arXiv subjects

Vinod Krishna

Publications and source records attributed to Vinod Krishna.

5 recordsLinked to original sources

arXiv2015

The context-dependence of mutations: a linkage of formalisms

Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological research, including biochemistry, genomics, protein and systems engineering, medicine, and evolutionary biology. However, the quantitative definitions of epistasis vary among fields, and its analysis beyond just pairwise effects remains obscure in general. Here, we show that different definitions of epistasis are versions of a single mathematical formalism - the weighted Walsh-Hadamard transform. We discuss that one of the definitions, the backgound-averaged epistasis, is the most informative when the goal is to uncover the general epistatic structure of a biological system, a description that can be rather different from the local epistatic structure of specific model systems. Key issues are the choice of effective ensembles for averaging and to practically contend with the vast combinatorial complexity of mutations. In this regard, we discuss possible approaches for optimally learning the epistatic structure of biological systems.

q-bio.QM↗

arXiv2010

A generalized mean field theory of coarse-graining

A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of this theory. The theory also applies to the opposite problem of reduction, where relevant information is extracted from available equilibrium ensemble data. These problems are central to the construction of coarse grained representations of complex systems, and commonly used coarse graining methods are derived as particular cases of the general theory.

cond-mat.stat-mech↗

arXiv2009

Time dependent density functional theory for nonadiabatic electronic dynamics

We show that the time dependent single electron, nuclear density matrix of an interacting electronic system coupled to nuclear degrees of freedom can be exactly reproduced by that of an electronic system with arbitrarily specified electron-electron interactions coupled to the same nuclear degrees of freedom, given the initial density matrix of the interacting system. This formalism enables the construction of rigorous time dependent density functional theories to study nonadiabatic electronic dynamics. We obtain the Runge-Gross and Van Leeuwen theorems as special cases in the adiabatic limit.

cond-mat.mtrl-sci↗

arXiv2007

Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limit

This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral formulation of the quantum nonadiabatic dynamics of Born Oppenheimer systems is described. Stationary phase approximations to the propagator for full quantum dynamics are derived. It is shown that quantum corrections to mixed quantum classical methods can be obtained through stationary phase approximations to the full quantum dynamics. A rigorous description of the quantum corrections due to electronic nonadiabatic coupling on the nuclear dynamics within the Ehrenfest framework is obtained. The fewest switches surface hopping method is shown to be obtained as a quasiclassical approximation to the dynamics and natural semiclassical extensions to include classically forbidden nonadiabatic transitions are suggested.

physics.chem-ph↗

arXiv2006

Quantum equations for vibrational dynamics on metal surfaces

A first-principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin equation with an electronic friction. In the mean field limit, the quantum noise and friction are related by the quantum fluctuation-dissipation theorem. The classical limit of this model is shown to agree with previously proposed models. A criterion is presented to describe the validity of the weak-coupling approximation and equations of motion for the dynamics in the presence of strong nonadiabatic coupling to electron-hole pairs are presented.

cond-mat.mtrl-sci↗