arXiv subjects

Soumya Mukherjee

Publications and source records attributed to Soumya Mukherjee.

16 recordsLinked to original sources

arXiv2026

Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer

We develop a gradient flow on the space of probability measures defined on matrix-valued parameters induced by regularized Muon, an analytically smoothed version of the idealized Muon optimizer. The key observation is that the regularized orthogonalization map is the gradient of a smooth Fenchel-dual smoothing of the nuclear norm. This identifies the (regularized) Muon update as a mirror/prox step in the update variable, with momentum acting as the dual coordinate. We use this structure to lift Muon from a single matrix parameter to finite-particle probability objectives of the form $J(ρ)=R\left(\int F d ρ\right)$, a setting motivated by mean-field descriptions of neural-network training, and derive the inertial continuous-time limit. Using this structure, we derive the finite-particle continuous-time limit under the inertial scaling of step size and momentum, and then pass to a phase-space mean-field equation over probability laws on parameter-momentum pairs. The resulting flow can be shown to be a damped Hamiltonian probability dynamics whose kinetic energy is induced by the regularized Muon mirror potential. We prove an exact Hamiltonian dissipation identity, showing that the Hamiltonian energy decreases monotonically. While the target objective itself need not be monotone along the inertial Muon dynamics, under additional gradient-dominance, bounded-momentum, and curvature/alignment assumptions, we obtain continuous and discrete-time exponential convergence rates for the objective gap. We also study the well-posedness of the mean-field limit equation and establish propagation of chaos guarantees for the interacting particle system. Finally, we extend the formulation to Hilbert-valued feature maps on product matrix spaces, yielding a blockwise Muon probability flow applicable to smooth transformer mixture-of-experts models.

stat.ML↗

arXiv2026

On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy

Gradient-flow sampling interprets a Gibbs distribution as the minimizer of an energy functional over probability measures and generates dynamics converging to this target. Under spherical Hellinger-Kantorovich (SHK) geometry, the flow couples transport and reaction and coincides with birth-death Langevin dynamics. In this work, we develop a perturbation theory for SHK gradient flows. For two potentials $V$ and $V^{\prime}$, we compare the associated flows from a common initialization and quantify how potential discrepancies propagate over time. A uniform perturbation bound yields dimension-free, pointwise control of the log-likelihood ratio and Rényi divergence, while additional structure allows us to derive bounds for the KL divergence as well. We apply these results to approximate sampling for the exponential mechanism in differential privacy. The likelihood-ratio control provides explicit time-dependent Pure-DP guarantees for SHK-based samplers, while the KL bound yields Approximate-DP certificates via hockey-stick divergence. We also derive a utility bound separating intrinsic exponential-mechanism suboptimality from finite-time sampling error.

stat.ML↗

arXiv2026

Rashba engineering at van der Waals interfaces

Two-dimensional transition metal dichalcogenide (TMD) interfaces offer a versatile platform for studying emergent quantum phenomena and enabling novel device functionalities. When distinct TMD monolayers are stacked vertically or laterally stitched, their interfaces can exhibit unique electronic band alignments, giving rise to long-lived interlayer excitons, charge transfer effects, and moiré superlattices with correlated states. Here, we demonstrate that the interface between a large variety of two different epitaxially grown TMD monolayers controls the intensity and sign of the Rashba spin splitting, which is probed using THz spintronic emission. Optimized TMD heterobilayers, such as HfSe$_2$/PtSe$_2$, show enhanced THz emission that surpass the spin-to-charge conversion efficiency of bulk TMDs, confirming the presence of Rashba states with large spin splitting at the interface. By combining spin- and angle-resolved photoemission spectroscopy with density functional theory, we reveal that the electronic hybridization between the two different TMD monolayers gives rise to extended in-gap states with strong Rashba spin-orbit coupling. The choice of TMD layers enables to engineer the sign and strength of spin-to-charge conversion in van der Waals heterobilayers opening up perspectives to build efficient and tunable THz spintronic emitters.

cond-mat.mes-hall↗

arXiv2026

Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamics

We propose a dense associative memory for empirical measures (weighted point clouds). Stored patterns and queries are finitely supported probability measures, and retrieval is defined by minimizing a Hopfield-style log-sum-exp energy built from the debiased Sinkhorn divergence. We derive retrieval dynamics as a spherical Hellinger Kantorovich (SHK) gradient flow, which updates both support locations and weights. Discretizing the flow yields a deterministic algorithm that uses Sinkhorn potentials to compute barycentric transport steps and a multiplicative simplex reweighting. Under local separation and PL-type conditions we prove basin invariance, geometric convergence to a local minimizer, and a bound showing the minimizer remains close to the corresponding stored pattern. Under a random pattern model, we further show that these Sinkhorn basins are disjoint with high probability, implying exponential capacity in the ambient dimension. Experiments on synthetic Gaussian point-cloud memories demonstrate robust recovery from perturbed queries versus a Euclidean Hopfield-type baseline.

