Interrogating the void : the difficulty of extracting information from many-body systems

In this thesis, I will explore some of the ways the information-theoretic properties of quantum many-body systems can be analyzed. I do this in two different settings. First, I will describe an approach to the "scrambling time problem," a conjecture of Susskind and Sekino that asserts that black holes can thermalize the information of objects that are dropped into them at the fastest rate consistent with unitarity. Specifically, I will analyze the dynamics of the Iizuka-Polchinksi model, a matrix model of a black hole whose response functions can be calculated exactly. Second, I will study the average information content of subsystems of a larger system. In particular, I will improve a result of Page giving the average entanglement entropy of such a subsystem in the ensemble of random, Haar-distributed states by refining it to a smaller, more physically relevant ensemble of states known as "matrix product states," which encode a notion of locality. In both these examples, fundamental obstacles arise that impede our analysis; I explain how these roadblocks are related to the difficulty of understanding the interactions between the exponentially large number the degrees of freedom such many-body systems contain.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Physics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2011

Author dc:creator

• Diab, Kenan S. (Kenan Sebastian)

Advisor dc:contributor.advisor

• John McGreevy.

• Physics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/65526

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/65526