arXiv subjects

Chaoming Song

Publications and source records attributed to Chaoming Song.

At least 19 recordsLinked to original sources

arXiv2025

Super Higher-Teichm\"uller Geometry and Loop Amplitudes

We construct a supersymmetric extension of the Fock-Goncharov cluster ensemble associated with a split basic classical Lie supergroup $G$ and a marked bordered surface $S$. The resulting structure defines a super higher-Teichm\"uller geometry: a split super--thickening of $(\mathscr A_{G,S}, \mathscr X_{G,S})$ equipped with a mutation atlas preserving a canonical super log-symplectic form. Each super seed carries an integer weight matrix $W$ encoding Cartan weights of an abelian odd slice, transforming by the column $g$--vector rule and giving rise to a flat logarithmic superconnection and a canonical super volume form. On this geometric foundation we define a canonical logarithmic superform $\Omega_{\mathrm{super}}^{(L)}$ on a loop fibration $\pi_L : \mathscr X^{(L)}_{G,S} \!\to\! \mathscr X_{G,S}$ as the relative lift of the base super volume. For $G = PGL(4|4)$, the corresponding super period $P_{\mathrm{super}} = \int_{C} \Omega_{\mathrm{super}}^{(L)}$ encodes the loop amplitude data of planar $N = 4$ super Yang--Mills, expressed through a unified and triangulation-independent formula that satisfies Steinmann and cluster adjacency, with the even sector given by Chen iterated integrals and the odd sector captured by an invariant BCFW delta.

math-ph↗

arXiv2025

Alignment Phase Transition in Socially Driven Motion

Collective human movement is a hallmark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and navigation. In contrast, alignment in low-speed, socially engaged contexts emerges not from locomotion goals but from interpersonal interaction. Using high-resolution spatial and orientation data from preschool classrooms, we uncover a sharp, distance-dependent transition in pairwise alignment patterns that reflects a spontaneous symmetry breaking between distinct behavioral phases. Below a critical threshold of approximately 0.65\,m, individuals predominantly align side-by-side; beyond this range, face-to-face orientations prevail. We show that this transition arises from a distance-dependent competition among three alignment mechanisms: parallelization, opposition, and reciprocation, whose interplay generates a bifurcation structure in the effective interaction potential. A Fourier-based decomposition of empirical orientation distributions reveals these mechanisms, enabling the construction of a minimal pseudo-potential model that captures the alignment transition as a non-equilibrium phase transition. Monte Carlo simulations using the inferred interaction terms closely reproduce the empirical patterns. These findings establish a quantitative framework for social alignment in low-speed human motion, extending active matter theory to a previously unexplored regime of socially mediated orientation dynamics, with implications for modeling coordination and control in biological collectives and artificial swarms.

physics.soc-ph↗

arXiv2025

Nonperturbative Renormalization as Riemann-Hilbert Decomposition of Schwinger-Dyson D-Module

We present a non-perturbative formulation of renormalization by viewing the regularized Schwinger-Dyson hierarchy as a meromorphic connection, that is, as a D-module on the product of spacetime with the regulator disc. The irregular Riemann-Hilbert correspondence splits this connection into a purely formal submodule that contains every ultraviolet pole and a holomorphic submodule that is finite at the regulator origin. In this setting, counterterms coincide with the formal Stokes data, the renormalized theory is identified with the analytic submodule, and the Callan-Symanzik flow appears as an isomonodromic deformation in the physical scale. Viewed through this lens, the Connes-Kreimer construction with its graph Hopf algebra, Bogoliubov recursion, and Birkhoff factorisation is simply the perturbative shadow cast by the global geometric decomposition of the full Schwinger-Dyson system.

hep-th↗

arXiv2025

Exact Ground States of Two Dimensional $\pm J$ Spin Glasses

We derive exact analytical expressions for the ground-state energy and entropy of the two-dimensional $\pm J$ Ising spin glass, uncovering a nested hierarchy of frustrations. Each level in this hierarchy contributes through the kernel and pseudo-determinant of effective operators, capturing the energy and entropy, respectively. At leading order, the structure coincides with geometric plaquette frustrations, while subleading corrections arise from magnetic adjacency matrices defined on percolated clusters in the dual lattice. Our results, supported by numerical simulations, provide a systematic framework for analyzing spin-glass ground states and offer new insight into glass order in finite dimensions.

cond-mat.dis-nn↗

arXiv2025

Switching exploration modes in human mobility

Recent advances in human mobility research have revealed consistent pairwise characteristics in movement behavior, yet existing mobility models often overlook the spatial and topological structure of mobility networks. By analyzing millions of devices' anonymized cell phone trajectories, we uncover a distinct modular organization within these networks, demonstrating that movements within spatial modules differ significantly from those between modules. This finding challenges the conventional assumption of uniform mobility dynamics and underscores the influence of heterogeneous environments on human movement. Inspired by switching behaviors in animal movement patterns, we introduce a novel "switch mechanism" to differentiate movement modes, allowing our model to accurately reproduce both the modular structures of trajectory networks and spatial mobility patterns. Our results provide new insights into the dynamics of human mobility and its impact on network formation, with broad applications in traffic prediction, disease transmission modeling, and urban planning. Beyond advancing the theoretical and practical understanding of mobility networks, this work opens new avenues for understanding societal dynamics at large.

