arXiv subjects

V. Kapoor

Publications and source records attributed to V. Kapoor.

3 recordsLinked to original sources

arXiv2015

Health risk modelling by transforming a multi-dimensional unknown distribution to a multi-dimensional Gaussian

The traditional approach of health risk modelling with multiple data sources proceeds via regression-based methods assuming a marginal distribution for the outcome variable. The data is collected for $N$ subjects over a $J$ time-period or from $J$ data sources. The response obtained from $i^{th}$ subject is $\vec{Y}_i=({Y}_{i1},\cdots, {Y}_{iJ})$. For $N$ subjects we obtain a $J$ dimensional joint distribution for the subjects. In this work we propose a novel approach of transforming any $J$ dimensional joint distribution to that of a $J$ dimensional Gaussian keeping the Shannon entropy constant. This is in stark contrast to the traditional approaches of assuming a marginal distribution for each $Y_{ij}$ by treating the $Y_{ij}'$s as independent observations. The said transformation is implemented in our computer package called ENTRA.

physics.data-an↗

arXiv2013

Periodicity of the time-dependent Kohn-Sham equation and the Floquet theorem

The Floquet theorem allows to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density functional theory as well, one could reduce in such cases time-dependent density functional theory to a time-independent Floquet density functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical {\em ab initio} solutions of the interacting time-dependent Schrödinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is {\em not} unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.

physics.atom-ph↗

arXiv2012

Floquet analysis of real-time wavefunctions without solving the Floquet equation

We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily discussed: (i) the observation of even harmonics for an inversion-symmetric potential with a single bound state; (ii) the dependence of the population of Floquet states on (gauge) transformations and the emergence of an invariant, observable photoelectron spectrum; (iii) the driving of resonant transitions between dressed states, i.e., the dressing of dressed states, and (iv) spectral enhancements at channel closings due to the ponderomotive shift of above-threshold ionization peaks.

physics.atom-ph↗