In this work, we investigate the charge, or Loschmidt echo of a system of spinless electrons described by a simple tight-binding Hamiltonian. For this system it is possible to construct a unitary operator, T, that reverses the time evolution of the electron degrees of freedom. The electron gas is prepared in an initially inhomogeneous state. After a free evolution for a time t0, the electrons are distributed more or less uniformly, and the unitary operator, T is applied. The time evolution is reversed, and at time 2t0 the local density returns to its initial value, demonstrating the Loschmidt echo. The effect of several factors that reduce the strength of the echo are considered: imperfect implimentaton of T, second-neighbor hopping terms, and coupling the electron to phonons.
","abstract_html":"<p>In this work, we investigate the charge, or Loschmidt echo of a system of spinless electrons described by a simple tight-binding Hamiltonian. For this system it is possible to construct a unitary operator, T, that reverses the time evolution of the electron degrees of freedom. The electron gas is prepared in an initially inhomogeneous state. After a free evolution for a time t<sub>0</sub>, the electrons are distributed more or less uniformly, and the unitary operator, T is applied. The time evolution is reversed, and at time 2t<sub>0</sub> the local density returns to its initial value, demonstrating the Loschmidt echo. The effect of several factors that reduce the strength of the echo are considered: imperfect implimentaton of T, second-neighbor hopping terms, and coupling the electron to phonons.</p>","abstract_has_math":false,"creators":["Liu, Baowei"],"institution":null,"degree_name":"Ph.D.","degree_level":"Campus Access Dissertation","degree_discipline":"Physics and Astronomy","degree_department":null,"school":null,"contributors":["Richard J Creswick"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T04:37:14Z","subjects":["Physical Sciences and Mathematics","Physics","Charge Echo","Electron Gas","Next-Nearest Neighbor Hopping","Perturbation","Phonon coupling","Tight-Binding Model"],"languages":[],"rights":["© 2010, Baowei Liu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarcommons.sc.edu/etd/1751","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Richard J Creswick"]},{"key":"dc:creator","label":"Author","values":["Liu, Baowei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics and Astronomy"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physical Sciences and Mathematics","Physics","Charge Echo","Electron Gas","Next-Nearest Neighbor Hopping","Perturbation","Phonon coupling","Tight-Binding Model"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© 2010, Baowei Liu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarcommons.sc.edu/etd/1751"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we investigate the charge, or Loschmidt echo of a system of spinless electrons described by a simple tight-binding Hamiltonian. For this system it is possible to construct a unitary operator, T, that reverses the time evolution of the electron degrees of freedom. The electron gas is prepared in an initially inhomogeneous state. After a free evolution for a time t0, the electrons are distributed more or less uniformly, and the unitary operator, T is applied. The time evolution is reversed, and at time 2t0 the local density returns to its initial value, demonstrating the Loschmidt echo. The effect of several factors that reduce the strength of the echo are considered: imperfect implimentaton of T, second-neighbor hopping terms, and coupling the electron to phonons.
"]},{"key":"dc:title","label":"Title","values":["Charge Echo In An Electron Gas"]}]}],"canonical_facts":{"dc:contributor":["Richard J Creswick"],"dc:creator":["Liu, Baowei"],"dc:description.abstract":["In this work, we investigate the charge, or Loschmidt echo of a system of spinless electrons described by a simple tight-binding Hamiltonian. For this system it is possible to construct a unitary operator, T, that reverses the time evolution of the electron degrees of freedom. The electron gas is prepared in an initially inhomogeneous state. After a free evolution for a time t0, the electrons are distributed more or less uniformly, and the unitary operator, T is applied. The time evolution is reversed, and at time 2t0 the local density returns to its initial value, demonstrating the Loschmidt echo. The effect of several factors that reduce the strength of the echo are considered: imperfect implimentaton of T, second-neighbor hopping terms, and coupling the electron to phonons.
"],"dc:identifier":["https://scholarcommons.sc.edu/etd/1751"],"dc:rights":["© 2010, Baowei Liu"],"dc:subject":["Physical Sciences and Mathematics","Physics","Charge Echo","Electron Gas","Next-Nearest Neighbor Hopping","Perturbation","Phonon coupling","Tight-Binding Model"],"dc:title":["Charge Echo In An Electron Gas"],"thesis:degree_discipline":["Physics and Astronomy"],"thesis:degree_level":["Campus Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T04:37:14Z"}