arXiv subjects

P. C. Deshmukh

Publications and source records attributed to P. C. Deshmukh.

11 recordsLinked to original sources

arXiv2026

Exact Thermoelectric Transport Coefficients and Figure of Merit for Graphene Photothermoelectric Devices from a Finite Zeta-Function Mott Series

The standard Mott formula is widely used to describe thermoelectric transport, but it becomes less accurate when the temperature is not much smaller than the Fermi energy. In this work, we develop an all-orders extension of the Mott approach using a series of Riemann zeta functions. We show that when the transport function is a polynomial, the series ends after a finite number of terms, giving exact results within the model. We apply this method to graphene photothermoelectric devices using a quadratic conductivity model. The results provide closed-form expressions for the Seebeck coefficient, Lorenz ratio, and electronic figure of merit. The analysis shows that the Seebeck coefficient reaches a maximum instead of increasing indefinitely, while the Wiedemann-Franz law can be significantly violated at higher temperatures. We also find that disorder reduces the thermoelectric performance and that the electronic figure of merit has an upper limit in the clean graphene model. Finally, we discuss the effect of radiative heat transport on the figure of merit. These results provide a simple analytical way to study graphene thermoelectric transport beyond the usual low-temperature Mott approximation.

cond-mat.stat-mech↗

arXiv2026

Lambert W Function Framework for Graphene Nanoribbon Quantum Sensing: Theory, Verification, and Multi-Modal Applications

We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W)=We^W$, provides exact analytical solutions to transcendental equations governing quantum confinement. Operating near the branch point singularity at $z=-1/e$ yields sensitivity enhancement factors scaling as $(z-z_c)^{-1/2}$, achieving 35-fold enhancement when the operating point lies within $δ=0.001$ of the branch point. Comprehensive numerical verification confirms: (i) all seven bound states for strength parameter $R=10$ satisfy the constraint $u^2+v^2=R^2$ to machine precision; (ii) the theoretical band gap formula $E_g=2π\hbar v_F/(3W)$ is analytically equivalent to the independently determined empirical relation $E_g=1.38/W$~eV$\cdot$nm, establishing the validity of the FSW-GNR analogy; (iii) a universal sensitivity factorization $S_X = \mathcal{G}_k \cdot η_{\rm enh} \cdot \mathcal{P}_X$ applies across biomedical (SARS-CoV-2, inflammatory markers, cancer biomarkers), environmental (CO$_2$, CH$_4$, NO$_2$, N$_2$O, H$_2$O), and physical (strain, magnetic field, temperature) sensing modalities. This unified framework provides analytically predictable design principles for next-generation graphene quantum sensors. The framework is analytic and predictive rather than microscopic or experimental: band-structure and adsorption parameters are taken as inputs from tight-binding, first-principles, and experimental sources, and the framework returns closed-form sensitivity and design relations built upon them. Reported detection limits are labelled throughout as either literature-demonstrated device values or values predicted by the present framework.

cond-mat.mes-hall↗

arXiv2023

Solar Cells, Lambert W and the LogWright Functions

Algorithms that calculate the current-voltage (I-V) characteristics of a solar cell play an important role in processes that aim to improve the efficiency of a solar cell. I-V characteristics can be obtained from different models used to represent the solar cell, and the single diode model is a simple yet accurate model for common field implementations. However, the I-V characteristics are obtained by solving implicit equations, which involve repeated iterations and inherent errors associated with numerical methods used. Some methods use the Lambert W function to get an exact explicit formula, but often causes numerical overflow problems. The present work discusses an algorithm to calculate I-V characteristics using the LogWright function, a transformation of the Lambert W function, which addresses the problem of arithmetic overflow that occurs in the Lambert W implementation. An implementation of this algorithm is presented and compared against other algorithms in the literature. It is observed that in addition to addressing the numerical overflow problem, the algorithm based on the LogWright function offers speed benefits while retaining high precision.

physics.comp-ph↗

arXiv2023

Great Inequality of Jupiter and Saturn I: The Planetary Three Body Problem, Heliocentric development by Lagrange multipliers, Perturbation Theory Formulation

In this paper, we undertake to present a self-contained and thorough analysis of the gravitational three body problem, with anticipated application to the Great Inequality of Jupiter and Saturn. The analysis of the three body Lagrangian is very convenient in heliocentric coordinates with Lagrange multipliers, the coordinates being the vector-sides $\vec{r}_i,\,i=1,2,3$ of the triangle that the bodies form. In two dimensions to begin with, the equations of motion are formulated into a dynamical system for the polar angles $θ_i$, angular momenta $\ell_i$ and eccentricity vectors $\vec{e}_i$. The dynamical system is simplified considerably by change of variables to certain auxiliary vector $\vec{f}_i=\hat{r}_i+\vec{e}_i$. We then begin to formulate the Hamiltonian perturbation theory of the problem, now in three dimensions. We first give the geometric definitions for the Delaunay action-angle variables of the two body problem. We express the three body Hamiltonian in terms of Delaunay variables in each sector $i=1,2,3$, revealing that it is a nearly integrable Hamiltonian. We then present the KAM theory perturbative approach that will be followed in future work, including the modification that will be required because the Hamiltonian is degenerate.

