Physics and Astronomy Quantum Nano Seminar
Dr. Ramis Movassagh, Northeastern University & MIT
Location
Wilder 202
Sponsored by
Physics & Astronomy Department
Audience
Public
Title: "Eigenvalues of Disordered Systems"
Abstract: The method of "Isotropic Entanglement" (IE), inspired by Free
Probability Theory and Random Matrix Theory, predicts the eigenvalue
distribution of quantum many-body (spin) systems with generic
interactions. At the heart is a "Slider", which interpolates between two
extrema by matching fourth moments. The first extreme treats the
non-commuting terms classically and the second treats them isotropically.
Isotropic means that the eigenvectors are in generic positions. We prove
Matching Three Moments and Slider Theorems and further prove that the
interpolation is universal, i.e., independent of the choice of local
terms. Our examples show that IE provides an accurate picture well beyond
what one expects from the first four moments alone. We then show that free
probability theory also captures the density of states of the Anderson
model with arbitrary disorder and with high accuracy. Lastly and time
permitting, we shall show a very recent result applicable to non-Hermitian
models. We prove that the complex conjugate eigenvalues of a real matrix
"attract" in response to additive real randomness.
Location
Wilder 202
Sponsored by
Physics & Astronomy Department
Audience
Public
