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Title: Random matrix theory and statistics of quantum transport in chaotic cavities
Author: Simm, Nicholas J.
ISNI:       0000 0004 2734 0021
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2012
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Over the past 60 years random matrix theory has become a strikingly powerful tool for the investigation of complex quantum systems. In the 1980's it was dis- covered that the conductance fluctuations of certain disordered mesoscopic devices exhibit universal behaviour. Subsequently, a random matrix model of quantum transport was developed that could account for this universality. In the last several years, this subject has experienced a renewed burst of activity with motivations ranging from experimental observations to semiclassical treatments of the trans- port problem. Focusing on the ballistic regime of chaotic cavities. this thesis introduces new techniques to attack the various ensemble averages required by a random matrix approach to quantum transport. We prove a number of conjectures concerning the higher order statistics of conductance and shot noise with B E {1.4}. An important component to our proofs are the novel use of certain 'Pfaffian integrable hierarchies that appear in these more challenging cases. The Virasoro constraints play a crucial role and they are used to calculate lower order statistics of transport observables for arbitrary B > O. This includes the Wigner time delay, whose universal statistics had remained somewhat elusive until now. We also consider the problem of calculating the full counting statistics of chaotic cavities. Exact results are obtained using the theory of orthogonal and skew-orthogonal polynomials for each B E {1, 2. 4}. Our results have the distinct advantage that they can also be studied in the limit of many open channels, thus allowing us to make contact with a number of recent semiclassical calculations. Particularly for the time delay problem. many of our random matrix predictions have yet to be verified semiclassically, thereby providing impetus for future work in this direction.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available