Sergey V. Malinin

Non-Equilibrium Thermodynamics and Topology of Currents

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as for global topological currents, and formulate variational, thermodynamic relations to establish large deviation properties of the topological currents. We illustrate the theory with a nontrivial example of a Heisenberg spin-chain with a topological driving of the Wess-Zumino type. The Cramér functional of the topological current is found explicitly in the instanton gas regime for the spin-chain model in the weak-noise limit. In the context of the Morse theory, we discuss a general reduction of continuous stochastic models with weak noise to effective Markov chains describing transitions between stable fixed points.

Transition times in the low-noise limit of stochastic dynamics

We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding the most probable trajectory. We demonstrate that finding the transition time distribution reduces to a one-dimensional problem. The resulting transition time distribution has a universal and compact form. We suggest that transition barriers can be estimated from a single-temperature experiment if both the life times and the transition times are measured.

Classical nonlinear response of a chaotic system. I. Collective resonances.

We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.

Exciton scattering approach for branched conjugated molecules and complexes. I. Formalism

We develop a formalism for the exciton scattering (ES) approach to calculation of the excited state electronic structure of branched conjugated polymers with insignificant numerical expense. The ES approach attributes electronic excitations in quasi-one-dimensional molecules to standing waves formed by the scattering of quantum quasiparticles. We derive the phenomenology from the microscopic description in terms of many-electron excitations. The presented model can be used to compute both excited state frequencies and transition dipoles in large molecules after the ES ingredients are extracted from smaller molecular fragments.

Exciton scattering approach for branched conjugated molecules and complexes. II. Extraction of the exciton scattering parameters from quantum-chemical calculations

We obtain the parameters of the exciton scattering (ES) model from the quantum-chemical calculations of the electronic excitations in simple phenylacetylene-based molecules. We determine the exciton dispersion and the frequency-dependent scattering matrices which describe scattering properties of the molecular ends as well as of meta- and orthoconjugated links. The extracted functions are smooth, which confirms the validity of the ES picture. We find a good agreement between the ES and quantum-chemical results for the excitation energies in simple test molecules.

Coulomb blockade and transport in a chain of one-dimensional quantum dots

A long one-dimensional wire with a finite density of strong random impurities is modeled as a chain of weakly coupled quantum dots. At low temperature T and applied voltage V its resistance is limited by breaks: randomly occurring clusters of quantum dots with a special length distribution pattern that inhibit the transport. Because of the interplay of interaction and disorder effects the resistance can exhibit T and V dependences that can be approximated by power laws. The corresponding two exponents differ greatly from each other and depend not only on the intrinsic electronic parameters but also on the impurity distribution statistics.

Exciton scattering approach for branched conjugated molecules and complexes. IV. Transition dipoles and optical spectra

The electronic excitation energies and transition dipole moments are the essential ingredients to compute an optical spectrum of any molecular system. Here we extend the exciton scattering (ES) approach, originally developed for computing excitation energies in branched conjugated molecules, to the calculation of the transition dipole moments. The ES parameters that characterize contributions of molecular building blocks to the total transition dipole can be extracted from the quantum-chemical calculations of the excited states in simple molecular fragments. Using these extracted parameters, one can then effortlessly calculate the oscillator strengths and optical spectra of various large molecular structures. We illustrate application of this extended ES approach using an example of phenylacetylene-based molecules. Absorption spectra predicted by the ES approach show close agreement with the results of the reference quantum-chemical calculations.

Exciton scattering approach for branched conjugated molecules and complexes. III. Applications.

The exciton scattering (ES) approach is an efficient tool to calculate the excited states electronic structure in large branched polymeric molecules. Using the previously extracted parameters, we apply the ES approach to a number of phenylacetylene-based test molecules. Comparison of ES predictions with direct quantum chemistry results for the excitation energies shows an agreement within several meV. The ES framework provides powerful insights into photophysics of macromolecules by revealing the connections between the molecular structure and the properties of the collective electronic states, including spatial localization of excitations controlled by the energy.

Exciton Scattering on Symmetric Branching Centers in Conjugated Molecules

The capability of the exciton scattering approach, an efficient methodology for excited states in branched conjugated molecules, is extended to include symmetric triple and quadruple joints that connect linear segments on the basis of the phenylacetylene backbone. The obtained scattering matrices that characterize these vertices are used in application of our approach to several test structures, where we find excellent agreement with the transition energies computed by the reference quantum chemistry. We introduce topological charges, associated with the scattering matrices, which help to formulate useful relations between the number of excitations in the exciton band and the number of repeat units. The obtained features of the scattering phases are analyzed in terms of the observed excited state electronic structure.

Effective tight-binding models for excitons in branched conjugated molecules

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices to be described in terms of a small number of lattice parameters which can be obtained from quantum-chemical computations using the exciton scattering approach as a tool. We illustrate the tight-binding model approach using the time-dependent Hartree-Fock computations in phenylacetylene oligomers. The on-site energies and hopping constants have been identified from the exciton dispersion and scattering matrices. In particular, resonant, as well as bound states, are reproduced for a symmetric quadruple branching center. The capability of the tight-binding model approach to describe the exciton-phonon coupling and energetic disorder in large branched conjugated molecules is briefly discussed.