arXiv subjects

Rishabh Mishra

Publications and source records attributed to Rishabh Mishra.

10 recordsLinked to original sources

arXiv2026

Ultrafast Two-Dimensional Spectroscopy Uncovers Ubiquitous Electron-Paramagnon Coupling in Cuprate Superconductors

The coupling between electronic excitations and collective bosonic modes is fundamental to the emergence of high-temperature superconductivity in cuprates. Despite extensive effort, conventional equilibrium and pump-probe optical spectroscopies still struggle to disentangle couplings to different bosonic modes when their energy scales overlap. Here we overcome this limitation using ultrafast two-dimensional electronic spectroscopy (2DES), which correlates coherent excitation and detection photon energies with femtosecond time resolution. Applied to optimally doped Bi$_2$Sr$_2$Ca$_{0.92}$Y$_{0.08}$Cu$_2$O$_{8+δ}$, 2DES reveals a pronounced off-diagonal resonance arising from the ultrafast generation of non-thermal bosons with energy $\hbarΩ_\mathbf{q}\simeq200$ meV. By comparing the measured spectra with a theoretical framework that explicitly includes the interaction between charge-transfer and magnetic excitations, we identify these bosons as paramagnons with momenta centered near $(π/2,π/2)$ and extending toward $(0,π)$ and $(π,0)$. The resonance persists across a large range of temperatures and doping concentrations, demonstrating that high-energy paramagnons are ubiquitously and strongly coupled to electronic excitations throughout the cuprate phase diagram. Time-domain analysis constrains the build-up of the paramagnon population to $\lesssim 10$ fs, placing a lower bound $λ\gtrsim 0.7$ on the coupling strength. More broadly, our results establish 2DES as a powerful approach for disentangling mode-selective electron-boson interactions and addressing decoherence dynamics, thereby establishing a new avenue for investigating strongly correlated quantum materials. These findings also provide a direct framework for future time-resolved resonant inelastic X-ray scattering experiments aimed at tracking the ultrafast dynamics of magnetic excitations.

cond-mat.supr-con↗

arXiv2026

Stall cells over an airfoil. Part 1: Three-dimensional flow organisation and vorticity dynamics

This study investigates the three-dimensional organisation and evolution of stall cells in the separated flow region over an airfoil. Using a hybrid RANS/LES approach based on the DDES-SST turbulence model, we characterise the formation and development of these structures, which remain challenging to capture experimentally. Initial validation confirms accurate reproduction of global loads when comparing with both experimental data and RANS simulations. The complex three-dimensional flow organisation is analysed through investigating the vorticity, revealing that spanwise variation of the separation location leads to non-uniform load distribution along the airfoil span. The mid-span experiences premature separation due to flow bifurcation, while flow attraction at $\pm1$ chord length successfully sustains attached flow further along the chord. The separated flow generates a shear layer culminating in a separation vortex tube, which exhibits a Crow-type instability when interacting with the counter-rotating trailing edge vortex tube. This instability induces a wave-like bending of the vortex tubes and shear layer, generating significant vertical vorticity (y-vorticity) that drives spanwise flow. We identify a previously unreported phenomenon where the maxima of spanwise velocity structures exhibit rotation around fixed spanwise axes, with the rotation angle evolving linearly with downstream distance according to $ζ= 14.5(x/c) - 0.8$. This study provides new insights into the mechanisms underlying stall cell formation and highlights the importance of three-dimensional effects in separated flows, which has implications for aerodynamic load prediction and control strategies.

physics.flu-dyn↗

arXiv2026

Stall cells over an airfoil. Part 2: A vortex-based analytical model for their formation and saturation

Stall cells are spanwise-periodic flow structures that spontaneously form on airfoils operating near stall, fundamentally altering the aerodynamic loading distribution. Despite decades of experimental observations, a complete theoretical framework connecting vortex dynamics to the characteristic flow patterns has remained elusive. In this work, we develop an analytical model for stall cell formation based on the interaction between finite-length, counter-rotating vortex tubes representing the separation vortex and trailing-edge vortex. Linear stability analysis of the coupled vortex system yields the growth rate and wavelength selection of the Crow-type instability responsible for the wave-like bending of the vortex structures. A weakly nonlinear analysis using the method of multiple scales is performed to derive the Stuart--Landau amplitude equation, providing an explicit expression for the saturation amplitude at which nonlinear effects arrest the instability growth and establish quasi-steady cellular structures. The vortex sheet representing the separated shear layer is coupled to the vortex tube dynamics through the Birkhoff--Rott equation, from which we derive the induced vertical vorticity $Ω_y$ that drives the alternating spanwise velocity characteristic of stall cells. The model predicts quantitatively the spanwise velocity magnitude, vertical vorticity distribution, and vortex sheet deformation. The resulting framework provides a unified, first-principles description connecting the Crow-type instability of counter-rotating vortex tubes to the observed flow topology of stall cells. The model is validated against the DDES simulation data presented in the companion paper, demonstrating strong agreement.

