arXiv subjects

Arnab Sen

Publications and source records attributed to Arnab Sen.

At least 19 recordsLinked to original sources

arXiv2026

Longest convex chains with i.i.d. points

Sample $n$ i.i.d. points from a triangle, according to some bounded density function. Given two vertices $A,B$ of the triangle, what is the maximum number of samples that form a convex chain with initial point $A$ and terminal point $B$? We show that to leading order, the answer is $cn^{1/3}$, generalizing a result of Ambrus and B\'ar\'any that considered uniformly distributed points. Furthermore, we express the constant $c$ using a variational formula whose maximizer (if unique) gives the limiting curve formed by the longest convex chain. By comparison, for $n$ i.i.d. samples from the unit square, the length of the longest monotone chain is asymptotically $c'n^{1/2}$. Despite the difference in scale, our formula is nicely connected to one established for $c'$ by Deuschel and Zeitouni.

math.PR↗

arXiv2026

Joint parameters estimation in cubic tensor model

We study joint parameter estimation from a single observation in high-dimensional Gibbs measures with cubic tensor interactions, motivated by dense ERGMs, arithmetic-progression models, and inhomogeneous random hypergraphs. Focusing on the maximum pseudolikelihood estimator, we give checkable conditions for joint consistency and asymptotic ill-conditioning. For the edge-triangle ERGM, pseudolikelihood is ill-conditioned in the ferromagnetic regime with nonnegative field, but consistent in a sufficiently strong antiferromagnetic regime. For the edge-three-star ERGM, it is ill-conditioned for all inverse temperatures and external fields. We also study consistency for arithmetic-progression, and inhomogeneous hypergraph models. Our proofs develop nonlinear large-deviation and mean-field approximation tools for cubic tensor Gibbs measures, which have scope for broad applications.

math.ST↗

arXiv2026

Dressed Floquet scars from protected zero modes in a Rydberg chain

In this Letter, we present an approximate analytic construction of two zero quasienergy quantum many-body scars in a periodically driven model of Rydberg atoms on a ring, which persist over a range of driving amplitudes and frequencies for finite sizes. An index theorem protects an exponentially large number (in system size) of exact zero energy modes of the Floquet Hamiltonian in this setting. Unlike most of these zero modes which continuously change with drive parameters, these two quantum many-body scars retain the memory of particular states. They can be expressed as {\it dressed versions} of two contrasting states, the Rydberg vacuum and a unitarily rotated variant of a volume-law scar [Ivanov and Motrunich, Phys. Rev. Lett. {\bf 134}, 050403 (2025)], respectively. We provide an analytic understanding of their existence using a Floquet perturbation theory and show their resilience beyond the perturbative regime using exact diagonalization in finite systems. Our study provides insight into the structure of protected zero modes in interacting Floquet settings.

cond-mat.quant-gas↗

arXiv2026

Emergent prethermal Bethe integrability in a periodically driven Rydberg chain

We study a chain of periodically driven Rydberg atoms and identify a class of drive protocols for which the system exhibits emergent prethermal Bethe integrability at special drive frequencies. We provide a perturbative analytic expression of its Floquet Hamiltonian in the large drive amplitude regime. We demonstrate integrability of the leading term of this Floquet Hamiltonian at special drive frequencies, which we identify, by mapping it to the Hamiltonian of the paradigmatic spin-$1/2$ ${\rm XXZ}$ chain. We support our analytical results by exact diagonalization studies on finite chains. Our numerical results on level statistics, half-chain entanglement entropy, and longitudinal magnetization of the driven chain brings out its emergent integrable nature at the special drive frequencies which persists up to a large prethermal timescale.

quant-ph↗

arXiv2026

Limiting Root Distribution of Random Log-concave Polynomials

We introduce two probabilistic models of random log-concave polynomials, the uniform model and the beta model, and study the asymptotic distribution of their zeros in the complex plane. In the uniform model, we show that the empirical root distribution converges to the uniform probability measure on the unit circle, placing the model in the same universality class as classical Kac polynomials. In contrast, in the beta model log-concavity is amplified through exponential scaling of the coefficients, leading to a new limiting distribution that is rotationally symmetric and absolutely continuous with respect to Lebesgue measure on the plane.

