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Ankit Mishra

Publications and source records attributed to Ankit Mishra.

18 recordsLinked to original sources
arXiv2026

Critical Quasilinear Schr\"odinger Equations on the Heisenberg Group: Existence and Nonexistence

We study the quasilinear Schr\"odinger equation \begin{align*} -\Delta_{\mathbb{H}} u +V(\xi)u-\Delta_{\mathbb{H}} (\left|u\right|^{2\alpha})\left|u\right|^{2\alpha-2} u= \lambda \left|u\right|^{q-2}u + \left|u\right|^{p-2}u \quad \text{ in } \mathbb{H}^N, \end{align*} where $\Delta_{\mathbb{H}}$ is the Kohn Laplacian on the Heisenberg group $\mathbb{H}^N$, $4\alpha \frac12$, and $2\alpha Q^{*}$ is the critical exponent, $Q=2N+2$ being the homogeneous dimension and $Q^{*}=\frac{2Q}{Q-2}$. For $p=2\alpha Q^{*}$ and $\lambda>0$, we obtain a nontrivial solution, assuming that the potential is bounded below by a positive constant and is either asymptotically constant from above or invariant under a discrete subgroup of $\mathbb{H}^N$. In the opposite direction, we prove a Poho\v{z}aev identity for $\Delta_{\mathbb{H}}$ and combine it with the Nehari identity, obtaining a family of identities from which the quasilinear energy disappears exactly at the exponent $2\alpha Q^{*}$. This yields a nonexistence theorem under a monotonicity condition on the potential with respect to anisotropic dilations and shows that no nontrivial solution exists for $\lambda \leq 0$; the sign of the subcritical perturbation determines solvability. Along the way, we show that every weak solution is bounded and decays exponentially in the Kor\'anyi gauge.

math.AP↗
arXiv2026

Positive and nodal solutions for a parametric quasilinear $Q$-sub-Laplacian problem with critical exponential growth on the Heisenberg group

In this article, we investigate the following modified quasilinear equation with parameter driven by the $Q$-subLaplacian: \begin{align*} \begin{cases} -\Delta_Q u - \Delta_Q\bigl(|u|^{2\alpha}\bigr)\,|u|^{2\alpha-2} u = \lambda f(\xi,u) & \text{in } \Omega, \\[2mm] u = 0 & \text{on } \partial\Omega, \end{cases} \end{align*} where $\Delta_Q(\cdot):= \mathrm{div}_{\mathbb{H}}\bigl(|\nabla_{\mathbb{H}}(\cdot)|^{Q-2}\nabla_{\mathbb{H}}(\cdot)\bigr)$ denotes the $Q$-subLaplacian on the Heisenberg group $\mathbb{H}^N$, $Q=2N+2$ is the homogeneous dimension, $\Omega \subset \mathbb{H}^N$ is a smooth bounded domain, $\lambda>0$, $\alpha > \frac{1}{2}$, and $f$ has critical or subcritical exponential growth of order $\exp\bigl(\beta|t|^{2\alpha Q/(Q-1)}\bigr)$. We prove three results: the existence of a nontrivial positive weak solution in the critical case for all large $\lambda$, and the existence of a least-energy nodal solution with exactly two nodal domains, under subcritical and critical exponential growth. A change of variables $u=g(v)$ reduces the problem to a quasilinear problem whose energy functional is of class $C^1$; the exponent $2\alpha Q/(Q-1)$ arises from the growth of $g$. We handled the exponential growth using the sharp Moser-Trudinger inequality of Cohn and Lu. The positive solution is obtained by the mountain pass theorem and the nodal solutions by minimization on a nodal Nehari set.

math.AP↗
arXiv2026

Quasilinear Schr\"odinger Critical Problem on the Heisenberg group \(\mathbb{H}^N\)

We study the existence of standing wave solutions for the following quasilinear Schr\"odinger equations with critical growth on the Heisenberg group $$ -\Delta_{\mathbb{H}} u +V(\xi)u-\Delta_{\mathbb{H}} (\left|u\right|^{2\alpha})\left|u\right|^{2\alpha-2} u= \lambda \left|u\right|^{q-2}u + \left|u\right|^{p-2}u \text{ in }\mathbb{H}^N $$ where $\mathbb{H}^N$ is Heisenberg group, $\Delta_{\mathbb{H}}$ is Kohn Laplacian operator, $4\alpha \frac{1}{2}.$ By a suitable nonlinear change of variables, the quasilinear equation is transformed into a semilinear one, allowing the use of variational methods in the Folland--Stein Sobolev space $S^{1,2}(\mathbb{H}^N)$. Applying the mountain pass theorem together with a concentration--compactness argument adapted to the sub-Riemannian framework, we establish the existence of a nontrivial solution.

