{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/109424"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/109424","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quantum dynamics in the condensed phase: path integrals, master equations and purity","abstract":"Rigorous approaches to the dynamics of quantum systems in large dissipative environments are extremely challenging, owing to the well-known exponential scaling. The work reported here builds up on existing highly accurate methods developed in our group, namely the quasi-adiabatic propagator (QuAPI) and the quantum-classical path integral (QCPI). In particular, we present the incorporation of Langevin friction by eliminating classical trajectories, and a time-dependent driving field to study light-matter interactions, to the framework of QCPI. We further introduce the possibility of using rigorous path integral methods in conjunction with master equation (GQME) methods and explore memory requirements of the different approaches. We show that while QuAPI and GQME have the same memory requirements, QCPI requires a much shorter quantum memory. This is associated with the ability of QCPI to include all classical memory effects within a time-dependent system propagator, a benefit which cannot be transferred to non-trajectory-based methods. Next, we turn our focus on a very interesting property of quantum mechanical systems, namely coherences, and its relation to purity of reduced systems. We show that while purity decays at high temperature classical regimes as predicted by short-time perturbative treatments and Gaussian decoherence mechanisms, pronounced quantum mechanical regimes see a significant long-time recovery in purity, even when coherent oscillations have completely decayed. A simple analysis shows three physically meaningful contributions to purity, one of which is purely quantum mechanical in origin and cannot be explained by classical decoherence, and is the dominating factor at long times in certain situations. We investigate the behavior in the exciton transfer in bacteriochlorophyll dimer, and show that purity is significantly recovered even at room temperatures in real systems. Finally, we investigate purity in the case of relaxation dynamics, where symmetry considerations lead to an entirely different picture. We identify distinct features for ground & excited state initial conditions, and show that in the latter case purity always goes through its minimum, corresponding to a maximally mixed state. We also demonstrate that, contrary to common understanding, the environment can even purify systems in an initially mixed state.","abstract_html":"Rigorous approaches to the dynamics of quantum systems in large dissipative environments are extremely challenging, owing to the well-known exponential scaling. The work reported here builds up on existing highly accurate methods developed in our group, namely the quasi-adiabatic propagator (QuAPI) and the quantum-classical path integral (QCPI). In particular, we present the incorporation of Langevin friction by eliminating classical trajectories, and a time-dependent driving field to study light-matter interactions, to the framework of QCPI. We further introduce the possibility of using rigorous path integral methods in conjunction with master equation (GQME) methods and explore memory requirements of the different approaches. We show that while QuAPI and GQME have the same memory requirements, QCPI requires a much shorter quantum memory. This is associated with the ability of QCPI to include all classical memory effects within a time-dependent system propagator, a benefit which cannot be transferred to non-trajectory-based methods. Next, we turn our focus on a very interesting property of quantum mechanical systems, namely coherences, and its relation to purity of reduced systems. We show that while purity decays at high temperature classical regimes as predicted by short-time perturbative treatments and Gaussian decoherence mechanisms, pronounced quantum mechanical regimes see a significant long-time recovery in purity, even when coherent oscillations have completely decayed. A simple analysis shows three physically meaningful contributions to purity, one of which is purely quantum mechanical in origin and cannot be explained by classical decoherence, and is the dominating factor at long times in certain situations. We investigate the behavior in the exciton transfer in bacteriochlorophyll dimer, and show that purity is significantly recovered even at room temperatures in real systems. Finally, we investigate purity in the case of relaxation dynamics, where symmetry considerations lead to an entirely different picture. We identify distinct features for ground & excited state initial conditions, and show that in the latter case purity always goes through its minimum, corresponding to a maximally mixed state. We also demonstrate that, contrary to common understanding, the environment can even purify systems in an initially mixed state.","abstract_has_math":false,"creators":["Chatterjee, Sambarta"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemistry","degree_department":null,"school":null,"contributors":["Makri, Nancy","Gruebele, Martin","Hirata, So","Wagner, Lucas K"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-03-05T21:38:18Z","date_published":"2021-03-05T21:38:18Z","updated_at":"2026-07-22T22:24:50Z","subjects":["Quantum dynamics","Path integrals","Numerically exact methods","Quantum master equation","Coherence","Decoherence","Purity"],"languages":["en"],"rights":["Copyright 2020 Sambarta Chatterjee"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/109424","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Makri, Nancy","Gruebele, Martin","Hirata, So","Wagner, Lucas K"]},{"key":"dc:creator","label":"Author","values":["Chatterjee, Sambarta"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-03-05T21:38:18Z","2020-12-02","2020-12"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemistry"]},{"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":["Quantum dynamics","Path integrals","Numerically exact methods","Quantum master equation","Coherence","Decoherence","Purity"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Sambarta Chatterjee"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/109424"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Rigorous approaches to the dynamics of quantum systems in large dissipative environments are extremely challenging, owing to the well-known exponential scaling. The work reported here builds up on existing highly accurate methods developed in our group, namely the quasi-adiabatic propagator (QuAPI) and the quantum-classical path integral (QCPI). In particular, we present the incorporation