Speaker: John Cardy, University of Oxford and IAS Time/Place: Thursday, 10/14, 11:30am; Hill 705 Title: "Entanglement Entropy in Extended Systems" Abstract: For a quantum system in a pure state, the von Neumann
entropy of a subsystem A has been used as a measure of the
entanglement between A and the rest of the system. I investigate the
geometric dependence of this quantity in the case when A consists of
the degrees of freedom in some large subregion of an extended system,
for example a quantum spin system or a quantum field theory in their
ground states. Near a quantum phase transition, the entanglement
entropy exhibits a universal dependence on the geometry.
THERE WILL BE A BROWN BAG LUNCH BETWEEN THE TWO
SEMINARS. COOKIES & COFFEE WILL BE PROVIDED. PLEASE BRING YOUR LUNCH.
Speaker: Sara Soffer, Rutgers University Time/Place:Thursday, 10/14, 1:30pm; Hill 705 Title: "Clustering Coefficient Without degree Correlations Biases" Abstract: Real
networks are characterized by large variations of the local
clustering coefficient, being orders of magnitude smaller for the
highly connected nodes. We show that these large variations are determined by
the degree correlations present in real networks. We introduce a new
definition of clustering coefficient in which the degree correlation
biases are filtered out. Using this new definition we show that real
networks are more clustered than we thought.
Joint work with Alexei Vázquez - Department of Physics and
Center for Complex Systems, University of Notre Dame.
---SPECIAL SEMINAR---PLEASE NOTE DAY
Speaker: H.T. Yau, Stanford University Time/Place:
WEDNESDAY 10/20; 1:30pm; Hill 705 Title: "Derivation of the
Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein
Condensate" Abstract: Click here for abstract.
Speaker: Thomas Chen, Courant Institute Time/Place:Thursday, 10/21, 11:30am; Hill 705 Title: "Localization lengths and
Boltzmann limit in higher mean for the weakly disordered 3-D Anderson
model " Abstract: We consider the quantum dynamics generated by
a random Schroedinger operator on Z^3, and derive lower bounds on the
localization lengths of its eigenvectors, which are similar to recent
results of Schlag, Schubin and Wolff for dimensions 1 and 2. The
method is based on an extension of techniques due to Erdoes and
Yau. Furthermore, it is shown that the Wigner transform of the wave
function converges weakly and in r-th mean to the solution of a linear
Boltzmann equation in the kinetic scaling limit, for any finite
r\in\R_+, and globally in macroscopic time. This extends previous
results where the convergence was proved for the expectation of the
Wigner transform.
---BROWN BAG LUNCH---
Speaker: Roderich Tumulka, University of Genoa, Italy Time/Place: Thursday, 10/21, 1:30pm; Room 705 Title: "Relativity and Quantum Nonlocality" Abstract: Relativity and quantum
nonlocality seem to be in conflict with each other. Nonlocality, which
follows from Bell's theorem (1964) and Aspect's experiment (1982),
requires that in certain situations causal influences travel faster
than light. How does nature do that? What is the mechanism? Due to
relativity, it would then seem that in some reference frames causal
influences have to travel backwards in time!
Among the many attempts to solve this puzzle, two concrete mechanisms
have been proposed; I will describe both of them in my talk. One,
developed in the 1990s, is based on Bohmian particle trajectories and
postulates a preferred foliation of space-time, or absolute
simultaneity, much against the spirit of relativity. The other
proposed solution of the puzzle invokes no modification of
relativity. It is based on an idea of Bell himself (1987) and was
worked out explicitly by myself (2004). It involves spontaneous
collapses of the wave function as originally proposed by Ghirardi,
Rimini and Weber (1986).
Speaker: Antti Kupiainen, University of Helsinki, Finland Time/Place: Thursday, 10/28, 11:30am; Room 705 Title: "Gaussian closure and Fourier's law" Abstract: We discuss lattices of
weakly coupled anharmonic oscillators subjected to heat baths on the
boundary. We introduce approximate equations for the time evolution of
an initial state and show they posess a stationary solution exhibiting
Fourier's law.
---BROWN BAG LUNCH---
Speaker:Giovanni Gallavotti, Universita di Roma/Rutgers University Time/Place: Thursday, 10/28, 1:30pm; Room 705 Title: TBA Abstract: TBA
Speaker: John Cardy, University of Oxford and IAS