Reetendra Singh | Searcharxiv

arXiv2026

Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator

This paper introduces a variable-order stable subordinator (VOSS) $S^{\alpha(t)}(t)$ with index $\alpha(t)\in(0,1)$, where $\alpha(t)$ is a right-continuous piecewise constant function. We drive the Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator (GSFPP-VO) defined by $\{N(S^{\alpha(t)}(t))\}_{t \geq 0}$, obtained by time-changing a homogeneous Poisson process $\{N(t,\lambda)\}_{t\geq 0}$ with rate parameter $\lambda>0$ by an independent VOSS. Explicit expressions for the Laplace transform, probability generating function, probability mass function, and moment generating function of the GSFPP-VO are derived, and these quantities are shown to satisfy partial differential equations. Finally, we establish the associated generalized distributions, analyze the hitting-time properties, and characterize the L\'evy measures of the GSFPP-VO.

math.PR↗

arXiv2025

Reversal of strain state in a Mott insulator thin film by controlling substrate morphology

The V2O3 phase diagram contains two insulating phases and one metallic phase with different lattice structures. The stability of these phases is very sensitive to pressure, offering a mechanism to tune phase transitions by inducing strain in thin films. The most studied source of strain is lattice mismatch between the film and the substrate. In this work, however, we find that the film/substrate thermal expansion mismatch can be made to play a dominant role by modifying the substrate morphology. When grown on sapphire, the lattice mismatch induces compressive strain in the V2O3 films, whereas thermal expansion mismatch induces tensile strain. We find that minute changes in substrate morphology may relax the compressive strain component, allowing the thermally-induced tensile component to overcome it. Thus, by simple annealing of the substrates to create either a flat or stepped morphology, strongly compressive or tensile strains may be induced in the films. This results in either full suppression of the metal-insulator transition or stabilization of insulating phases at all temperatures, exhibiting many orders of magnitude differences in film resistivity. To elucidate the strain relaxation mechanism, we use high-resolution scanning transmission electron microscopy (HRSTEM) to image the atomic steps in the substrate and the adjacent crystallographic defects in the V2O3. These findings offer a hitherto underexplored mechanism to tune strain in thin films, deepen our understanding of the effects of structural degrees of freedom on phase stability of a canonical Mott insulator and may allow for applications requiring insulator-metal switching above room temperature.

cond-mat.mtrl-sci↗