stat.ML↗

arXiv2026

Assessing Utility of Differential Privacy for RCTs

Randomized controlled trials (RCTs) have become powerful tools for assessing the impact of interventions and policies in many contexts. They are considered the gold standard for causal inference in the biomedical fields and many social sciences. Researchers have published an increasing number of studies that rely on RCTs for at least part of their inference. These studies typically include the response data that has been collected, de-identified, and sometimes protected through traditional disclosure limitation methods. In this paper, we empirically assess the impact of privacy-preserving synthetic data generation methodologies on published RCT analyses by leveraging available replication packages (research compendia) in economics and policy analysis. We implement three privacy-preserving algorithms, that use as a base one of the basic differentially private (DP) algorithms, the perturbed histogram, to support the quality of statistical inference. We highlight challenges with the straight use of this algorithm and the stability-based histogram in our setting and described the adjustments needed. We provide simulation studies and demonstrate that we can replicate the analysis in a published economics article on privacy-protected data under various parameterizations. We find that relatively straightforward (at a high-level) privacy-preserving methods influenced by DP techniques allow for inference-valid protection of published data. The results have applicability to researchers wishing to share RCT data, especially in the context of low- and middle-income countries, with strong privacy protection.

stat.AP↗

arXiv2025

Minimax Optimal Kernel Two-Sample Tests with Random Features

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over general (non-Euclidean) domains. While a substantial amount of work has been done on this topic, only recently have minimax optimal two-sample tests been constructed that incorporate, unlike MMD, both the mean element and a regularized version of the covariance operator. However, as with most kernel algorithms, the optimal test scales cubically in the sample size, limiting its applicability. In this paper, we propose a spectral-regularized two-sample test based on random Fourier feature (RFF) approximation and investigate the trade-offs between statistical optimality and computational efficiency. We show the proposed test to be minimax optimal if the approximation order of RFF (which depends on the smoothness of the likelihood ratio and the decay rate of the eigenvalues of the integral operator) is sufficiently large. We develop a practically implementable permutation-based version of the proposed test with a data-adaptive strategy for selecting the regularization parameter. Finally, through numerical experiments on simulated and benchmark datasets, we demonstrate that the proposed RFF-based test is computationally efficient and performs almost similarly (with a small drop in power) to the exact test.

math.ST↗

arXiv2025

Construction of First Principle Based Adiabatic and Diabatic Hamiltonian for TiO$_6^{8-}$ unit of BaTiO$_3$ Crystal: Photoemission Spectra and Ferroelectricity

The ferroelectric property of BaTiO$_3$ crystal arises from the strong Pseudo Jahn-Teller (PJT) interactions between the non-degenerate ground electronic state, $^1A_{1g}$ and the degenerate $^1T_{1u}$ symmetry states through the nuclear distortions of $t_{1u}$ modes in TiO$_6^{8-}$ unit. In a $d^0$ electronic configuration of $Ti^{4+}$ ion, the PJT interaction leads to a stabilization effect, which has been explored using Beyond Born-Oppenheimer (BBO) theory. The $^1T_{1u}$ excited states form a three-state degeneracy, exhibiting feeble Jahn-Teller (JT) distortions over the $t_{2g}$ planes. For the first time, we compute \textit{ab initio} adiabatic potential energy surfaces (PESs) and non-adiabatic coupling terms (NACTs), and thereafter, diabatic PESs and couplings for the perovskite unit, TiO$_6^{8-}$. Using a Time-Dependent Discrete Variable Representation (TDDVR) approach, the theoretical photoemission spectra exhibit good agreement with the experimental ones. Moreover, the experimental observation on order parameter associated with ferroelectric properties of BaTiO$_3$ crystal show close resemblance with present and other theoretical predictions.

cond-mat.mtrl-sci↗

arXiv2025

Responses of any arbitrary initially stressed reference and the stress-free reference

