arXiv subjects

Eric R. Bittner

Publications and source records attributed to Eric R. Bittner.

At least 73 records · Page 4Linked to original sources

arXiv2012

Quantum motion of charges in $π$-conjugated polymers: kinkiness induces localization

We develop a model for charge trapping on conjugated polymer chains using a continuous representation of the polymer. By constraining the motion to along the chain, we find that kinks along the chain serve as points of attraction and can induce localization and spontaneous buckling of the chain. We implement this in a model system of a conjugated polymer donor and fullerene acceptor to mimic a polymer based photovoltaic system. We find that geometric fluctuations of the polymer give rise to deep potential energy traps at kinks which are often stronger than the Coulomb interaction between the electron and hole.

cond-mat.soft↗

arXiv2012

Theory of vibronic assistance in the nonequilibrium condensation of exciton polaritons in optically--pumped organic single crystal microcavities

We present a reaction/diffusion model for the formation of a lower polariton condensate in a micro cavity containing an organic semiconducting molecular crystalline film. Our model--based upon an anthracene film sandwiched between two reflecting dielectric mirrors--consists of three coupled fields corresponding to a gas of excitons created by an external driving pulse, a reservoir of vibron states formed by the coupling between a ground-state vibrational model and a cavity photon, and a lower polariton condensate. We show that at finite temperature, the presence of the vibron reservoir can augment the exciton population such that a lower critical pumping threshold is required to achieve condensation.

cond-mat.quant-gas↗

arXiv2011

Estimating the conditions for polariton condensation in organic thin-film microcavities

We examine the possibility of observing Bose condensation of a confined two-dimensional polariton gas in an organic quantum well. We deduce a suitable parameterization of a model Hamiltonian based upon the cavity geometry, the biexciton binding energy, and similar spectroscopic and structural data. By converting the sum-over-states to a semiclassical integration over $d$-dimensional phase space, we show that while an ideal 2-D Bose gas will not undergo condensation, an interacting gas with the Bogoliubov dispersion $H(p)\approx s p$ close to $p=0$ will undergo Bose condensation at a given critical density and temperature. We show that $T_c/\sqrt{ρ_c}$ is sensitive to both the cavity geometry and to the biexciton binding energy. In particular, for strongly bound biexcitons, the non-linear interaction term appearing in the Gross-Pitaevskii equation becomes negative and the resulting ground state will be a localized soliton state rather than a delocalized Bose condensate.

cond-mat.quant-gas↗

arXiv2010

Quantum dynamics and super-symmetric quantum mechanics

In my talk I will present an overview of our recent work involving the use of supersymmetric quantum mechanics (SUSY-QM). I begin by discussing the mathematical underpinnings of SUSY-QM and then discuss how we have used this for developing novel theoretical and numerical approaches suitable for studying molecular systems. I will conclude by discussing our attempt to extend SUSY-QM to multiple dimensions.

quant-ph↗

arXiv2010

Isotopic Effect and Temperature Dependent Intramolecular Excitation Energy Transfer in a Model Donor-Acceptor Dyad

We consider here the non-adiabatic energy transfer dynamics for a model bi-chromophore system consisting of a perylenediimide unit linked to a ladder-type poly-(para-phenylene) oligomer. Starting from a semi-empirical parameterization of a model electron/phonon Hamiltonian, we compute the golden-rule rate for energy transfer from the LPPP5 donor to the PDI acceptor. Our results indicate that the non-adiabatic transfer is promoted by the out-of-plane wagging modes of the C-H bonds even though theses modes give little or no contribution to the Franck Condon factors in this system. We also predict a kinetic isotope effect of $k^{(H)}/k^{(D)} = 1.7 - 2.5$ depending upon the temperature.

cond-mat.mtrl-sci↗

arXiv2009

A Supersymmetric Approach to Excited States via Quantum Monte Carlo

We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrödinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.

hep-th↗

arXiv2008

On the internal photorelaxation mechanism of DNA

We propose a model for the photo-deactivation mechanism for DNA based upon accurate quantum chemical and molecular dynamical evaluations of model Watson/Crick nucleoside pairs and stacked pairs. Our results corroborate recent ultrafast experimental studies on DNA oligonucleotides and suggest that following photo-excitation to a local $π-π^*$ state, the excitation is rapidly delocalized over several (3-4) bases on an ultrafast time-scale. However, this delocalized state is unstable with respect to the motions of the protons involved in hydrogen-bonding between Watson/Crick pairs and rapidly re-localizes to a charge-transfer state on a longer time-scale ranging from 10 to 100 ps. This state, too, is unstable and relaxes via a conical intersection with the ground state near the geometry of the enol- and imino-tautomeric form. We suggest that this internal deactivation mechanism is responsible for the intrinsic photostability of DNA.

cond-mat.soft↗

arXiv2008

Hamiltonian approach for the wave packet dynamics: Beyond Gaussian wave functions

It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential.

