Lattice Equations Of Motion Research Articles

Lattice formulation of axion inflation. Application to preheating

We present a lattice formulation of an interaction ϕ/Λ F̃ F between an axion and some U(1) gauge sector with the following properties: it reproduces the continuum theory up to \U0001d4aa(dxμ2) corrections, it preserves exact gauge invariance and shift symmetry on the lattice, and it is suitable for self-consistent expansion of the Universe. The lattice equations of motion can no longer be solved by explicit methods, but we propose an implicit method to overcome this difficulty, which preserves the relevant system constraints down to arbitrary (tunable) precision. As a first application we study, in a comoving grid in (3+1) dimensions, the last efolds of axion-inflation with quadratic potential and the preheating stage following afterwards. We fully account for the inhomogeneity and non-linearity of the system, including the gauge field contribution to the expansion rate of the Universe and its backreaction into the axion dynamics. We characterize in detail, as a function of the coupling, the energy transfer from the axion to the gauge field. Two coupling regimes are identified, sub- and super-critical, depending on whether the final energy fraction stored in the gauge field is below or above ∼ 50% of the total energy. The Universe is very efficiently reheated for super-critical couplings, rapidly entering in a radiation dominated stage. Our results on preheating confirm previously published results.

Effect of disorder on exciton dissociation in conjugated polymers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474218 and 11575116).

By using a multi-configurational time-dependent Hartree–Fock (MCTDHF) method for the time-dependent Schrödinger equation and a Newtonian equation of motion for lattice, we investigate the disorder effects on the dissociation process of excitons in conjugated polymer chains. The simulations are performed within the framework of an extended version of the Su–Schrieffer–Heeger model modified to include on-site disorder, off-diagonal, electron–electron interaction, and an external electric field. Our results show that Coulomb correlation effects play an important role in determining the exciton dissociation process. The electric field required to dissociate an exciton can practically impossibly occur in a pure polymer chain, especially in the case of triplet exciton. However, when the on-site disorder effects are taken into account, this leads to a reduction in mean dissociation electric fields. As the disorder strength increases, the dissociation field decreases effectively. On the contrary, the effects of off-diagonal disorder are negative in most cases. Moreover, the dependence of exciton dissociation on the conjugated length is also discussed.

Effect of dynamic disorder on charge transport along a pentacene chain

The lattice equation of motion and a numerical solution of the time-dependent Schr\"odinger equation provide us with a microscopic picture of charge transport in highly ordered molecular crystals. We have chosen the pentacene single crystal as a model system, and we study charge transport as a function of phonon-mode time-dependent fluctuations in the intermolecular electron transfer integral. For comparison, we include similar fluctuations also in the intramolecular potentials. The variance in these energy quantities is closely related to the temperature of the system. The pentacene system is shown to be very sensitive to fluctuation in the intermolecular transfer integral, revealing a transition from adiabatic to nonadiabatic polaron transport for increasing temperatures. The extension of the polaron at temperatures above 200 K is limited by the electron localization length rather than the interplay between the electron transfer integral and the electron-phonon coupling strength.

Photo-generation of polaron pairs in coupled chains of polyacetylene

The dynamics of photo-excitations to describe the generation mechanism of charged polaron pairs belonging to parallel conjugated polymer chains is investigated. The interchain interaction of two parallel chains is studied numerically through the dynamics of the electron-lattice system in the presence of an electric field by using the an extension of the Su–Schrieffer–Heeger model. The electric field is introduced in terms of a time-dependent vector potential which is present in the Hamiltonian through a Peierls substitution of the phase factor to the transfer integral. The lattice dynamical relaxation from the photo-excited states in a few tenths of femtosecond to charged polarons belonging to neighboring chains is determined by the numerical resolution of the electronic and lattice equations of motion. It is shown in the present study that interchain interactions are determinant in the photo-carrier quantum efficiency calculation in conjugated polymers.

