Quantum dynamics in the condensed phase: path integrals, master equations and purity

Chatterjee, Sambarta

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https://hdl.handle.net/2142/109424 Copy

Description

Title

Quantum dynamics in the condensed phase: path integrals, master equations and purity

Author(s)

Chatterjee, Sambarta

Issue Date

2020-12-02

Director of Research (if dissertation) or Advisor (if thesis)

Makri, Nancy

Doctoral Committee Chair(s)

Makri, Nancy

Committee Member(s)

• Gruebele, Martin
• Hirata, So
• Wagner, Lucas K

Department of Study

Chemistry

Discipline

Chemistry

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Quantum dynamics
• Path integrals
• Numerically exact methods
• Quantum master equation
• Coherence
• Decoherence
• 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.

Graduation Semester

2020-12

Type of Resource

Thesis

Permalink

http://hdl.handle.net/2142/109424

Copyright and License Information

Copyright 2020 Sambarta Chatterjee

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