quant-ph↗

arXiv2008

Electron transfer dynamics using projected modes

For electron-phonon Hamiltonians with the couplings linear in the phonon operators we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of freedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. We show that for the $n$-level electronic system the minimum number of modes in the first group is $n_s=(n^2+n-2)/2$. The separation of the normal modes into two groups allows one to develop new approximation schemes. We apply one of such schemes to study exitonic relaxation in a model semiconducting molecular heterojuction.

cond-mat.mtrl-sci↗

arXiv2007

Calculations of the Exciton Coupling Elements Between the DNA Bases Using the Transition Density Cube Method

Excited states of the of the double-stranded DNA model (A)$_{12}\cdot$(T)_{12} were calculated in the framework of the exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy $ππ^{*}$ excitations of the individual nucleobases obtained from TDDFT calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal-dipole approximation (IDA) methods were found significantly different for the small inter-chromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of the structural fluctuations were incorporated by averaging the properties of the excited states over a large number of conformations obtained from the MD simulations.

cond-mat.soft↗

arXiv2007

Phonon-driven ultrafast exciton dissociation at donor-acceptor polymer heterojunctions

A quantum-dynamical analysis of phonon-driven exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parameterized for three electronic states and 24 vibrational modes. Two interfering decay pathways are identified: a direct charge separation, and an indirect pathway via an intermediate bridge state. Both pathways depend critically on the dynamical interplay of high-frequency C=C stretch modes and low-frequency ring-torsional modes. The ultrafast, highly non-equilibrium dynamics is consistent with time-resolved spectroscopic observations.

cond-mat.soft↗

arXiv2006

Time-convolutionless master equation dynamics for charge-transfer processes between semiconducting polymers

We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not applicable. Here we apply the approach to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to an Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers. In this later system, we show how both slow and fast phonon modes contribute to the decay of an exciton across a heterojunction interface.

cond-mat.mtrl-sci↗

arXiv2006

Frenkel Exciton Model of Ultrafast Excited State Dynamics in AT DNA Double Helices

Recent ultrafast experiments have implicated intrachain base-stacking rather than base-pairing as the crucial factor in determining the fate and transport of photoexcited species in DNA chains. An important issue that has emerged concerns whether or not a Frenkel excitons is sufficient one needs charge-transfer states to fully account for the dynamics. In we present an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine side of a model B DNA poly(dA).poly(dT) duplex. Our calculations indicate that over several hundred femtoseconds, the adenosine exciton remains a cohesive excitonic wave packet on the adenosine side of the chain where as the thymidine exciton rapidly decomposes into mobile electron/hole pairs along the thymidine side of the chain. In both cases, the very little transfer to the other chain is seen over the time-scale of our calculations. We attribute the difference in these dynamics to the roughly 4:1 ratio of hole vs. electron mobility along the thymidine chain. We also show that this difference is is robust even when structural fluctuations are introduced in the form of static off-diagonal disorder.

cond-mat.dis-nn↗

arXiv2006

Exciton dissociation at donor-acceptor polymer heterojunctions: quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a TFB:F8BT polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C$=$C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree (MCTDH) method.

cond-mat.mtrl-sci↗

arXiv2006

Time-convolutionless master equation for mesoscopic electron-phonon systems

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

cond-mat.mtrl-sci↗

arXiv2006

Excited state dynamics in DNA double helices

Recent ultrafast experiments have implicated that intrachain base-stacking rather than base-pairing mediate the fate and transport of photoexcited species in DNA chains. Here use an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine side of a model B DNA poly(dA).poly(dT) duplex. Our calculations indicate that over several hundred femtoseconds, the adenosine exciton remains a cohesive excitonic wave packet on the adenosine side of the chain where as the thymidine exciton rapidly decomposes into mobile electron/hole pairs along the thymidine side of the chain. In both cases, the very little transfer to the other chain is seen over the time-scale of our calculations. We attribute the difference in these dynamics to the roughly 4:1 ratio of hole vs. electron mobility along the thymidine chain.

cond-mat.soft↗

arXiv2005

An orbital-free self-consistent field approach for molecular clusters and liquids

We present an ``orbital'' free density functional theory for computing the quantum ground state of atomic clusters and liquids. Our approach combines the Bohm hydrodynamical description of quantum mechanics with an information theoretical approach to determine an optimal quantum density function in terms of density approximates to a statistical sample. The ideas of Bayesian statistical analysis and an expectation-maximization procedure are combined to develop approximations to the quantum density and thus find the approximate quantum force. The quantum force is then combined with a Lennard-Jones force to simulate clusters of Argon atoms and to obtain the ground state configurations and energies. As demonstration of the utility and flexibility of the approach, we compute the lowest energy structures for small rare-glass clusters. Extensions to many atom systems is straightforward.

cond-mat.soft↗

arXiv2005

Exactly solvable approximating models for Rabi Hamiltonian dynamics

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

quant-ph↗