Impact of ring torsion on the intrachain mobility in conjugated polymers

In this thesis we explore in particular the dynamics of a special type of quasi-particle in pi-conjugated materials termed polaron, the origin of which is intimately related to the strong interactions between the electronic and the vibrational degrees of freedom within these systems. In order to conduct such studies with the particular focus of each appended paper, we simultaneously solve the time-dependent Schrodinger equation and the lattice equation of motion with a three-dimensional extension of the famous Su-Schrieffer-Heeger (SSH) model Hamiltonian. In particular, we demonstrate in Paper I the applicability of the method to model transport dynamics in molecular crystals in a region were neither band theory nor perturbative treatments such as the Holstein model and extended Marcus theory apply. In Paper II we expand the model Hamiltonian to treat the revolution of phenylene rings around the sigma-bonds and demonstrate the great impact of stochastic ring torsion on the intra-chain mobility in conjugated polymers using poly[phenylene vinylene] (PPV) as a model system. Finally, in Paper III we go beyond the original purpose of the methodology and utilize its great flexibility to study radiationless relaxations of hot excitons.

Polaron dynamics in highly ordered molecular crystals

From a numerical solution of the time-dependent Schrödinger equation and the lattice equation of motion we obtain a microscopic picture of polaron transport in highly ordered molecular crystals in the presence of an external electric field. We have chosen the pentacene single crystal as a model system, but study the transport as a function of the intermolecular interaction strength, J. We observe a smooth transition from a nonadiabatic to an adiabatic polaronic drift process over the regime 20 < J < 120 meV. For intermolecular interaction strengths above ∼120 meV the polaron is no longer stable and the transport becomes band like.

Electric Conduction Due to an Acoustic Bipolaron in One-Dimensional Electron-Lattice System

In order to estimate the mobility of an acoustic bipolaron in a typical non-degenerated polymer such as polydiacetylene (PDA), which can be regarded as a one-dimensional electron-lattice system, the dynamical behavior of an acoustic bipolaron in an external electric field is numerically investigated in the presence of a phenomenological damping of the lattice motion. In these simulations, we use the Su, Schrieffer and Heeger (SSH) Hamiltonian extended to include on-site and nearest-neighbor Coulomb repulsion terms, and the damping is introduced by adding a phenomenological friction term in the lattice equation of motion. The repulsive interactions are treated within the unrestricted time-dependent Hartree–Fock approximation. It is confirmed that the mobility of a bipolaron increases with the increase of the repulsion strength and that the relevant quantity determining the mobility of a bipolaron is its width as far as the phenomenological friction is kept fixed. The mobility of a bipolaron is compared wit...

Influence of surface impurity on impact response of lattices

An analytical and computational study has been made of the influence of surface impurity on the normal impact response of two identical crystal lattices. Identical monolayers of adsorbed atoms are considered to cover each host lattice. The incoming lattice is assumed to move with uniform initial speed, impacting an initially motionless lattice. A nonlinear differential-integral equation governing the impact response of the surface impurity is derived and then solved analytically by asymptotic expansion for compressive interaction. For numerical calculations, oxygen surface impurity and a copper host lattice are considered, with surface interaction force determined from quantum-mechanical results. Because the surface interaction force exhibits a gradual long-range change in force with distance, surface oscillations do not occur during impact. The time required for the surface of an impacted lattice to accelerate to the classical continuum shock velocity is shown to depend on impact velocity and two parameters from the quantum-mechanical calculations. The subsequent distance at which breakdown of weak shock-wave motion far into the interior of the lattice occurs is determined by a simple approximation. Shock responses in the lattice beyond the breakdown distance are determined by numerical integration of both the lattice equations of motion, with quadratic nonlinear force interaction between atoms, and the Korteweg–de Vries (KdV) equation. The asymptotic solution for velocity response of the surface impurity provides the initial condition for numerical integration of the KdV equation. The calculations for both sets of equations show a good correspondence in the structure of the shock wave far into the lattice.