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Mathematical Aspects of Quantum Dynamics

Objective

The main goal of this proposal is to reach
a better mathematical understanding of
the dynamics of quantum mechanical
systems. In particular I plan to work
on the following three projects along
this direction. A. Effective Evolution
Equations for Macroscopic Systems.
The derivation of effective evolution
equations from first principle microscopic
theories is a fundamental task of statistical
mechanics. I have been involved in
several projects related to the derivation
of the Hartree and the Gross-Piteavskii
equation from many body quantum
dynamics. I plan to continue to work on
these problems and to use these results
to obtain new information on the many
body dynamics. B. Spectral Properties
of Random Matrices. The correlations
among eigenvalues of large random
matrices are expected to be independent
of the distribution of the entries. This
conjecture, known as universality, is
of great importance for random matrix
theory. In collaboration with L. Erdos and
H.-T. Yau, we established the validity of
Wigner's semicircle law on
microscopic scales, and we proved the
emergence of eigenvalue repulsion. In
the future, we plan to continue to study
Wigner matrices to prove, on the longer
term, universality. C. Locality Estimates in
Quantum Dynamics. Anharmonic lattice
systems are very important models in
non-equilibrium statistical mechanics.
With B. Nachtergaele, H. Raz, and R.
Sims, we proved Lieb-Robinson type
inequalities (giving an upper bound on
the speed of propagation of signals), for
a certain class of anharmonicity. Next, we
plan to extend these results to a larger
class of anharmonic potentials, and to
apply these bounds to establish other
fundamental properties of the dynamics
of anharmonic systems, such as the
existence of its thermodynamical limit.

Field of science

  • /natural sciences/physical sciences/classical mechanics/statistical mechanics
  • /social sciences/law

Call for proposal

ERC-2009-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

UNIVERSITAT ZURICH
Address
Ramistrasse 71
8006 Zürich
Switzerland
Activity type
Other
EU contribution
€ 269 898
Principal investigator
Benjamin Schlein (Dr.)
Administrative Contact
Benjamin Schlein (Prof.)

Beneficiaries (3)

UNIVERSITAT ZURICH
Switzerland
EU contribution
€ 269 898
Address
Ramistrasse 71
8006 Zürich
Activity type
Other
Principal investigator
Benjamin Schlein (Dr.)
Administrative Contact
Benjamin Schlein (Prof.)
THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE

Participation ended

United Kingdom
EU contribution
€ 5 347,20
Address
Trinity Lane The Old Schools
CB2 1TN Cambridge
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Keith Cann (Mr.)
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN

Participation ended

Germany
EU contribution
€ 474 754,80
Address
Regina Pacis Weg 3
53113 Bonn
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Daniela Hasenpusch (Ms.)