{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/97237"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/97237","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and 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.","abstract_html":"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.","abstract_has_math":false,"creators":["Dwivedi, Vatsal"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Stone, Michael","Ryu, Shinsei","Eckstein, James","Bronski, Jared"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-10T19:14:15Z","date_published":"2017-08-10T19:14:15Z","updated_at":"2026-07-22T22:24:32Z","subjects":["Chiral kinetic theory","Transfer matrices"],"languages":["en"],"rights":["Copyright 2017 Vatsal Dwivedi"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/97237","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stone, Michael","Ryu, Shinsei","Eckstein, James","Bronski, Jared"]},{"key":"dc:creator","label":"Author","values":["Dwivedi, Vatsal"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-08-10T19:14:15Z","2016-12-15","2017-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Chiral kinetic theory","Transfer matrices"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Vatsal Dwivedi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/97237"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Vatsal Dwivedi, accepted the attached license on 2016-12-13 at 15:32.","The student, Vatsal Dwivedi, submitted this Dissertation for approval on 2016-12-13 at 15:37.","This Dissertation was approved for publication on 2016-12-15 at 14:35.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10512 on 2017-08-10 at 13:36:35","Made available in DSpace on 2017-08-10T19:14:15Z (GMT). No. of bitstreams: 3 DWIVEDI-DISSERTATION-2017.pdf: 3479662 bytes, checksum: 0931a4e5e74c965cde0be4475d339e1a (MD5) LICENSE.txt: 4211 bytes, checksum: f4176fa0970ba78d22f06ad8ecca4af8 (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 36be135e7a4daaedccd735ccb573fcbe (MD5) Previous issue date: 2016-12-15"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices"]}]}],"canonical_facts":{"dc:contributor":["Stone, Michael","Ryu, Shinsei","Eckstein, James","Bronski, Jared"],"dc:creator":["Dwivedi, Vatsal"],"dc:date":["2017-08-10T19:14:15Z","2016-12-15","2017-05"],"dc:description":["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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms","The student, Vatsal Dwivedi, accepted the attached license on 2016-12-13 at 15:32.","The student, Vatsal Dwivedi, submitted this Dissertation for approval on 2016-12-13 at 15:37.","This Dissertation was approved for publication on 2016-12-15 at 14:35.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10512 on 2017-08-10 at 13:36:35","Made available in DSpace on 2017-08-10T19:14:15Z (GMT). No. of bitstreams: 3 DWIVEDI-DISSERTATION-2017.pdf: 3479662 bytes, checksum: 0931a4e5e74c965cde0be4475d339e1a (MD5) LICENSE.txt: 4211 bytes, checksum: f4176fa0970ba78d22f06ad8ecca4af8 (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 36be135e7a4daaedccd735ccb573fcbe (MD5) Previous issue date: 2016-12-15"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/97237"],"dc:language":["en"],"dc:rights":["Copyright 2017 Vatsal Dwivedi"],"dc:subject":["Chiral kinetic theory","Transfer matrices"],"dc:title":["Aspects of symplectic dynamics and topology: gauge anomalies, chiral kinetic theory and transfer matrices"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:32Z"}