arXiv subjects

Seogjoo Jang

Publications and source records attributed to Seogjoo Jang.

7 recordsLinked to original sources

arXiv2017

Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [ J. Chem. Phys. 138 , 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general, and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.

quant-ph↗

arXiv2016

Can quantum transition state theory be defined as an exact t=0+ limit?

The definition of the classical transition state theory (TST) as a t= 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t=0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t=0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t=0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative path integral quantum rate expression is then formulated based on the linear response theory. It is shown that the t=0+ limit of the new rate expression vanishes in the exact quantum limit.

physics.chem-ph↗

arXiv2016

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Caldeira and Leggett, Physica A 121, 587 (1983)] is extended for a nonequilibrium influence functional, which has been obtained for general cases where the ground and the excited electronic state baths can be different. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional with respect to time up to the second order. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation, but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived through short time expansion of the effective action followed by Gaussian integrations in analytically continued complex domain of space. This leads to a compact form of GQFPE with time dependent kernels and additional terms, which make the resulting equation the Dekker form [H. Dekker, Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit.

quant-ph↗

arXiv2014

Real time quantum dynamics preaveraged over imaginary time path integral: A formal basis for both Centroid Molecular Dynamics and Ring Polymer Molecular Dynamics

An exact real time quantum dynamics preaveraged over imaginary time path integral is formulated for general condensed phase equilibrium ensemble. This formulation results in the well-known centroid dynamics approach upon filtering of centroid constraint, and provides a rigorous framework to understand and analyze a related quantum dynamics approximation method called ring polymer molecular dynamics. The formulation also serves as the basis for developing new kinds of quantum dynamics that utilize the cyclic nature of the imaginary time path integral.

quant-ph↗

arXiv2013

Generalized master equation for modular exciton density transfer

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations at small length scales into dynamics over large length scales, without assumptions of time scale separation or specific forms of intra-module quantum dynamics. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over many coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons.

quant-ph↗

arXiv2013

Coherent quantum dynamics in donor-bridge-acceptor systems: Beyond the hopping and super-exchange mechanisms

The population transfer dynamics of model donor-bridge-acceptor systems is studied by comparing a recently developed polaron-transformed quantum master equation (PQME) with the well-known Redfield and Forster theories of quantum transport. We show that the PQME approach reduces to these two theories in their respective limits of validity and naturally interpolates between them as a function of the system-bath coupling strength. By exploring the parameter space of our model problem, we identify novel regimes of transport dynamics in bridged systems like those encountered in biological and organic energy transfer problems. Furthermore, we demonstrate that three-level systems like the ones studied herein represent ideal minimal models for the identification of quantum coherent transport as embodied in super-exchange phenomena that cannot be captured by Forster-like hopping approaches.

cond-mat.mes-hall↗

arXiv2002

Nonequilibrium generalization of Förster-Dexter theory for excitation energy transfer

Förster-Dexter theory for excitation energy transfer is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation-bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed.

cond-mat.stat-mech↗