Doctor of Philosophy, Columbia University (2016)
Master of Philosophy, Columbia University (2015)
Master of Arts, Columbia University (2013)
Master of Arts, CUNY Queens College (2011)
Bachelor of Arts, CUNY Queens College (2009)
Thomas Markland, Postdoctoral Faculty Sponsor
Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions
The Journal of Chemical Physics
View details for DOI 10.1063/1.4975388
Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths
The Journal of Chemical Physics
View details for DOI 10.1063/1.4973646
Generalized quantum master equations in and out of equilibrium: When can one win?
JOURNAL OF CHEMICAL PHYSICS
2016; 144 (18)
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
View details for DOI 10.1063/1.4948612
View details for Web of Science ID 000377711900006
View details for PubMedID 27179469
Energy Transfer from Quantum Dots to Graphene and MoS2: The Role of Absorption and Screening in Two-Dimensional Materials.
2016; 16 (4): 2328-2333
We report efficient nonradiative energy transfer (NRET) from core-shell, semiconducting quantum dots to adjacent two-dimensional sheets of graphene and MoS2 of single- and few-layer thickness. We observe quenching of the photoluminescence (PL) from individual quantum dots and enhanced PL decay rates in time-resolved PL, corresponding to energy transfer rates of 1-10 ns(-1). Our measurements reveal contrasting trends in the NRET rate from the quantum dot to the van der Waals material as a function of thickness. The rate increases significantly with increasing layer thickness of graphene, but decreases with increasing thickness of MoS2 layers. A classical electromagnetic theory accounts for both the trends and absolute rates observed for the NRET. The countervailing trends arise from the competition between screening and absorption of the electric field of the quantum dot dipole inside the acceptor layers. We extend our analysis to predict the type of NRET behavior for the near-field coupling of a chromophore to a range of semiconducting and metallic thin film materials.
View details for DOI 10.1021/acs.nanolett.5b05012
View details for PubMedID 26928675
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.
The Journal of chemical physics
2016; 144 (18): 184104
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
View details for DOI 10.1063/1.4948408
View details for PubMedID 27179468
Extending the applicability of Redfield theories into highly non-Markovian regimes
JOURNAL OF CHEMICAL PHYSICS
2015; 143 (19)
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna-Matthews-Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
View details for DOI 10.1063/1.4935443
View details for Web of Science ID 000366524700011
View details for PubMedID 26590528
Charge Hopping Dynamics along a Disordered Chain in Quantum Environments: Comparative Study of Different Rate Kernels
JOURNAL OF PHYSICAL CHEMISTRY B
2015; 119 (24): 7659-7665
This work presents a computational study of charge hopping dynamics along a one-dimensional chain with Gaussian site energy disorder and linearly coupled quantum bath. Time-dependent square displacements are calculated directly from numerical solutions of Pauli master equations, for five different rate kernels: exact Fermi golden rule (FGR) rate expression, stationary phase interpolation (SPI) approximation, semiclassical (SC) approximation, classical Marcus rate expression, and Miller-Abrahams expression. All results demonstrate diffusive behavior in the steady state limit. The results based on the FGR rate expression show that the charge transport in the quantum bath can be much more sensitive to the disorder than the prediction from the classical Marcus expression. While the SPI approximation captures this general trend reasonably well, the SC approximation tends to be unreliable at both quantitative and qualitative levels and becomes even worse than the classical Marcus expression under certain conditions. These results offer useful guidance in the choice of approximate rate kernels for larger-scale simulations and also demonstrate significant but fragile positive effects of quantum environments on the charge hopping dynamics.
View details for DOI 10.1021/jp511933m
View details for Web of Science ID 000356754800055
View details for PubMedID 25803833
- ESR analyses for teeth from the open-air site at Attirampakkam, India: Clues to complex U uptake and paleoenvironmental change RADIATION MEASUREMENTS 2007; 42 (6-7): 1243-1249