math.PR↗

arXiv2026

Complexity of the p-spin Hamiltonian with a Non-Rotationally Invariant Potential

We investigate the complexity of the Hamiltonian in the pure $p$-spin spin glass model accompanied with a polynomial-type potential on $\mathbb{R}^N$. In this Hamiltonian, the Gaussian field is anisotropic, and the potential lacks rotational invariance. Our main result derives the logarithmic limit for the expected number of critical points in terms of a variational formula. As a consequence, by identifying the critical location of the phase transition from our representation, we provide an upper bound for the ground state energy of the model.

math.PR↗

arXiv2025

Correlation Decay for Maximum Weight Matchings on Sparse Graphs

We study correlation decay for the maximum weight matching problem on sparse graphs with i.i.d. edge weights. We show exponential decay of correlations when the underlying graphs are locally tree-like with uniformly bounded degree and the edge weights are exponential. We also prove a polynomial rate of decay of correlations for any finite graph with maximum degree at most three, again for exponential edge weights. As consequences of the correlation decay property, we obtain the existence of the maximum weight matching on infinite graphs, local weak convergence of the maximum weight matching, and a law of large numbers for its total weight.

math.PR↗

arXiv2025

Metric response of relative entropy: A universal indicator of quantum criticality

The information-geometric origin of fidelity susceptibility and its utility as a universal probe of quantum criticality in many-body settings have been widely discussed. Here we explore the metric response of quantum relative entropy (QRE), by tracing out all but $n$ adjacent sites from the ground state of spin chains of finite length $N$, as a parameter of the corresponding Hamiltonian is varied. The diagonal component of this metric defines a susceptibility of the QRE that diverges at quantum critical points (QCPs) in the thermodynamic limit. We study two spin-$1/2$ models as examples, namely the integrable transverse field Ising model (TFIM) and a non-integrable Ising chain with three-spin interactions. We demonstrate distinct scaling behaviors for the peak of the QRE susceptibility as a function of $N$: namely a square logarithmic divergence in TFIM and a power-law divergence in the non-integrable chain. This susceptibility encodes uncertainty of entanglement Hamiltonian gradients and is also directly connected to other information measures such as Petz-R\'enyi entropies. We further show that this susceptibility diverges even at finite $N$ if the subsystem size, $n$, exceeds a certain value when the Hamiltonian is tuned to its classical limits due to the rank of the RDMs being finite; unlike the divergence associated with the QCPs which require $N \rightarrow \infty$.

cond-mat.stat-mech↗

arXiv2025

POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality

In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty or information, posing a challenge for real-world applications such as 3D-GS SLAM. We propose to quantify information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution widely used in literature. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal covariance approximation which provides a measure of correlation at the expense of a greater computation cost.

cs.CV↗

arXiv2024

Scar-induced imbalance in staggered Rydberg ladders

We demonstrate that the kinematically-constrained model of Rydberg atoms on a two-leg ladder with staggered detuning, $\Delta \in [0,1]$, has quantum many-body scars (QMBS) in its spectrum and represents a non-perturbative generalization of the paradigmatic PXP model defined on a chain. We show that these QMBS result in coherent many-body revivals and site-dependent magnetization dynamics for both N\'eel and Rydberg vacuum initial states around $\Delta=1$. The latter feature leads to eigenstate thermalization hypothesis (ETH)-violating finite imbalance at long times in a disorder-free system. This is further demonstrated by constructing appropriate local imbalance operators that display nonzero long-time averages for N\'eel and vacuum initial states. We also study the fidelity and Shannon entropy for such dynamics which, along with the presence of long-time finite imbalance, brings out the qualitatively different nature of QMBS in PXP ladders with $\Delta \sim 1$ from those in the PXP chain. Finally, we identify additional exact mid-spectrum zero modes that stay unchanged as a function of $\Delta$ and violate ETH.

quant-ph↗

arXiv2024

On the Replica Symmetric Solution in General Diluted Spin Glasses

We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which the model exhibits replica symmetry and the free energy can be explicitly represented as the evaluation of an energy functional at the unique fixed point of a recursive distributional equation. One is called the high temperature regime, where the temperature and the sparsity parameter are essentially inversely proportional to each other; the other is the subcritical regime defined as $\alpha p (p-1)\leq 1$. In particular, the fact that the second regime is independent of the temperature parameter further allows us to deduce an analogous representation of the ground state energy in the subcritical regime. Along the way, we revisit several well-known formulas and also derive new ones for the free and ground state energies in the constraint satisfaction problem, Potts model, XY model, and continuous hardcore model.