physics.soc-ph↗

arXiv2025

A New Circle Theorem for Two Dimensional Ising Spin Glasses

The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the real axis in the thermodynamic limit. However, in frustrated systems such as antiferromagnets and spin glasses, the zeros deviate from this structure, making it challenging to extend the Lee-Yang theory to disordered systems. In this work, we establish a new circle theorem for two-dimensional Ising spin glasses, proving that the square of the partition function exhibits zeros densely packed along the unit circle. Numerical simulations on the square lattice confirm our theoretical predictions, demonstrating the validity of the circle law for quenched disorder. Furthermore, our results uncover a finite-temperature crossover in $\pm J$ spin glasses, characterized by the emergence of a spectral gap in the angular distribution of zeros. This result extends the Lee-Yang framework to disordered systems, offering new insights into spin-glass criticality.

cond-mat.dis-nn↗

arXiv2024

Correlated Growth of Causal Networks

The study of causal structure in complex systems has gained increasing attention, with many recent studies exploring causal networks that capture cause-effect relationships across diverse fields. Despite increasing empirical evidence linking causal structures to network topological correlations, the mechanisms underlying the emergence of these correlations in causal networks remain poorly understood. In this work, we propose a general growth framework for causal networks, incorporating two key types of correlations: causal and dynamic. We analytically demonstrate that degree correlations emerge as a consequence of marginal dependencies on these correlations. Our theoretical predictions align quantitatively with empirical data from four large-scale innovation networks. Our theory not only sheds light on the origins of topological correlations but also provides a general framework for understanding correlated growth across causal systems.

physics.soc-ph↗

arXiv2024

Dynamical Phase Transitions in Non-equilibrium Networks

Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum systems, DPTs have remained largely unexplored in classical settings. Recent experiments on complex systems, from social networks to financial markets, have revealed abrupt dynamical changes analogous to quantum DPTs, motivating the search for a theoretical understanding. Here, we present a minimal model for nonequilibrium networks, demonstrating that nonlinear interactions among network edges naturally give rise to DPTs. Specifically, we show that network degree diverges at a finite critical time, following a universal hyperbolic scaling, consistent with empirical observations. Our analytical results predict that key network properties, including degree distributions and clustering coefficients, exhibit critical scaling as criticality approaches. These findings establish a theoretical foundation for understanding emergent nonequilibrium criticality across diverse complex systems.

physics.soc-ph↗

arXiv2024

Quantifying the Dynamics of Innovation Abandonment Across Scientific, Technological, Commercial, and Pharmacological Domains

Despite the vast literature on the diffusion of innovations that impacts a broad range of disciplines, our understanding of the abandonment of innovations remains limited yet is essential for a deeper understanding of the innovation lifecycle. Here, we analyze four large-scale datasets that capture the temporal and structural patterns of innovation abandonment across scientific, technological, commercial, and pharmacological domains. The paper makes three primary contributions. First, across these diverse domains, we uncover one simple pattern of preferential abandonment, whereby the probability for individuals or organizations to abandon an innovation increases with time and correlates with the number of network neighbors who have abandoned the innovation. Second, we find that the presence of preferential abandonment fundamentally alters the way in which the underlying ecosystem breaks down, inducing a novel structural collapse in networked systems commonly perceived as robust against abandonments. Third, we derive an analytical framework to systematically understand the impact of preferential abandonment on network dynamics, pinpointing specific conditions where it may accelerate, decelerate, or have an identical effect compared to random abandonment, depending on the network topology. Together, these results deepen our quantitative understanding of the abandonment of innovation within networked social systems, with implications for the robustness and functioning of innovation communities. Overall, they demonstrate that the dynamics of innovation abandonment follow simple yet reproducible patterns, suggesting that the uncovered preferential abandonment may be a generic property of the innovation lifecycle.

physics.soc-ph↗

arXiv2024

Exact Quantum Trace Formula from Complex Periodic Orbits

The Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we explore the full quantum version of the trace formula using the Lefschetz thimble method by incorporating complexified periodic orbits. Upon complexification, classical real periodic orbits are transformed into cycles on compact Riemann surfaces. Our key innovation lies in the simultaneous complexification of the periods of cycles, resulting in a fully quantum trace formula that accounts for all contributions classified by the homology classes of the associated Riemann surfaces. This formulation connects the quantum spectrum to contributions across all complex time directions, encompassing all relevant homology classes. Our approach naturally unifies and extends two established methodologies: periodic orbits in real time, as in Gutzwiller's original work, and quantum tunneling in imaginary time, as in the instanton method.