physics.class-ph↗

arXiv2022

Lambert W Lines and Finite Square Well Sensors

The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular strengths of the FSW at which the system can become unusually sensitive to changes in the well depth or geometry. In the present paper we explore that sensitivity, and exhibit a 3-D visualization of the solutions.

quant-ph↗

arXiv2016

Relativistic calculations of angular dependent photoemission time delay

Angular dependence of photoemission time delay for the valence $np_{3/2}$ and $np_{1/2}$ subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.

physics.atom-ph↗

arXiv2015

Band structure and transport studies of half Heusler compound DyPdBi: An efficient thermoelectric material

The discovery of Heusler alloys has revolutionized the research field of intermetallics due to the ease with which one can derive potential candidates for multifunctional applications. During recent years, many half Heusler alloys have been investigated for their thermoelectric properties. The f electron based rare earth ternary half Heusler compound DyPdBi has its f energy levels located close to the Fermi energy level. Other research efforts have emphasized that such materials have good thermoelectric capabilities. We have explored using first principles the electronic band structure of DyPdBi by use of different exchange correlation potentials in the density functional theoretical framework. Transport coefficients that arise in the study of thermoelectric properties of DyPdBi have been calculated and illustrate its potential as an efficient thermoelectric material. Both the theoretically estimated Seebeck coefficient and the power factor agree well with the available experimental results. Our calculations illustrate that it is essential to include spin-orbit coupling in these models of f electron half Heusler materials.

cond-mat.mtrl-sci↗

arXiv2015

Attosecond time delay in the photoionization of Mn in the region of the $3p \rightarrow 3d$ giant resonance

The initial insight into time delay in Mn photoionization in the region of the $3p \to 3d$ giant autoionization resonance is gained in the framework of the "spin-polarized" random phase approximation with exchange. The dramatic effect of the giant autoionization resonance on time delay of photoemission from the $3d$ and $4s$ valence subshells of the Mn atom is unraveled. Strong sensitivity of the time delay of the $4s$ photoemission to the final-state term of the ion-remainder [${\rm Mn^{+}}(4s^{1},$$^{5}S)$ vs.~${\rm Mn^{+}}(4s^{1},$$^{7}S)$] is discovered. It is shown that photoionization time delay in the autoionizing resonance region is explicitly associated with the resonance lifetime, which can, thus, be directly measured in attosecond time delay experiments. Similar features are expected to emerge in photoionization time delays of other transition-metal and rare-earth atoms with half-filed subshells that possess giant autoionization resonances as well.

physics.atom-ph↗

arXiv2014

Attosecond time delay in the photoionization of endohedral atoms A@C$_{60}$: A new probe of confinement resonances

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C$_{60}$ cage have been studied theoretically using both relativistic and non-relativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the $4d$ shell of Xe@C$_{60}$ and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C$_{60}$ [PRL 111, 203003 (2013)]

physics.atom-ph↗

arXiv2007

{\it Ab initio} calculations of forbidden transition probabilities and lifetimes of low-lying states in V$^{4+}$

Electric quadrupole (E2) and magnetic dipole (M1) transition amplitudes among the low-lying states of quadruply ionized vanadium V$^{4+}$, important in various field of experimental and astrophysics are presented very accurately. Most of these results are reported for the first time in the literature. Relativistic coupled-cluster theory with single, double and leading triple excitations has been employed for these calculations. Estimation of different correlation effects arising through the above formalism have been highlighted by studying core and valence electrons excitations to the excited states. The lifetime of the first excited $D$- state is found to be long.

physics.atom-ph↗

arXiv2007

Accurate estimations of circumstellar and interstellar lines of quadruply ionized vanadium using the coupled cluster approach

Accurate {\it ab initio} calculations have been carried out to study the valence electron removal energies and oscillator strengths of astrophysically important electromagnetic transitions of quadruply ionized vanadium, $V^{4+}$. Many important electron correlations are considered to all-orders using the relativistic coupled-cluster theory. Calculated ionization potentials and fine structure splittings are compared with the experimental values, wherever available. To our knowledge, oscillator strengths of electric dipole transitions are predicted for the first time for most of the transitions. The transitions span in the range of ultraviolet, visible and near infrared regions and are important for astrophysical observations.

physics.atom-ph↗