arXiv subjects

Vaibhav Mohanty

Publications and source records attributed to Vaibhav Mohanty.

5 recordsLinked to original sources

arXiv2026

Diffusion with conserved marginal distributions and information theory in fracton hydrodynamics

Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that conserving complete multipole-moment groups leads to subdiffusive dynamics governed by a nonlinear diffusion equation, raising the question of whether hydrodynamic equations would also be nonlinear when the conservation law is imposed only at the subsystem level. Here we show that subsystem symmetries generically produce nonlinear hydrodynamic equations with shear-only transport, in which any localization present in the initial marginal distributions is preserved at long times by the conservation of those marginals. A linear regime emerges only as a limiting case for small fluctuations around a uniform background. We derive the deterministic and fluctuating parts of the hydrodynamic equations in arbitrary dimensions and obtain the corresponding maximum-entropy equilibrium distributions under constrained marginals. We also show that marginal-conserving diffusion provides a concrete hydrodynamic realization of partial multipole-moment conservation, and we offer an information-theoretic interpretation in which total correlation decays monotonically even when pairwise mutual information does not.

cond-mat.stat-mech↗

arXiv2025

Probabilistic Genotype-Phenotype Maps Reveal Mutational Robustness of RNA Folding, Spin Glasses, and Quantum Circuits

Recent studies of genotype-phenotype (GP) maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype -- represented as a sequence -- maps deterministically to a single phenotype, such as a discrete structure. Here, we introduce probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a vector of phenotype probabilities, as a more realistic and universal language for investigating robustness in a variety of physical, biological, and computational systems. We study three model systems to show that PrGP maps offer a generalized framework which can handle uncertainty emerging from various physical sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in spin glass ground state finding, and (3) superposition and entanglement in quantum circuits, which are realized experimentally on IBM quantum computers. In all three cases, we observe a novel biphasic robustness scaling which is enhanced relative to random expectation for more frequent phenotypes and approaches random expectation for less frequent phenotypes. We derive an analytical theory for the behavior of PrGP robustness, and we demonstrate that the theory is highly predictive of empirical robustness.

cond-mat.stat-mech↗

arXiv2022

Robustness and Stability of Spin Glass Ground States to Perturbed Interactions

Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.

cond-mat.dis-nn↗

arXiv2018

A 5-Dimensional Tonnetz for Nearly Symmetric Hexachords

The standard 2-dimensional Tonnetz describes parsimonious voice-leading connections between major and minor triads as the 3-dimensional Tonnetz does for dominant seventh and half-diminished seventh chords. In this paper, I present a geometric model for a 5-dimensional Tonnetz for parsimonious voice-leading between nearly symmetric hexachords of the mystic-Wozzeck genus. Cartesian coordinates for points on this discretized grid, generalized coordinate collections for 5-simplices corresponding to mystic and Wozzeck chords, and the geometric nearest-neighbors of a selected chord are derived.

math.HO↗

arXiv2018

Dodecatonic Cycles and Parsimonious Voice-Leading in the Mystic-Wozzeck Genus

This paper develops a unified voice-leading model for the genus of mystic and Wozzeck chords. These voice-leading regions are constructed by perturbing symmetric partitions of the octave, and new Neo-Riemannian transformations between nearly symmetric hexachords are defined. The behaviors of these transformations are shown within visual representations of the voice-leading regions for the mystic-Wozzeck genus.

math.HO↗