|
|
|
||||||||||||||||
|
|||||||||||||||||
 |
|
|
|
|
|
|
||||||||||||||||||||
|
Mathematical Horizons for Quantum Physics(28 Jul - 21 Sep 2008)... Jointly organized with Centre for Quantum Technology
Organizing Committee
· Confirmed Visitors
· Overview
· Activities · Membership Application
Co-chairs
Secretary
Quantum theory is one of the most
important intellectual developments in the early twentieth
century. Since then there has been much interplay between
theoretical physics and mathematics, both pure and applied.
Arguably, the field of Mathematical Physics, equally at home
in mathematics and in physics, emerged from John von
Neumann’s seminal work on the spectral theory of linear
operators in Hilbert space which was triggered by the birth
of quantum theory in the mid 1920s. Yet this is just one
historical example of how the mathematical insights and
tools that are developed in the course of answering
challenging mathematical questions arising from physical
problems have contributed to the advance of both mathematics
and physics. In this tradition, it is the objective of this
IMS Programme to bring together Mathematicians, whose work
has a bearing on quantum physics, with researchers in
Mathematical Physics and Theoretical Physics, whose work
will benefit from the mathematical progress. The
collaboration between these scientists of different
background, different expertise, and different scientific
culture will bear fruit on the research of all participants
by intellectual cross-fertilization. In quantum physics, the
observables are represented by (self-adjoint) linear
operators on a Hilbert space, and states of the system are
described as normalized positive linear functionals on an
operator algebra. In the historically earliest stage, the
spectrum of light emitted from atoms was explained by the
spectral analysis of atomic Hamilton operators, and these
investigations developed into the broad research field of
Schrodinger operators. The modular theory of operator
algebras brought about new contact points between
mathematics and physics, which turned out to be beneficial
for vast developments both in Mathematics and Theoretical
Physics. Operator algebra theory became quite powerful and
its applications in other branches of mathematics is
described by the adjective “non-commutative.” An example is
probability theory, widely used in classical physics. The
non-commutative probability theory is now well developed,
typically called free probability theory, which has its
earliest origin in Wigner’s analysis of the spectrum of
heavy atoms and is mathematically rooted in operator algebra
theory. The Programme will consist of four
overlapping three-week Sessions, each devoted to a selected
topic. In Session 1, the problem of bringing a given state
(such as the ground state or an equilibrium state) to a
target state by perturbing the interaction with a
time-dependent external laser field is studied as a typical
subject of quantum control. The time evolution is described
by a one-parameter automorphism group and some general
theory of its perturbation exists in operator algebra
theory, but the specific form of problems in quantum control
can stimulate a new development of non-commutative analysis
in addition to solving physical problems. The random matrix,
whose connection with quantum chaos is being studied, is a
typical subject of non-commutative probability theory. (Note
that probability theory and analysis are very closely
related, especially free probability theory is based on
operator algebra theory.) Programme Structure Each Session has a Session
Organizer who is in charge of defining the Session and the
selection of the Discussion Leaders and the participants. At
the start of each Session, there will be presentations by
the Discussion Leaders to lay the groundwork. There follows
an intense period of about 20 days of discussions and close
collaborations among the participants. The Session ends with
talks summarizing the progress accomplished and a
round-table discussion defining future problems and areas of
close collaboration. Session 1: Quantum Control and Dynamics
Topical Problems
Session 2: Operator Algebras in Quantum Information
Topical Problems
Session 3: Non-equilibrium Statistical Mechanics
Topical Problems
Session 4: Strongly Interacting Many-Particle Systems
Topical Problems
For attendance at these activities, please complete the
online registration form.
The Institute for Mathematical Sciences invites applications for membership for participation in the above program. Limited funds to cover travel and living expenses are available to young scientists. Applications should be received at least three (3) months before the commencement of membership. Application form is available in (MSWord|PDF|PS) format for download.
For enquiries on scientific aspects of the program, please email Jun Suzuki at physj(AT)nus.edu.sg. Organizing Committee · Confirmed Visitors · Overview · Activities · Membership Application |
|||||||||||||||||||||||||
 |
||||||||||||||||||||||||||
 |
