University of Illinois Urbana-Champaign

Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices

Dwivedi, Vatsal

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DWIVEDI-DISSERTATION-2017.pdf

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https://hdl.handle.net/2142/97237

Description

Title
Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices
Author(s)
Dwivedi, Vatsal
Issue Date
2016-12-15
Director of Research (if dissertation) or Advisor (if thesis)
Stone, Michael
Doctoral Committee Chair(s)
Ryu, Shinsei
Committee Member(s)
  • Eckstein, James
  • Bronski, Jared
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-08-10T19:14:15Z
Keyword(s)
  • Chiral kinetic theory
  • Transfer matrices
Abstract
This thesis presents some work on two quite disparate kinds of dynamical systems described by Hamiltonian dynamics. The first part describes a computation of gauge anomalies and their macroscopic effects in a semiclassical picture. The geometric (symplectic) formulation of classical mechanics is used to describe the dynamics of Weyl fermions in even spacetime dimensions, the only quantum input to the symplectic form being the Berry curvature that encodes the spin-momentum locking. The (semi-)classical equations of motion are used in a kinetic theory setup to compute the gauge and singlet currents, whose conservation laws reproduce the nonabelian gauge and singlet anomalies. Anomalous contributions to the hydrodynamic currents for a gas of Weyl fermions at a finite temperature and chemical potential are also calculated, and are in agreement with similar results in literature which were obtained using thermodynamic and/or quantum field theoretical arguments. The second part describes a generalized transfer matrix formalism for noninteracting tight-binding models. The formalism is used to study the bulk and edge spectra, both of which are encoded in the spectrum of the transfer matrices, for some of the common tight-binding models for noninteracting electronic topological phases of matter. The topological invariants associated with the boundary states are interpreted as winding numbers for windings around noncontractible loops on a Riemann sheet constructed using the algebraic structure of the transfer matrices, as well as with a Maslov index on a symplectic group manifold, which is the space of transfer matrices.
Graduation Semester
2017-05
Type of Resource
text
Permalink
http://hdl.handle.net/2142/97237
Copyright and License Information
Copyright 2017 Vatsal Dwivedi

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