math.PR↗

arXiv2024

Joint parameter estimations for spin glasses

Spin glass models with quadratic-type Hamiltonians are disordered statistical physics systems with competing ferromagnetic and anti-ferromagnetic spin interactions. The corresponding Gibbs measures belong to the exponential family parametrized by (inverse) temperature $\beta>0$ and external field $h\in\mathbb{R}$. Given a sample from these Gibbs measures, a statistically fundamental question is to infer the temperature and external field parameters. In 2007, Chatterjee (Ann. Statist. 35 (2007), no.5, 1931-1946) first proved that in the absence of external field $h=0$, the maximum pseudolikelihood estimator for $\beta$ is $\sqrt{N}$-consistent under some mild assumptions on the disorder matrices. It was left open whether the same method can be used to estimate the temperature and external field simultaneously. In this paper, under some easily verifiable conditions, we prove that the bivariate maximum pseudolikelihood estimator is indeed jointly $\sqrt{N}$-consistent for the temperature and external field parameters. The examples cover the classical Sherrington-Kirkpatrick model and its diluted variants.

math.PR↗

arXiv2024

Observation of sequential three-body dissociation of camphor molecule -- a native frame approach

The three-body dissociation dynamics of the dicationic camphor molecule (C$_{10}$H$_{16}$O$^{2+}$) resulting from Auger decay are investigated using soft X-ray synchrotron radiation. A photoelectron-photoion-photoion coincidence (PEPIPICO) method, a combination of a velocity map imaging (VMI) spectrometer and a time-of-flight (ToF) spectrometer is employed to measure the 3D momenta of ions detected in coincidence. The ion mass spectra and the ion-ion coincidence map at photon energies of 287.9 eV (below the C 1s ionization potential) and 292.4 eV (above the C 1s ionization potential for skeletal carbon) reveal that fragmentation depends on the final dicationic state rather than the initial excitation. Using the native frame method, three new fragmentation channels are discussed; (1) CH$_2$CO$^+$ + C$_7$H$_{11}^+$ + CH$_3$, (2) CH$_3^+$ + C$_7$H$_{11}^+$ + CH$_2$CO, and (3) C$_2$H$_5^+$ + C$_6$H$_9^+$ + CH$_2$CO. The dominating nature of sequential decay with deferred charge separation is clearly evidenced in all three channels. The results are discussed based on the experimental angular distributions and momenta distributions, corroborated by geometry optimization of the ground, monocationic, and dicationic camphor molecule.

physics.chem-ph↗

arXiv2024

Fate of many-body localization in an Abelian lattice gauge theory

We address the fate of many-body localization (MBL) of mid-spectrum eigenstates of a matter-free $U(1)$ quantum-link gauge theory Hamiltonian with random couplings on ladder geometries. Apart from level spacing distribution indicators like disorder-averaged mean level spacing, we also consider an intensive estimator $\mathcal{D} \in [0,1/4]$, which acts as a measure of elementary plaquettes on the lattice that are active or inert in mid-spectrum eigenstates as well as the concentration of these eigenstates in Fock space, with $\mathcal{D}$ equal to its maximum value of $1/4$ for Fock states in the electric flux basis. We calculate its distribution, $p(\mathcal{D})$, for $L_x \times L_y$ lattices, with $L_y=2$ and $4$, as a function of (a dimensionless) disorder strength $\alpha$ ($\alpha=0$ implies zero disorder) using exact diagonalization in many disorder realizations. Although finite-size estimators based on level spacings do not give a reliable critical disorder strength, $\alpha_c(L_y)$, beyond which MBL prevails as $L_x \rightarrow \infty$; a different estimator based on the skewness of $p(\mathcal{D})$ gives $\alpha_c(L_y=2)=31.04 \pm 0.54$ using data for $L_x \leq 14$ due to faster convergence. $p(\mathcal{D})$ for wider ladders with $L_y=4$ show a lower tendency to localize, suggesting a lack of MBL in two dimensions. A remarkable observation is the resolution of the (monotonic) infinite-temperature autocorrelation function of single plaquette diagonal operators in typical high-energy Fock states into a plethora of emergent timescales of increasing spatio-temporal heterogeneity as the disorder is increased. At intermediate $\alpha$ as well as for $\alpha$ slightly below $\alpha_c (L_y)$, a fraction of randomly selected initial Fock states display striking oscillatory temporal behavior of such plaquette operators in spatial regions formed out of connected plaquettes.

