| Date: | Wed, 16 Feb 2011 |
| From: | Elette Chantae Boyle |
| Subject: | Ramis Movassagh @ SPAMS Tomorrow at 5pm, 4-231 |
Hello all,
This week in SPAMS, Ramis will tell us about Isotropic Entanglement: what it is,
and why it is cool.
Ramis's suggested Prerequisites: Since this involves quantum mechanics, you do
NOT 'even' need common sense. It is entirely possible that the last two words
could be replaced by "to be sober". Just come by and enjoy the show!
We will have Persian food after.
Also, remember the new room this term, 4-231.
See you there!
-Jenn & Elette
-----------------------
Title: Isotropic Entanglement
Abstract: We propose a method which we call "Isotropic Entanglement" (IE), that
takes inspiration from Free Probability Theory and other ideas in Random Matrix
Theory to predict the eigenvalue distribution of quantum many body (spin)
systems with generic interactions. At the heart of this method is a sliding
scale, "the Slider", which interpolates the quantum problem between two extrema
by matching fourth moments. The first extreme treats the non-commuting terms in
the Hamiltonian classically and the second treats them isotropically. By
isotropic we mean that the non-commuting subsets have eigenvectors that are in
generic positions. We prove The Matching Three Moments and Slider theorems and
further prove that the interpolation of the quantum problem in terms of the
classical and isotropic is universal, i.e., independent of the choice of local
terms. Examples show that IE provides an accurate picture of the spectra well
beyond what one expects from the first four moments alone.
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