arXiv subjects

Sathwik Bharadwaj

Publications and source records attributed to Sathwik Bharadwaj.

21 records · Page 2Linked to original sources

arXiv2020

Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{μν}+β_{μν}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties.

hep-th↗

arXiv2019

Electromagnetic calculations for multiscale and multiphysics simulations: a new perspective

Present day electromagnetic field calculations have limitations that are due to techniques employing edge-based discretization methods. While these vector finite element methods solve the issues of tangential continuity of fields and the removal of spurious solutions, resulting fields do not have a unique directionality at nodes in the discretization mesh. This review presents electromagnetic field calculations in waveguides, cavity fields, and photonic crystals. We develop Hermite interpolation polynomials and node-based finite element methods based on variational principles. We show that the Hermite-finite element method (HFEM) delivers high accuracy and suitable for multiscale calculations with mixed physics. We use group representation theory to derive the HFEM polynomial basis set in two-dimensions. The energy level degeneracy in a cubic cavity can be denumerably large even though the symmetry of the cube. We show that the additional operators available for the problem lead to accidental degeneracy. We discuss this remarkable degeneracy and its reduction in detail. We consider photonic crystals corresponding to a 2D checkerboard superlattice structure, and the Escher drawing of the Horsemen which satisfies the nonsymmorphic group pg. We show that HFEM is able to deliver high accuracy in such spatially complex examples with far less computational effort than Fourier expansion methods. The algorithms developed here hold the promise of successful modeling of multi-physics systems. This general method is applicable to a broad class of physical systems, to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.

physics.comp-ph↗

arXiv2019

Tuning spatial entanglement in interacting few-electron quantum dots

Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant. In this article, we develop a fully variational action integral formulation for calculating accurate few-electron wavefunctions in configuration space, irrespective of potential geometry. To evaluate the Coulomb integrals with high accuracy, a novel numerical integration method using multiple Gauss quadratures is proposed. Using this approach, we investigate the confinement of two electrons in double quantum dots, and evaluate the spatial entanglement. We investigate the dependence of spatial entanglement on various geometrical parameters. We derive the two-particle wavefunctions in the asymptotic limit of the separation distance between quantum dots, and obtain universal saturation values for the spatial entanglement. Resonances in the entanglement values due to avoided level-crossings of states are observed. We also demonstrate the formation of electron clusters, and show that the entanglement value is a good indicator for the formation of such clusters. Further, we show that a precise tuning of the entanglement values is feasible with applied external electric fields.

cond-mat.mes-hall↗