cond-mat.dis-nn↗

arXiv2024

Disorder Chaos in Short-Range, Diluted, and L\'evy Spin Glasses

In a recent breakthrough [arXiv:2301.04112], Chatterjee proved site disorder chaos in the Edwards-Anderson (EA) short-range spin glass model utilizing the Hermite spectral method. In this paper, we demonstrate the further usefulness of this Hermite spectral approach by extending the validity of site disorder chaos in three related spin glass models. The first, called the mixed even $p$-spin short-range model, is a generalization of the EA model where the underlying graph is a deterministic bounded degree hypergraph consisting of hyperedges with even number of vertices. The second model is the diluted mixed $p$-spin model, which is allowed to have hyperedges with both odd and even number of vertices. For both models, our results hold under general symmetric disorder distributions. The main novelty of our argument is played by an elementary algebraic equation for the Fourier-Hermite series coefficients for the two-spin correlation functions. It allows us to deduce necessary geometric conditions to determine the contributing coefficients in the overlap function, which in spirit is the same as the crucial Lemma 1 in [arXiv:2301.04112]. Finally, we also establish disorder chaos in the L\'evy model with stable index $\alpha \in (1, 2)$.

math.PR↗

arXiv2024

Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study

We investigate the dynamical phases and phase transitions arising in a classical two-dimensional anisotropic $XY$ model under the influence of a periodically driven temporal external magnetic field in the form of a symmetric square wave. We use a combination of finite temperature classical Monte Carlo simulation, implemented within a CPU + GPU paradigm, utilizing local dynamics provided by the Glauber algorithm and a phenomenological equation-of-motion approach based on relaxational dynamics governed by the time-dependent free energy within a mean-field approximation to study the model. We investigate several parameter regimes of the variables (magnetic field, anisotropy, and the external drive frequency) that influence the anisotropic $XY$ system. We identify four possible dynamical phases -- Ising-SBO, Ising-SRO, $XY$-SBO and $XY$-SRO. Both techniques indicate that only three of them (Ising-SRO, Ising-SBO, and $XY$-SRO) are stable dynamical phases in the thermodynamic sense. Within the Monte Carlo framework, a finite size scaling analysis shows that $XY$-SBO does not survive in the thermodynamic limit giving way to either an Ising-SBO or a $XY$-SRO regime. The finite size scaling analysis further shows that the transitions between the three remaining dynamical phases either belong to the two-dimensional Ising universality class or are first-order in nature. The mean-field calculations yield three stable dynamical phases, i.e., Ising-SRO, Ising-SBO and $XY$-SRO, where the final steady state is independent of the initial condition chosen to evolve the equations of motion, as well as a region of bistability where the system either flows to Ising-SBO or $XY$-SRO (Ising-SRO) depending on the initial condition. Unlike the stable dynamical phases, the $XY$-SBO represents a transient feature that is eventually lost to either Ising-SBO or $XY$-SRO.

cond-mat.stat-mech↗

arXiv2024

Minimal spanning arborescence

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient trees, the infinite volume limit exists almost surely. We also prove that for nonamenable, unimodular graphs, the limit is almost surely one-ended assuming a certain sufficient condition that guarantees the existence of the limit. This object cannot be studied using well-known algorithms, such as Kruskal's or Prim's algorithm, to sample the minimal spanning tree which has been instrumental in getting analogous results about them (Lyons, Peres, and Schramm). Instead, we use a recursive algorithm due to Chu, Liu, Edmonds, and Bock, which leads to a novel stochastic process which we call the \emph{loop contracting random walk}. This is similar to the well-known and widely studied loop erased random walk, except instead of erasing loops we contract them. The full algorithm bears similarities with the celebrated Wilson's algorithm to generate uniform spanning trees and can be seen as a certain limit of the original Wilson's algorithm.

math.PR↗

arXiv2023

Emergent criticality in a constrained boson model

We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition separates a unique gapped ground state from a gapless one; the latter phase exhibits a broken $Z_2$ symmetry which we tie to the presence of the subsystem symmetries in the model. The intermediate critical point separating these phases exhibits an additional emergent $Z_2$ symmetry which we identify. This emergence leads to a critical theory which seems to be different from those in the Ising universality class. Instead, within the data obtained from finite-size scaling analysis, we find the critical theory to be not inconsistent with Ashkin-Teller universality in the sense that the transitions of the model reproduces a critical line with variable correlation length exponent $\nu$ but constant central charge $c$ close to unity. We verify this scenario via explicit exact-diagonalization computations, provide an effective Landau-Ginzburg theory for such a transition, and discuss the connection of our model to the PXP model describing Rydberg atom arrays.

cond-mat.str-el↗