相关论文: A Note on Kinematic Flow and Differential Equation…

The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…

The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic…

Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1,2]. It was proven that simple and…

We uncover a geometric organization of the differential equations for the wavefunction coefficients of conformally coupled scalars in power-law cosmologies. To do this, we introduce a basis of functions inspired by a decomposition of the…

Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent…

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…

We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…

We consider $L$-loop two-point tadpole (watermelon) integral with arbitrary masses, regularized both dimensionally and analytically. We derive differential equation system and recurrence relations (shifts of dimension and denominator…

We study equal-time in-in correlators of massless scalar fields in flat space at one loop. Using the time-ordered decomposition of correlators together with a cosmological analogue of the Baikov representation, we systematically construct…

Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic…

Flexible structures in an incoming perpendicular flow typically undergo elastic reconfiguration that reduces drag; however, at higher velocities, they are prone to dynamical instabilities that entail complex wake dynamics and fluctuating…

We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions $(f,\Lambda)$ in one variable. Topology of the Liouville fibration of the given integrable system near…

We present a unified framework that connects four-dimensional duality-invariant nonlinear electrodynamics and two-dimensional integrable sigma models via the Courant-Hilbert and new auxiliary field formulations, both governed by a common…

Quantum self-oscillatory phases are ubiquitous in driven-dissipative systems. Classically, each phase is defined by its flow pattern and how stationary sets organize phase space (e.g. fixed points and limit cycles), with transitions…

We extend kinematic flow to momentum-integrated loop-level cosmological correlators, focusing on banana loops of conformally coupled scalars in power-law cosmologies and, in de Sitter, on arbitrary mixtures of massless and conformally…

Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence,…

We develop a Hamiltonian description of point particles in (2+1)-dimensions using connection and frame-field variables for general relativity. The topology of each spatial hypersurface is that of a punctured two-sphere with particles…

Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…

To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the…

We consider composite quantum-dynamical systems that can be partitioned into weakly interacting subsystems, similar to system-bath type situations. Using a factorized wave function ansatz, we mathematically characterize dynamical scale…