arXiv subjects

Eric R. Bittner

Publications and source records attributed to Eric R. Bittner.

87 records · Page 5Linked to original sources

arXiv2005

Exciton and charge-transfer dynamics in polymer semiconductors

Organic semiconducting polymers are currently of broad interest as potential low-cost materials for photovoltaic and light-emitting display applications. I will give an overview of our work in developing a consistent quantum dynamical picture of the excited state dynamics underlying the photo-physics. We will also focus upon the quantum relaxation and reogranization dynamics that occur upon photoexcitation of a couple of type II donor-acceptor polymer heterojunction systems. Our results stress the significance of vibrational relaxation in the state-to- state relaxation and the impact of curve crossing between charge- transfer and excitonic states. Furthermore, while a tightly bound charge-transfer state (exciplex) remain the lowest excited state, we show that the regeneration of the optically active lowest excitonic state in TFB:F8BT is possible via the existence of a steady-state involving the bulk charge-transfer state. Finally, we will discuss ramifications of these results to recent experimental studied and the fabrication of efficient polymer LED and photovoltaics.

cond-mat.mtrl-sci↗

arXiv2005

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.

cond-mat.stat-mech↗

arXiv2005

Exciton Dissociation Dynamics in Model Donor-Acceptor Polymer Heterojunctions: I. Energetics and Spectra

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band off-set in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band off-set at the heterojunction, the exciton will remain the lowest energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the off-set is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases.

cond-mat.mtrl-sci↗

arXiv2004

Interchain versus intrachain hole transmission through desoxyribonucleic acid molecular wires

We present a methodology for computing the current-voltage response of a molecular wire within the Landauer-Buttiker formalism based upon transforming the cummulative transmission probability into an eigenvalue problem. The method is extremely simple to apply since does not involve construction of the molecular Greens function, and hence avoids the use of complex integration contours to avoid poles. We use this method to study the effect of base-pair sequence on the conductivity of holes in DNA chains containing A-T bridges between guanine chains. Our results indicate that sequence plays a substantial role in ballistic transport via tunneling resonances tuned by sequence and interchain interactions. We also find that ballistic transport is dominated by intrachain transport and that hole transmission is insensitive to interchain fluctuations.

cond-mat.mtrl-sci↗

arXiv2003

Current producing states in molecular semiconductors: photo-current from a molecular wire

We present a methodology for computing photocurrent production in molecular semiconducting molecules. Our model combines a single-configuration interaction picture with the Schwinger-Keldysh non-equilibrium Greens function approach to compute the current response of a molecular semi-conducting wire following excitation. We give detailed analysis of the essential excitonic, charge-transfer, and dipole states for poly-(phenylenevinylene) chains of length 32 and 48 repeat units under an electric field bias and use this to develop a reduced dimensional tunneling model which accounts for chain-length and field-dependent behavior.

cond-mat.mtrl-sci↗

arXiv2003

Quantum initial value representations using approximate Bohmian trajectories

Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that time-correlation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems.

quant-ph↗

arXiv2003

Energy relaxation dynamics and universal scaling laws in organic light emitting diodes

Electron-hole (e-h) capture in luminescent conjugated polymers (LCPs) is modeled by the dissipative dynamics of a multilevel electronic system coupled to a phonon bath. Electroinjected e-h pairs are simulated by a mixed quantum state, which relaxes via phonon-driven internal conversions to low-lying charge-transfer (CT) and excitonic (XT) states. The underlying two-band polymer model reflects PPV and spans monoexcited configuration interaction singlets (S) and triplets (T), coupled to Franck-Condon active C=C stretches and ring-torsions. Focusing entirely upon long PPV chains, we consider the recombination kinetics of an initially separated CT pair. Our model calculations indicated that S and T recombination proceeds according to a branched, two-step mechanism dictated by near e-h symmetry. The initial relaxation occurs rapidly with nearly half of the population going into excitons ($S_{XT}$ or $T_{XT}$), while the remaining portion remains locked in metastable CT states. While formation rates of $S_{CT}$ and $T_{CT}$ are nearly equal, $S_{XT}$ is formed about twice as fast $T_{XT}$ in concurrence with experimental observations of these systems. Furthermore, breaking e-h symmetry suppresses the XT to CT branching ratio for triplets and opens a slow CT$\to$ XT conversion channel exclusively for singlets due to dipole-dipole interactions between geminate and non-geminate configurations. Finally, our calculations yield a remarkable linear relation between chain length and singlet/triplet branching ratio which can be explained in terms of the binding energies of the respective final excitonic states and the scaling of singlet-triplet energy gap with chain length.

cond-mat.mtrl-sci↗

arXiv2003

Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids

Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementation are discussed, including fitting of the fields to gaussian clusters.

quant-ph↗

arXiv2002

Interplay between the repulsive and attractive interaction and the spacial dimensionality of an excess electron in a simple fluid