The constitutive relation for an initially stressed reference is often determined by using the response of a virtual stress-free reference. However, identifying the constitutive relation of the original stress-free body can be challenging without conducting destructive tests. This paper presents three approaches for determining the response of a stress-free reference -- or any arbitrary initially stressed reference -- when the response of a particular initially stressed reference is known. Unlike standard practice, these approaches of changing reference configurations do not begin with a known stress-free state. The first and third approaches directly derive the constitutive relations of one stressed reference from another. {The first approach is applicable to a specific constitutive relation of the known initially stressed state,} while the third approach extends the first and is applicable to any constitutive form. The second approach uses any general response of a given stressed reference to identify the stress-free material. The response of the stress-free material is further analyzed and processed to determine the response of any stressed reference. We observe that even when the known initially stressed state is Green elastic, the arbitrarily stressed or stress-free references may exhibit implicit elasticity. (complete abstract is available in the published version)

cond-mat.mtrl-sci↗

arXiv2025

Uniform Kernel Prober

The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In practice, however, one faces the issue of the choice of prediction tasks and the availability of test data from the chosen tasks while comparing the relative performance of different features. In this work, we develop a class of pseudometrics called Uniform Kernel Prober (UKP) for comparing features or representations learned by different statistical models such as neural networks when the downstream prediction tasks involve kernel ridge regression. The proposed pseudometric, UKP, between any two representations, provides a uniform measure of prediction error on test data corresponding to a general class of kernel ridge regression tasks for a given choice of a kernel without access to test data. Additionally, desired invariances in representations can be successfully captured by UKP only through the choice of the kernel function and the pseudometric can be efficiently estimated from $n$ input data samples with $O(\frac{1}{\sqrt{n}})$ estimation error. We also experimentally demonstrate the ability of UKP to discriminate between different types of features or representations based on their generalization performance on downstream kernel ridge regression tasks.

stat.ML↗

arXiv2024

Quasi-classical Trajectory Calculations on a Two-state Potential Energy Surface Including Nonadiabatic Coupling Terms as Friction for D+ + H2 Collisions

Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy surface including nonadiabatic coupling terms as friction terms for D+ + H2 collisions. It is shown that the resulting dynamics correctly accounts for nonreactive charge transfer, reactive non charge transfer and reactive charge transfer processes. In addition, it leads to the formation of triatomic DH2+ species as well.

physics.chem-ph↗

arXiv2024

Investigation of magnetic order influenced phonon and electron dynamics in MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ through terahertz time-domain spectroscopy

MnBi$_{2}$Te$_{4}$, the first topological insulator with inherent magnetic ordering, has attracted significant attention recently for providing a platform to realize several exotic quantum phenomena at relatively higher temperatures. In this work, we have carried out an exhaustive investigation of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ thin films using THz time-domain spectroscopy. The extracted real THz conductivity displays a strong IR active E$_u$ phonon absorption peak (at $\sim$1.5 THz) merged on top of the Drude-like contributions from bulk and surface electrons. The extracted parameters from the THz conductivity data fitted to the Drude-Fano-Lorentz model, show significant changes in their temperature dependence around the magnetic ordering Néel temperature of $\sim$ 25K, which is suggestive of the coupling between magnetic ordering and electronic band structure. The frequency of the E$_u$ phonon displays an anomalous blue-shift with increasing temperatures by $\sim$ 0.1 THz ($\sim$7 %) for MnBi$_{2}$Te$_{4}$ and $\sim$0.2 THz ($\sim$13 %) for Sb doped MnBi$_{2}$Te$_{4}$ between 7K and 250K. The line-shape of the E$_u$ phonon mode in Sb doped MnBi$_{2}$Te$_{4}$ shows significant Fano asymmetry compared to that of MnBi$_{2}$Te$_{4}$, indicating that Sb doping plays an important role in the Fano interference between the phonons and the electrons, in this system. These results indicate that the anomalous phonon behaviour seen in MBT arise mainly from positive cubic anharmonicity induced self energy parameter, whereas both anharmonicity and the electron phonon coupling are at play in making the relatively higher anomalous blue shift of phonons in MBST. Our studies provide the first comprehensive understanding of the phonon and electron dynamics of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ in the THz range using time-domain THz spectroscopy.

cond-mat.mtrl-sci↗

arXiv2024

Probing of magnetic dimensional crossover in CrSiTe$_{3}$ through picosecond strain pulses

Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic ordering (SRMO) in two-dimensional van der Waals materials holds profound implications for fundamental research and technological advancements. However, directly observing the intricate stages of this magnetic dimensional crossover (MDC) remains a significant experimental challenge. While magneto-elastic coupling offers a promising avenue, detecting the minute lattice response to SRMO proves challenging. Recent investigations utilizing second harmonic generation have unveiled a two-step MDC in a van der Waals ferromagnetic insulator. However, an unambiguous detection of MDC through the time-resolved techniques remains elusive. To meet this goal, we have executed an alternative approach by employing picosecond acoustic strain pulses generated by femtosecond lasers to probe the various stages of MDC through the magneto-elastic coupling for the first time. By analyzing the shape of the strain pulse in both the time and frequency domains as a function of temperature, we clearly demonstrate the detection of the subtle influence of spin fluctuations on the lattice. Additionally, the ultrafast carrier dynamics also show signatures of MDC. Our measurements pave the way towards characterizing magnetic materials in time-resolved experiments that are crucial in designing a new generation of spin-based optoelectronic devices.