math.AP↗
arXiv2026

Stochastic Multipath Routing for High-Throughput Entanglement Distribution in Quantum Repeater Networks

Quantum repeater networks distribute entanglement over lossy links while many users share a limited pool of entangled pairs. Most existing routing schemes either always use a single best path or rely on global optimizations that are hard to run in real time. Here we propose and analyze a simple alternative: a stochastic multipath rule in which each entanglement request is sent at random along one of several edge-disjoint repeater paths, with a single parameter that controls the bias between shorter and longer routes. Using a distance-dependent lossy network model with finite per-link capacities and probabilistic entanglement swapping, we develop an analytic description of the resulting end-to-end entanglement rate as a function of this bias and validate it with large-scale numerical simulations. We find that an intermediate bias consistently outperforms both deterministic extremes across distances, traffic patterns, attenuation, swapping noise, and congestion, bringing the rate close to simple capacity upper bounds and making link usage more even across networks. These results identify stochastic multipath routing as a lightweight classical control strategy for boosting performance and scalability in near-term quantum repeater networks.

quant-ph↗
arXiv2025

Heterotic Footprints in Classical Gravity: PM dynamics from On-Shell soft amplitudes at one loop

We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton (EMD) theory. Working in the classical (Post-Minkowskian) regime, we extract the conservative two-body potential by expanding the one loop amplitudes in the soft regime. We show explicitly that, as in GR, the relevant soft amplitudes are infrared (IR) finite once the long-range interactions are consistently treated via Lippmann-Schwinger equation and the associated IR subtraction. The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude. Our results track the separate roles of electromagnetic and dilatonic charges in both the conservative dynamics and the eikonal phase, and they reduce smoothly to the GR limit when the charges and dilaton coupling are switched off. Where applicable, we compare with existing results in the literature and find agreement. These findings provide amplitude-based benchmarks for compact-object dynamics in EMD and furnish building blocks for waveform modeling in beyond-GR scenarios.

hep-th↗
arXiv2024

Monitoring cis-to-trans isomerization of azobenzene using Brillouin microscopy

Brillouin spectroscopy is commonly used to study the acoustic properties of materials. Here we explored its feasibility in studying the photoinduced isomerization of azobenzene. The isomerization of azobenzene changes the solution elastic modulus, and Brillouin scattering is sensitive to these changes. In this study, we experimentally demonstrated the photoswitching of azobenzene in DMSO using our home-made VIPA-based high-resolution optical Brillouin spectrometer, and confirmed the results by ultraviolet-visible spectrophotometry. Remarkable Brillouin frequency shift variations were quantitatively recorded upon irradiation, and it was found that this method can indeed be used to monitor the isomerization process in situ. Importantly, our strategy also allows us to provide the relationship between the ratio of trans- and cis- azobenzene and the Brillouin frequency shift. This shows that Brillouin spectroscopy has broad prospects for the characterization of azobenzene isomerization and other photo responsive materials.

physics.optics↗
arXiv2023

Molecular Autonomous Pathfinder using Deep Reinforcement Learning

Diffusion in solids is a slow process that dictates rate-limiting processes in key chemical reactions. Unlike crystalline solids that offer well-defined diffusion pathways, the lack of similar structural motifs in amorphous or glassy materials poses a great scientific challenge in estimating slow diffusion time. To tackle this problem, we have developed an AI-guided long-time atomistic simulation approach: Molecular Autonomous Pathfinder (MAP) framework based on Deep Reinforcement Learning (RL), where RL agent is trained to uncover energy efficient diffusion pathways. We employ Deep Q-Network architecture with distributed prioritized replay buffer enabling fully online agent training with accelerated experience sampling by an ensemble of asynchronous agents. After training, the agents provide atomistic configurations of diffusion pathways with their energy profile. We use a piecewise Nudged Elastic Band to refine the energy profile of the obtained pathway and corresponding diffusion time on the basis of transition state theory. With MAP, we have successfully identified atomistic mechanisms along molecular diffusion pathways in amorphous silica, with time scales comparable to experiments.

