Path integral calculations of coupled spin and dendrimeric systems

Dani, Reshmi

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https://hdl.handle.net/2142/117725 Copy

Description

Title

Path integral calculations of coupled spin and dendrimeric systems

Author(s)

Dani, Reshmi

Issue Date

2022-09-19

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

Makri, Nancy

Doctoral Committee Chair(s)

Makri, Nancy

Committee Member(s)

• Luthey-Schulten, Zan
• Vura-Weis, Josh
• Pogorelov, Taras

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
• Extended systems

Abstract

Extended systems like interacting spin chains, dendrimers and excitonic transfer complexes are essential to further our understanding of emergent behavior in complex condensed phase systems. Quantum mechanics plays a very important role in investigating such systems. However, exact quantum dynamics calculations of such condensed phase systems are extremely challenging owing to the exponential scaling of quantum mechanics. The work presented in this thesis utilizes the path integral methods developed in the Makri group to perform fully quantum mechanical simulations of such extended systems. The kinds of systems studied here can be broadly divided into two classes: spin chains (quantum transverse field Ising chain) and extended systems with Frenkel interactions (dendrimers, excitonic ring and chains). For the spin systems, the path integral methods are used to obtain real time dynamics of finite-length Ising chains where each spin is coupled to a dissipative bath. The calculations performed emulate a quantum quench experiment, where the chain is initially prepared in the ferromagnetic ‘aligned’ phase and is made to evolve with parameters corresponding to the paramagnetic phase. The corresponding dynamics depends on the system and bath parameters and the temperature. Considerable edge effects are observed too. Another kind of studied in this thesis is the model dendrimer. This is very different from the spin chains and adjacent segments in the dendrimer are known to interact through Frenkel excitations. Almost all examples of dendrimers used to funnel energy have a decreasing site energy towards the core to create an efficient energy funnel. We show here than even in the absence of an explicit energy bias, excitonic couplings can form a funnel to drive the excitation energy from the periphery to the core. The dynamics of the excitation energy in these systems is highly non-trivial and strongly affected by quantum mechanical effects. We show by eigenstate analysis and path integral time dynamics that for certain combinations of these excitonic couplings, we get more EET into the dendrimer core. Some combinations also exhibit frustration (analogous to spin systems) which causes considerable slowdown of the dynamics. Lastly, we present our investigations for a multistate system coupled to a general bath with terms local in the system basis. We show here that the time derivatives of populations are given in terms of imaginary components of coherences, i.e. off-diagonal elements of the reduced density matrix. When the process exhibits rate dynamics, we show that these imaginary components (or flux) exhibit a “plateau” region i.e. a region where the slope changes very slowly. All state-to-state rates can be obtained from the early “plateau” values of these imaginary components. We generalize the reactive flux method and its non-equilibrium version to multi-state processes and show that even in the completely incoherent limit of rate kinetics, the time evolution of populations is governed by coherences. Further, we also show that equilibrium population of the different species is also determined by these imaginary components, more precisely the short time evolution up to the plateau time. We take advantage of the newly formed methods in the Makri lab to perform numerically exact quantum simulations of these extended systems coupled to dissipative baths to reveal the interesting features and the complex interplay between the different time and energy scales in the system which is highly non-trivial and requires a fully quantum mechanical treatment to capture fully what goes on in these systems.

Graduation Semester

2022-12

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Reshmi Dani

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