physics.flu-dyn↗

arXiv2025

Spectral Reconstruction for Under-Resolved Turbulence Measurements Using a Variational Cutoff Dissipation Model

This technical note addresses the challenge of accurate turbulence characterization using robust, bandwidth-limited sensors which fail to resolve the high-wavenumber dissipation range. To correct the resulting underestimation of turbulent kinetic energy (TKE), a novel analytical spectral model is derived from a variational principle governing cascade resistance, yielding a Ginzburg-Landau domain wall solution. Unlike classical asymptotic decay formulations such as the Pao or Pope models, the proposed formulation features bounded spectral support with a hard energetic cutoff at the Kolmogorov wavenumber ($k_η$) and requires no adjustable parameters beyond the Kolmogorov constant ($C_K$). Validation against high-Reynolds-number experimental data confirms that the model accurately captures the spectral rolloff and achieves superior TKE recovery, restoring over 98\% of the variance from spectra truncated as early as $kη=0.15$, thereby offering a robust tool for industrial and aeroacoustic flow diagnostics.

physics.flu-dyn↗

arXiv2025

Direct measurement of coherent nodal and antinodal dynamics in underdoped Bi-2212

The physics of strongly correlated materials is deeply rooted in electron interactions and their coupling to low-energy excitations. Unraveling the competing and cooperative nature of these interactions is crucial for connecting microscopic mechanisms to the emergence of exotic macroscopic behavior, such as high-temperature superconductivity. Here we show that polarization-resolved multidimensional coherent spectroscopy (MDCS) is able to selectively drive and measure coherent Raman excitations in different parts of the Fermi surface, where the superconducting gap vanishes or is the largest (respectively called Nodal and Antinodal region) in underdoped Bi-2212. Our evidence reveal that in the superconducting phase, the energy of Raman excitations in the nodal region is anti-correlated with the energy of electronic excitations at $\sim$1.6~eV, and both maintain coherence for over 44~fs. In contrast, excitations in the antinodal region show significantly faster decoherence ($<$18~fs) and no measurable correlations. Importantly, this long-lived coherence is specific to the superconducting phase and vanishes in the pseudogap and normal phases. This anti-correlation reveals a coherent link between the transition energy associated with the many body Cu-O bands and the energy of electronic Raman modes that map to the near-nodal superconducting gap. The different coherent dynamics of the nodal and antinodal excitations in the superconducting phase suggest that nodal fluctuations are protected from dissipation associated with scattering from antiferromagnetic fluctuations and may be relevant to sustaining the quantum coherent behaviour associated with high temperature superconductivity.

cond-mat.supr-con↗

arXiv2025

Global Well-Posedness of the 3D Navier-Stokes Equations in the Limiting Case: Infinitely Nested Logarithmic Improvements

This paper establishes a complete framework for infinitely nested logarithmic improvements to regularity criteria for the three-dimensional incompressible Navier-Stokes equations. Building upon our previous works on logarithmically improved and multi-level logarithmically improved criteria, we demonstrate that the limiting case of infinitely nested logarithms fully bridges the gap between subcritical and critical regularity. Specifically, we prove that if the initial data $u_0 \in L^2(\mathbb{R}^3)$ satisfies the condition $\|(-Δ)^{1/4}u_0\|_{L^q(\mathbb{R}^3)} \leq C_0Ψ(\|u_0\|_{\dot{H}^{1/2}})$, where $Ψ$ incorporates infinitely nested logarithmic factors with appropriate decay conditions, then there exists a unique global-in-time smooth solution to the Navier-Stokes equations. This result establishes global well-posedness at the critical regularity threshold $s = 1/2$. The proof relies on infinitely nested commutator estimates, precise characterization of the critical exponent function in the limiting case, and careful analysis of the energy cascade. We also derive the exact Hausdorff dimension bound for potential singular sets in this limiting case, proving that the dimension reduces to zero. Through systematic construction of the limiting function spaces and detailed analysis of the associated ODEs, we demonstrate that infinitely nested logarithmic improvements provide a pathway to resolving the global regularity question for the Navier-Stokes equations.

math.AP↗

arXiv2025

Global Well-Posedness of the 3D Navier-Stokes Equations under Multi-Level Logarithmically Improved Criteria