cond-mat.mtrl-sci↗
arXiv2023

A sub-functor for Ext and Cohen-Macaulay associated graded modules with bounded multiplicity-II

Let $(A,\mathfrak{m})$ be a \CM\ local ring, then notion of $T$-split sequence was introduced in part-1 of this paper for $\mathfrak{m}$-adic filtration with the help of numerical function $e^T_A$. We have explored the relation between AR-sequences and $T$-split sequences. For a Gorenstein ring $(A,\mathfrak{m})$ we define a Hom-finite Krull-Remak-Schmidt category $\mathcal{D}_A$ as a quotient of the stable category $\CMS(A)$. This category preserves isomorphism, i.e. $M\cong N$ in $\mathcal{D}_A$ if and only if $M\cong N$ in $\CMS(A)$.This article has two objectives; first objective is to extend the notion of $T$-split sequence, and second objective is to explore function $e^T_A$ and $T$-split sequence. When $(A,\mathfrak{m})$ be an \anram\ \CM\ local ring and $I$ be an $\mathfrak{m}$-primary ideal then we extend the techniques in part-1 of this paper to the integral closure filtration with respect to $I$ and prove a version of Brauer-Thrall-II for a class of such rings.

math.AC↗
arXiv2022

On associated graded modules of maximal Cohen-Macaulay modules over hypersurface rings

Let $A=Q/(f)$ where $(Q,\mathfrak{n})$ be a complete regular local ring of dimension $d+1$, $f\in \mathfrak{n}^i\setminus\mathfrak{n}^{i+1}$ for some $i\geq 2$ and $M$ an MCM $A-$module with $e(M)=μ(M)i(M)+1$ then we prove that depth $G(M)\geq d-1$. If $(A,\mathfrak{m})$ is a complete hypersurface ring of dimension $d$ with infinite residue field and $e(A)=3$, let $M$ be an MCM $A$-module with $μ(M)=2$ or $3$ then we prove that depth $G(M)\geq d-μ(M)+1$. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.

math.AC↗
arXiv2022

Eigenvector localization in hypergraphs: pair-wise vs higher-order links

Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector localization of hypergraphs Laplacians. By defining a single parameter \gamma which measures the relative strengths of pair-wise and higher-order interactions, we analyze the impact of interactions on localization properties. For, \gamma < 1 there exists no impact of pairwise links on eigenvector localization while the higher-order interactions instigate localization in the larger eigenvalues. For \gamma > 1, pair-wise interactions cause localization of eigenvector corresponding to small eigenvalues, where as higherorder interactions, despite being much lesser than the pair-wise links, keep driving localization of the eigenvectors corresponding to larger eigenvalues. The results will be useful to understand dynamical phenomena such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions.

cond-mat.stat-mech↗
arXiv2022

Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios distribution of various model networks, namely, small-world, Erdős-Rényi random, and (dis)assortative random having a diagonal disorder in the corresponding adjacency matrices. Without any diagonal disorder, the eigenvalues ratio distribution of these model networks depict Gaussian orthogonal ensemble (GOE) statistics. Upon adding diagonal disorder, there exists a gradual transition from the GOE to Poisson statistics depending upon the strength of the disorder. The critical disorder (wc) required to procure the Poisson statistics increases with the randomness in the network architecture. We relate wc with the time taken by the maximum entropy random walker to reach the steady-state. These analyses will be helpful to understand the role of eigenvalues other than the principal one for various network dynamics such as transient behaviour.

cond-mat.dis-nn↗
arXiv2022

On associated graded modules of maximal Cohen-Macaulay modules over hypersurface rings

Let $(A,\mathfrak{m})$ be a hypersurface ring with dimension $d$, and $M$ a MCM $A-$module with red$(M)\leq 2$ and $μ(M)=2$ or $3$ then we have proved that depth $G(M)\geq d-μ(M)+1$. If $e(A)=3$ and $μ(M)=4$ then in this case we have proved that depth$G(M)\geq d-3$. Next we consider the case when $e(M)=μ(M)i(M)+1$ and prove that depth $G(M)\geq d-1$. When $A = Q/(f)$ where $Q = k[[X_1,\cdots, X_{d+1}]]$ then we give estimates for $\depth G(M)$ in terms of a minimal presentation of $M$. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.