quant-ph↗

arXiv2024

Universal expansion of human mobility across urban scales

Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like home-centricity and hierarchical spatial organization. However, identifying universal characteristics or an underlying principle that quantitatively links these disparate perspectives has remained a challenge. Here, we reveal such a connection by analyzing the spatial structure of individual daily mobility trajectories using network-based modules. We discover a universal scaling law: the spatial extent (radius) of these mobility modules expands sublinearly with increasing distance from home, a pattern consistent across three orders of magnitude. Furthermore, we demonstrate that these modules precisely map onto the nested hierarchy of urban systems, corresponding to local, city-level, and regional scales as distance from home increases. These findings deepen our understanding of human mobility dynamics and demonstrate the profound connection between classical urban theory, human geography, and mobility studies.

physics.soc-ph↗

arXiv2023

Exact 3D Conformal Blocks from Fractional Calculus

We uncover a striking connection between conformal blocks and fractional calculus. By employing a modified form of half-derivates, we derived explicitly the exact form of the three-dimensional conformal block, expressed as the product of two hypergeometric 4F3 functions. This result provides a rigorous proof of Hogervorst's formula, conjectured nearly a decade ago. Furthermore, we demonstrate its implications for the conformal bootstrap, potentially leading to new analytical techniques and numerical tools that deepen our understanding of conformal field theory.

hep-th↗

arXiv2023

Kramers-Wannier Duality and Random Bond Ising Model

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on vertices and dual vertices respectively, thereby explicitly demonstrating the Kramers-Wannier duality. The implications of our derived formula for the random bond Ising model are further elucidated.

cond-mat.stat-mech↗

arXiv2023

Crossing Symmetric Dispersion Relations without Spurious Singularities

Recently, there has been renewed interest in a crossing-symmetric dispersion relation from the 1970s due to its implications for both regular quantum field theory and conformal field theory. However, this dispersion relation introduces nonlocal spurious singularities and requires additional locality constraints for their removal, a process that presents considerable technical challenges. In this Letter, we address this issue by deriving a new crossing-symmetric dispersion relation that is free of spurious singularities, resulting in a compact form of the contact terms in crossing-symmetric blocks. Our results establish a solid foundation for the Polyakov bootstrap in conformal field theories and the crossing-symmetry S-matrix bootstrap in quantum field theories.

hep-th↗

arXiv2023

Random packing in three dimensions

Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an unambiguous and universally accepted definition of random packing. This paper introduces an innovative standpoint, depicting random packing as spheres closest to a quenched Poisson field of random points. We furnish an efficacious algorithm to probe this proposed model numerically. We unearth a unique out-of-equilibrium thermodynamic phenomenon, akin to a `latent heat', that emerges at $\phi_J \approx 0.65$ in three dimensions. This phenomenon is accompanied by global and local structural rearrangements, marking a jamming transition from an unjammed state to a jammed one. Notably, such a `jamming' transition is absent for two-dimensional random packing. Our innovative approach paves a new avenue for defining random packing and provides novel insights into the behavior of amorphous materials.

cond-mat.soft↗

arXiv2023

Zero Curvature Condition for Quantum Criticality

Quantum criticality often lies beyond the scope of the conventional Landau paradigm, and a unifying framework has yet to emerge, due in part to the wide variety of quantum orders. We propose a geometric approach to quantum phase transitions (QPTs) that shifts focus from microscopic order to the competition between non-commuting operators. This competition is encoded in the boundary geometry of their expectation values, defining a quantum observable space (QOS). We show that QPTs occur at zero-curvature points on the QOS boundary, signaling maximal commutativity and suggesting an underlying integrable structure at criticality.

quant-ph↗

arXiv2023

Correlated Impact Dynamics in Science

Science progresses by building upon previous discoveries. It is commonly believed that the impact of scientific papers, as measured by citations, is positively correlated with the impact of past discoveries built upon. However, analyzing over 30 million papers and nearly a billion citations across multiple disciplines, we find that there is a long-term positive citation correlation, but a negative short-term correlation. We demonstrate that the key to resolving this paradox lies in a new concept, called "capacity", which captures the amount of originality remaining for a paper. We find there is an intimate link between capacity and impact dynamics that appears universal across the diverse fields we studied. The uncovered capacity measure not only explains the correlated impact dynamics across the sciences but also improves our understanding and predictions of high-impact discoveries.

physics.soc-ph↗

arXiv2023

Quantum Geometry of Expectation Values

We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that the boundary of expectation value space corresponds to the ground state, which presents a natural bound that generalizes Heisenberg's uncertainty principle. To demonstrate the versatility of our framework, we present several practical applications, including providing a stronger nonlinear quantum bound that violates the Bell inequality and an explicit construction of the density functional. Our approach provides an alternative time-independent quantum formulation that transforms the linear problem in a high-dimensional Hilbert space into a nonlinear algebro-geometric problem in a low dimension, enabling us to gain new insights into quantum systems.

quant-ph↗