# <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

Lind 400

**Landscape of unitary Transformation in controlled**

quantum dynamics

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**

approximation

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

of emerging

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

leads to

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

dissipation

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.[1] Instantaneous dissipation is described by

a Lindblad term containing electronic transition rates,[2] while the

delayed

dissipation is given by a time integral derived from the

time-correlation

function (TCF) of atomic displacements in the medium.[3] We

consider cases where the TCF decays exponentially (fast) or as an

inverse

power (slowly). An initial thermal equilibrium can not be

assumed when

there are long lasting interactions between the primary region

and the

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).[4]

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,

7311.

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

Foundation.**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.