This paper extends our previous results on logarithmically improved regularity criteria for the three-dimensional Navier-Stokes equations by establishing a comprehensive framework of multi-level logarithmic improvements. We prove that if the initial data $u_0 \in L^2(\mathbb{R}^3)$ satisfies a nested logarithmically weakened condition $\|(-Δ)^{s/2}u_0\|_{L^q(\mathbb{R}^3)} \leq \frac{C_0}{\prod_{j=1}^{n} (1 + L_j(\|u_0\|_{\dot{H}^s}))^{δ_j}}$ for some $s \in (1/2, 1)$, where $L_j$ represents $j$-fold nested logarithms, then the corresponding solution exists globally in time and is unique. The proof introduces a novel sequence of increasingly precise commutator estimates incorporating multiple layers of logarithmic corrections. We establish the existence of a critical threshold function $Φ(s,q,\{δ_j\}_{j=1}^n)$ that completely characterizes the boundary between global regularity and potential singularity formation, with explicit asymptotics as $s$ approaches the critical value $1/2$. This paper further provides a rigorous geometric characterization of potential singular structures through refined multi-fractal analysis, showing that any singular set must have Hausdorff dimension bounded by $1 - \sum_{j=1}^n \frac{δ_j}{1+δ_j} \cdot \frac{1}{j+1}$. Our results constitute a significant advancement toward resolving the global regularity question for the Navier-Stokes equations, as we demonstrate that with properly calibrated sequences of nested logarithmic improvements, the gap to the critical case can be systematically reduced.

math.AP↗

arXiv2025

Global Well-Posedness for the 3D Navier-Stokes Equations under Logarithmically Improved Criteria: Connections to Turbulence Theory

This paper introduces a novel class of initial data for which the three-dimensional incompressible Navier--Stokes equations yield unique global-in-time solutions. Building on a logarithmically improved regularity criterion, we impose a logarithmically subcritical condition on the initial data. Specifically, if \[ u_0 \in L^2(\mathbb{R}^3) \quad \text{and} \quad \|(-Δ)^{s/2}u_0\|_{L^q(\mathbb{R}^3)} \le \frac{C_0}{\Bigl(1+\log\bigl(e+\|u_0\|_{\dot{H}^s}\bigr)\Bigr)^δ}, \] for some $s \in (1/2,1)$ under appropriate scaling, then the corresponding solution exists globally and is unique. The proof employs refined commutator estimates for the fractional Laplacian together with new energy methods that exploit this logarithmic improvement to prevent singularity formation. Furthermore, we establish links between these improved criteria and turbulence theory. We derive precise relationships connecting the regularity conditions with turbulent intermittency, showing that the logarithmic enhancements correspond to anomalous scaling exponents in the turbulent energy spectrum. Additionally, we characterize the local structure of potential singularities and provide tight bounds on the energy flux in turbulent cascades. This approach bridges the gap between subcritical and critical regularity for the Navier--Stokes equations and offers a robust mathematical foundation for key phenomena observed in turbulence.

math.AP↗

arXiv2022

Exciton-polaron interactions in monolayer WS$_2$

Interactions between quasiparticles are of fundamental importance and ultimately determine the macroscopic properties of quantum matter. A famous example is the phenomenon of superconductivity, which arises from attractive electron-electron interactions that are mediated by phonons or even other more exotic fluctuations in the material. Here we introduce mobile exciton impurities into a two-dimensional electron gas and investigate the interactions between the resulting Fermi polaron quasiparticles. We employ multi-dimensional coherent spectroscopy on monolayer WS$_2$, which provides an ideal platform for determining the nature of polaron-polaron interactions due to the underlying trion fine structure and the valley specific optical selection rules. At low electron doping densities, we find that the dominant interactions are between polaron states that are dressed by the same Fermi sea. In the absence of bound polaron pairs (bipolarons), we show using a minimal microscopic model that these interactions originate from a phase-space filling effect, where excitons compete for the same electrons. We furthermore reveal the existence of a bipolaron bound state with remarkably large binding energy, involving excitons in different valleys cooperatively bound to the same electron. Our work lays the foundation for probing and understanding strong electron correlation effects in two-dimensional layered structures such as moiré superlattices.

cond-mat.mes-hall↗

arXiv2021

Direct Measurement of Biexcitons in Monolayer WS2

The optical properties of atomically thin transition metal dichalcogenides (TMDCs) are dominated by Coulomb bound quasi-particles, such as excitons, trions, and biexcitons. Due to the number and density of possible states, attributing different spectral peaks to the specific origin can be difficult. In particular, there has been much conjecture around the presence, binding energy and/or nature of biexcitons in these materials. In this work, we remove any ambiguity in identifying and separating the optically excited biexciton in monolayer WS2 using two-quantum multidimensional coherent spectroscopy (2Q-MDCS), a technique that directly and selectively probes doubly-excited states, such as biexcitons. The energy difference between the unbound two-exciton state and the biexciton is the fundamental definition of biexciton binding energy and is measured to be 26 \pm 2 meV. Furthermore, resolving the biexciton peaks in 2Q-MDCS allows us to identify that the biexciton observed here is composed of two bright excitons in opposite valleys.

cond-mat.mes-hall↗