math.AC↗
arXiv2020

Computational framework for polymer synthesis to study dielectric properties using polarizable reactive molecular dynamics

The increased energy and power density required in modern electronics poses a challenge for designing new dielectric polymer materials with high energy density while maintaining low loss at high applied electric fields. Recently, an advanced computational screening method coupled with hierarchical modelling has accelerated the identification of promising high energy density materials. It is well known that the dielectric response of polymeric materials is largely influenced by their phases and local heterogeneous structures as well as operational temperature. Such inputs are crucial to accelerate the design and discovery of potential polymer candidates. However, an efficient computational framework to probe temperature dependence of the dielectric properties of polymers, while incorporating effects controlled by their morphology is still lacking. In this paper, we propose a scalable computational framework based on reactive molecular dynamics with a valence-state aware polarizable charge model, which is capable of handling practically relevant polymer morphologies and simultaneously provide near-quantum accuracy in estimating dielectric properties of various polymer systems. We demonstrate the predictive power of our framework on high energy density polymer systems recently identified through rational experimental-theoretical co-design. Our scalable and automated framework may be used for high-throughput theoretical screenings of combinatorial large design space to identify next-generation high energy density polymer materials.

physics.chem-ph↗
arXiv2020

Cohen-Macaulay local rings with $e_2 = e_1-e+1$

In this paper we study Cohen-Macaulay local rings of dimension $d$, multiplicity $e$ and second Hilbert coefficient $e_2$ in the case $e_2 = e_1 - e + 1$. Let $h = μ(\mathfrak{m}) - d$. If $e_2 \neq 0$ then in our case we can prove that type $A \geq e - h -1$. If type $A = e - h -1$ then we show that the associated graded ring $G(A)$ is Cohen-Macaulay. In the next case when type $A = e - h$ we determine all possible Hilbert series of $A$. In this case we show that the Hilbert Series of $A$ completely determines depth $G(A)$.

math.AC↗
arXiv2020

Multifractal analysis of eigenvectors of smallworld networks

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq->1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transition

cond-mat.dis-nn↗
arXiv2020

EZFF: Python Library for Multi-Objective Parameterization and Uncertainty Quantification of Interatomic Forcefields for Molecular Dynamics

Parameterization of interatomic forcefields is a necessary first step in performing molecular dynamics simulations. This is a non-trivial global optimization problem involving quantification of multiple empirical variables against one or more properties. We present EZFF, a lightweight Python library for parameterization of several types of interatomic forcefields implemented in several molecular dynamics engines against multiple objectives using genetic-algorithm-based global optimization methods. The EZFF scheme provides unique functionality such as the parameterization of hybrid forcefields composed of multiple forcefield interactions as well as built-in quantification of uncertainty in forcefield parameters and can be easily extended to other forcefield functional forms as well as MD engines.

physics.comp-ph↗
arXiv2020

Predictive Synthesis of Quantum Materials by Probabilistic Reinforcement Learning

Predictive materials synthesis is the primary bottleneck in realizing new functional and quantum materials. Strategies for synthesis of promising materials are currently identified by time-consuming trial and error approaches and there are no known predictive schemes to design synthesis parameters for new materials. We use reinforcement learning to predict optimal synthesis schedules, i.e. a time-sequence of reaction conditions like temperatures and reactant concentrations, for the synthesis of a prototypical quantum material, semiconducting monolayer MoS$_{2}$, using chemical vapor deposition. The predictive reinforcement leaning agent is coupled to a deep generative model to capture the crystallinity and phase-composition of synthesized MoS$_{2}$ during CVD synthesis as a function of time-dependent synthesis conditions. This model, trained on 10000 computational synthesis simulations, successfully learned threshold temperatures and chemical potentials for the onset of chemical reactions and predicted new synthesis schedules for producing well-sulfidized crystalline and phase-pure MoS$_{2}$, which were validated by computational synthesis simulations. The model can be extended to predict profiles for synthesis of complex structures including multi-phase heterostructures and can also predict long-time behavior of reacting systems, far beyond the domain of the MD simulations used to train the model, making these predictions directly relevant to experimental synthesis.

cond-mat.mtrl-sci↗