of Langevin friction by eliminating classical trajectories, and a time-dependent driving field to study light-matter interactions, to the framework of QCPI. We further introduce the possibility of using rigorous path integral methods in conjunction with master equation (GQME) methods and explore memory requirements of the different approaches. We show that while QuAPI and GQME have the same memory requirements, QCPI requires a much shorter quantum memory. This is associated with the ability of QCPI to include all classical memory effects within a time-dependent system propagator, a benefit which cannot be transferred to non-trajectory-based methods. Next, we turn our focus on a very interesting property of quantum mechanical systems, namely coherences, and its relation to purity of reduced systems. We show that while purity decays at high temperature classical regimes as predicted by short-time perturbative treatments and Gaussian decoherence mechanisms, pronounced quantum mechanical regimes see a significant long-time recovery in purity, even when coherent oscillations have completely decayed. A simple analysis shows three physically meaningful contributions to purity, one of which is purely quantum mechanical in origin and cannot be explained by classical decoherence, and is the dominating factor at long times in certain situations. We investigate the behavior in the exciton transfer in bacteriochlorophyll dimer, and show that purity is significantly recovered even at room temperatures in real systems. Finally, we investigate purity in the case of relaxation dynamics, where symmetry considerations lead to an entirely different picture. We identify distinct features for ground & excited state initial conditions, and show that in the latter case purity always goes through its minimum, corresponding to a maximally mixed state. We also demonstrate that, contrary to common understanding, the environment can even purify systems in an initially mixed state.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-03-04 without embargo terms","The student, Sambarta Chatterjee, accepted the attached license on 2020-12-02 at 10:35.","The student, Sambarta Chatterjee, submitted this Dissertation for approval on 2020-12-02 at 10:45.","This Dissertation was approved for publication on 2020-12-02 at 15:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16031 on 2021-03-04 at 15:35:55","Made available in DSpace on 2021-03-05T21:38:18Z (GMT). No. of bitstreams: 3 CHATTERJEE-DISSERTATION-2020.pdf: 2303318 bytes, checksum: f6354f361770f6c2a71cde68c1f8db93 (MD5) LICENSE.txt: 4216 bytes, checksum: 843b968dcab5a198cfd59459a7a81997 (MD5) PROQUEST_LICENSE.txt: 4562 bytes, checksum: 143bd9961f864ce0882dc47282fc9883 (MD5) Previous issue date: 2020-12-02"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Quantum dynamics in the condensed phase: path integrals, master equations and purity"]}]}],"canonical_facts":{"dc:contributor":["Makri, Nancy","Gruebele, Martin","Hirata, So","Wagner, Lucas K"],"dc:creator":["Chatterjee, Sambarta"],"dc:date":["2021-03-05T21:38:18Z","2020-12-02","2020-12"],"dc:description":["Rigorous approaches to the dynamics of quantum systems in large dissipative environments are extremely challenging, owing to the well-known exponential scaling. The work reported here builds up on existing highly accurate methods developed in our group, namely the quasi-adiabatic propagator (QuAPI) and the quantum-classical path integral (QCPI). In particular, we present the incorporation of Langevin friction by eliminating classical trajectories, and a time-dependent driving field to study light-matter interactions, to the framework of QCPI. We further introduce the possibility of using rigorous path integral methods in conjunction with master equation (GQME) methods and explore memory requirements of the different approaches. We show that while QuAPI and GQME have the same memory requirements, QCPI requires a much shorter quantum memory. This is associated with the ability of QCPI to include all classical memory effects within a time-dependent system propagator, a benefit which cannot be transferred to non-trajectory-based methods. Next, we turn our focus on a very interesting property of quantum mechanical systems, namely coherences, and its relation to purity of reduced systems. We show that while purity decays at high temperature classical regimes as predicted by short-time perturbative treatments and Gaussian decoherence mechanisms, pronounced quantum mechanical regimes see a significant long-time recovery in purity, even when coherent oscillations have completely decayed. A simple analysis shows three physically meaningful contributions to purity, one of which is purely quantum mechanical in origin and cannot be explained by classical decoherence, and is the dominating factor at long times in certain situations. We investigate the behavior in the exciton transfer in bacteriochlorophyll dimer, and show that purity is significantly recovered even at room temperatures in real systems. Finally, we investigate purity in the case of relaxation dynamics, where symmetry considerations lead to an entirely different picture. We identify distinct features for ground & excited state initial conditions, and show that in the latter case purity always goes through its minimum, corresponding to a maximally mixed state. We also demonstrate that, contrary to common understanding, the environment can even purify systems in an initially mixed state.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-03-04 without embargo terms","The student, Sambarta Chatterjee, accepted the attached license on 2020-12-02 at 10:35.","The student, Sambarta Chatterjee, submitted this Dissertation for approval on 2020-12-02 at 10:45.","This Dissertation was approved for publication on 2020-12-02 at 15:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16031 on 2021-03-04 at 15:35:55","Made available in DSpace on 2021-03-05T21:38:18Z (GMT). No. of bitstreams: 3 CHATTERJEE-DISSERTATION-2020.pdf: 2303318 bytes, checksum: f6354f361770f6c2a71cde68c1f8db93 (MD5) LICENSE.txt: 4216 bytes, checksum: 843b968dcab5a198cfd59459a7a81997 (MD5) PROQUEST_LICENSE.txt: 4562 bytes, checksum: 143bd9961f864ce0882dc47282fc9883 (MD5) Previous issue date: 2020-12-02"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/109424"],"dc:language":["en"],"dc:rights":["Copyright 2020 Sambarta Chatterjee"],"dc:subject":["Quantum dynamics","Path integrals","Numerically exact methods","Quantum master equation","Coherence","Decoherence","Purity"],"dc:title":["Quantum dynamics in the condensed phase: path integrals, master equations and purity"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Chemistry"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:50Z"}