitation in
CO/Cu(001) and Ag3/Si(111).
1. D. A. Micha, A. Leathers, and B. Thorndyke in Quantum Dynamics of Complex Molecular Systems (Springer-Verlag, 2006) D. A. Micha and I.
Burghardt, eds., pp. 165-194.
2. D. A. Micha and A. Santana, J. Phys. Chem. A 2003, 107,
3. A. S. Leathers and D. A. Micha, J. Phys. Chem. A 2006, 110, 749.
4. A. S. Leather, D. A. Micha, and D. S. Kilin, Density matrix
treatment for an electronically excited adsorbate on a solid
surface, to be published.
Work partly supported by the NSF of the USA, and by the Dreyfus
- Quantum dissipation and quantum transport: Exact theory
and efficient implementation
YiJing Yan (Hong Kong University of Science and Technology)Xiao Zheng (Hong Kong University of Science and Technology)
Joint work with Jinshuang Jin.
We present a hierarchical equations-of-motion (HEOM) formalism of quantum dissipation theory
[J. Chem. Phys. 128, 234703 (2008)], which is formally exact, practically tractable, and numerically
convergent. It characterizes the transient current transport dynamics of arbitrary dissipative many-electron
systems, in contact with electrodes under arbitrary temperatures and external fields. The HEOM
approach provides a useful theoretical tool to study various transient and stationary properties of
many-body systems far away from equilibrium. With an efficient hybrid scheme accounting for the bath
correlation functions, we demonstrate accurate transient response current driven by time-dependent
applied voltages in both sequential and cotunneling regimes.
- Explicit, implicit and parametric invariant manifolds for model reduction in chemical kinetics
Vladimir Sobolev (Samara State University)
In this joint work with Elena Shchepakina we use a geometric singular perturbations method for reducing the model order in chemical kinetics problems. The method relies on the theory of integral manifolds, which essentially replaces the original system by another system on an integral manifold with dimension equal to that of the slow subsystem. Explicit, implicit and parametric representations of a slow invariant manifolds are used.