cond-mat.mtrl-sci↗

arXiv2023

Non-adiabatic coupling as friction in the formation of H3+: A classical mechanical study

By going beyond the Born-Oppenheimer approximation and treating the non-adiabatic coupling terms (NACTs) as equivalent to a frictional force in a molecular system, the classical equations of motion are solved for a test case of H3+. Using an ab initio potential energy surface for the ground electronic state and its NACTs with the first excited state of H3+, it is shown that (D+, H2) collisions are slowed enough to result in trapping and formation of a stable DH2+.

physics.chem-ph↗

arXiv2022

Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy

Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the `texture anisotropy'. This anisotropy can stem from preferential grain alignment in polycrystalline materials, aligned micro-cracks, or structural reinforcement, such as collagen bundles in biological tissues, steel rods in prestressed concrete and reinforcing fibres in composites. Here we establish a framework for initially stressed solids with transverse texture anisotropy. We consider that the strain energy per unit mass of the reference is an explicit function of the elastic deformation gradient, the initial stress tensor, and the texture anisotropy. We determine the corresponding constitutive relations and develop examples of nonlinear strain energies which depend explicitly on the initial stress and direction of texture anisotropy. As an application, we then employ these models to analyse the stress distribution of an inflated initially stressed cylinder with texture anisotropy, and the tension of a welded metal plate. We also deduce the elastic moduli needed to describe linear elasticity from stress reference with transverse texture anisotropy. As an example we show how to measure the stress with small-amplitude shear waves.

physics.class-ph↗

arXiv2020

Symmetry-Adapted Tight-Binding Electronic Structure Analysis of Carbon Nanotubes with Defects, Kinks, Twist, and Stretch

This paper applies a symmetry-adapted method to examine the influence of deformation and defects on the electronic structure and band structure in carbon nanotubes. First, the symmetry-adapted approach is used to develop the analog of Bloch waves. Building on this, the technique of perfectly-matched layers is applied to develop a method to truncate the computational domain of electronic structure calculations without spurious size effects. This provides an efficient and accurate numerical approach to compute the electronic structure and electromechanics of defects in nanotubes. The computational method is applied to study the effect of twist, stretch, and bending, with and without various types of defects, on the band structure of nanotubes. Specifically, the effect of stretch and twist on band structure in defect-free conducting and semiconducting nanotubes is examined, and the interaction with vacancy defects is elucidated. Next, the effect of localized bending or kinking on the electronic structure is studied. Finally, the paper examines the effect of 5-8-5 Stone-Wales defects. In all of these settings, the perfectly-matched layer method enables the calculation of localized non-propagating defect modes with energies in the bandgap of the defect-free nanotube.

cond-mat.mes-hall↗

arXiv2019

Topological Studies related to Molecular Systems formed soon after the Big Bang: HeH2+ as the Precursor for HeH+

In the early universe, following the nucleosynthesis, conditions were right for recombination processes to take place yielding neutral atoms H, He and Li. The understanding so far in astrophysics is that the first molecule to be formed was HeH+ by radiative association (He + H+ -> HeH+ + h(nu) and He+ + H -> HeH+ + h(nu). The recent report by Guesten et al (Nature, 568, 357, 2019) of detection of HeH+ in planetary Nebula NGC 7027 confirms its presence, but it does not conclusively prove the origin of this species. To create molecules from free moving quasi-ions surrounded by an electronic cloud, the Born-Oppenheimer-Huang (BOH) theory furnishes two kinds of forces, namely, one that results from the Potential Energy Surfaces (PESs) and the other from Non-Adiabatic Coupling Terms (NACTs). Whereas the PESs are known to manage slow moving quasi-ions the NACTs, with their, frequently, infinitely large values at the vicinity of the singularities can control the fast moving quasi-ions. To achieve that the BOH equation indicates that the NACTs are affecting the fast moving quasi-ions directly and if they are attributed with dissipative features or in other words to behave as a Friction Force they indeed could serve (like any other ordinary friction) as moderators for the fast atomic(ionic) species. It is proposed in the present paper that the triatomic HeH2+ was the precursor to HeH+ and it could have been formed by the (He, H, H)+ nuclei coming together under the electron cloud, facilitated by the NACTs between different electronic states acting as an astronomical friction force. This is possible because of the singularities in the NACTs for triatomic systems and NOT for diatomic systems. Although the existence of HeH2+ was established in the laboratory in 1996, it has not been detected in the interstellar media so far. But, there is no reason why it cannot be detected in near future.

physics.chem-ph↗