The behavior of an excess electron in a one, two and three dimensional classical liquid has been studied with the aid of Chandler, Singh and Richardson (CSR) theory [J. Chem. Phys. {\bf 81} 1975 (1984)] . The size or dispersion of the wavepacket associated with the solvated electron is very sensitive to the interaction between the electron and fluid atoms, and exhibits complicated behavior in its density dependence. The behavior is interpreted in terms of an interplay among four causes: the excluded volume effect due to solvent, the pair attractive interaction between the electron and a solvent atom, the thermal wavelength of the electron ($λ_e$), a balance of the attractive interactions from different solvent atoms and the range of repulsive interaction between electron and solvent atom. Electron self-trapping behavior in all the dimensions has been studied for the same solvent-solvent and electron-solvent interaction potential and the results are presented for the same parameter in every dimension to show the comparison between the various dimensions.

cond-mat.stat-mech↗

arXiv2001

Quantum Liouville-space trajectories for dissipative systems

In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum equations-of-motion for Liouville-space trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and non-local quantum potential which continuously produces coherences in the system. These trajectories are then used to propagate an adaptive Lagrangian grid which carries the density matrix, $ρ(x,y)$, and the action, $A(x,y)$, thereby providing a complete hydrodynamic-like description of the dynamics.

quant-ph↗

arXiv2000

Quantum tunneling dynamics using hydrodynamic trajectories

In this paper we compute quantum trajectories arising from Bohm's causal description of quantum mechanics. Our computational methodology is based upon a finite-element moving least-squares method (MWLS) presented recently by Wyatt and co-workers (Lopreore and Wyatt, Phys. Rev. Lett. {\bf 82}, 5190 (1999)). This method treats the "particles" in the quantum Hamilton-Jacobi equation as Lagrangian fluid elements which carry the phase, $S$, and density, $ρ$, required to reconstruct the quantum wavefunctions. Here, we compare results obtained via the MWLS procedure to exact results obtained either analytically or by numerical solution of the time dependent Schrödinger equation. Two systems are considered: firstly, dynamics in a harmonic well and secondly tunneling dynamics in a double well potential. In the case of tunneling in the double well potential, the quantum potential acts to lower the barrier separating the right and left hand sides of the well permitting trajectories to pass from one side to another. However, as probability density passes from one side to the other, the effective barrier begins to rise and eventually will segregate trajectories in one side from the other. We note that the MWLS trajectories exhibited long time stability in the purely harmonic cases. However, this stability was not evident in the barrier crossing dynamics. Comparisons to exact trajectories obtained via wave packet calculations indicate that the MWLS trajectories tend to underestimate the effects of constructive and destructive interference effects.

quant-ph↗

arXiv1999

Car-Parrinello Molecular Dynamics on excited state surfaces

This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the electronic excitation energy of the system, we derive coupled equations of motion for the RPA amplitudes, the single particle orbitals, and the nuclear coordinates. These equations scale linearly with basis size and can be implemented with only a single holonomic constraint. Test calculations on a model two level system give exact agreement with analytical results. Furthermore, we examined the computational efficiency of the method by modeling the excited state dynamics of a one-dimensional polyene lattice. Our results indicate that the present method offers a considerable decrease in computational effort over a straight-forward configuration interaction (singles) plus gradient calculation performed at each nuclear configuration.

cond-mat↗

arXiv1997

Numerical Simulations of Free Radical Reactions

We present an overview of the role of quantum coherence in influencing nonadiabatic processes in the condensed phase. Equations of motion for mixed quantum-classical dynamics are derived from the Consistent Histories interpretation of quantum mechanics. Application of the methods toward computing the excited state lifetime of an excess electron in water and heavy water provides a unique demonstration of our method.

physics.chem-ph↗

arXiv1997

Decoherent Histories and Non-adiabatic Quantum Molecular Dynamics

The role of quantum coherence loss in mixed quantum-classical dynamical systems is explored in the context of the theory of quantum decoherence introduced recently by Bittner and Rossky. (J. Chem. Phys. {\bf 103}, 8130 (1995)). This theory, which is based upon the consistent histories interpretation of quantum mechanics, introduces decoherence in the quantum subsystem by carefully considering the relevant time and length scales over which one must consider the effects of phase interference between alternative histories of the classical subsystem. Such alternative histories are an integral part of any quantum-classical computational scheme which employ transitions between discrete quantum states; consequently, the coherences between alternative histories have a profound effect on the transition probability between quantum states. In this paper, we review the Bittner-Rossky theory and detail a computational algorithm suitable for large-scale quantum molecular dynamics simulations which implements this theory. Application of the algorithm towards the relaxation of a photoexcited aqueous electron compare well to previous estimates of the excited state survival time as well as to the experimental measurements.

physics.chem-ph↗

arXiv1994

Many-Body effects and resonances in universal quantum sticking of cold atoms to surfaces

The role of shape resonances and many-body effects on universal quantum sticking of ultra cold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the the transition amplitude between an ultra cold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom-surface potentials, virtual phonons can only rescale the strength of the atom-surface coupling and do not rescale the range of the coupling. Thus, universal sticking behaviour at ultra-low energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal $s(E)\propto\sqrt{E}$ can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of sub-millikelvin H atoms from superfluid $^4$He films.

chem-ph↗