相关论文: Investigating the Phase Space Dynamics of Hamilton…

We introduce and demonstrate the usage of the origin-fate map (OFM) as a tool for the detailed investigation of phase space transport in reactant-product type systems. For these systems, which exhibit clearly defined start and end states,…

We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that contains no minimum. Using this method we show the phase…

In this paper we unveil the geometrical template of phase space structures that governs transport in a Hamiltonian system described by a potential energy surface with an entrance/exit channel and two wells separated by an index-1 saddle.…

In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using…

We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and…

High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as…

We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of these four dimensional objects in the five dimensional phase…

A recent paper [V. L. Campo et. al., Phys. Rev. Lett. 99, 240403 (2007) has proposed a two-parameter scaling method to determine the phase diagram of the fermionic Hubbard model from optical lattice experiments. Motivated by this proposal,…

Atypically large fluctuations in macroscopic non-equilibrium systems continue to attract interest. Their probability can often be determined by the optimal fluctuation method (OFM). The OFM brings about a conditional variational problem,…

Chaotic transport is related to the complex dynamical evolution of chaotic trajectories in Hamiltonian systems, which models various physical processes. In magnetically confined plasma, it is possible to qualitatively describe the…

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…

High mobility environment leads to severe Doppler effects and poses serious challenges to the conventional physical layer based on the widely popular orthogonal frequency division multiplexing (OFDM). The recent emergence of orthogonal time…

Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…

In this paper we explore the phase space structures governing isomerization dynamics on a potential energy surface with four wells and an index-2 saddle. For this model, we analyze the influence that coupling both degrees of freedom of the…

The goal of this paper is to apply the method of Lagrangian descriptors to reveal the phase space mechanism by which a Caldera-type potential energy surface (PES) exhibits the dynamical matching phenomenon. Using this technique, we can…

Objects driven through periodically modulated potential-energy landscapes in two dimensions can become locked in to symmetry-selected directions that are independent of the driving force's orientation. We investigate this problem in the…

Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…

We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…

We develop a bifurcation-theoretic description of Friedmann--Robertson--Walker cosmologies with a scalar field $\phi$, a barotropic fluid of index $\gamma$, and spatial curvature. For the strict exponential potential…

The Out-of-Time-Order Correlator (OTOC) is a standard algebraic diagnostic of quantum information scrambling, but it offers limited direct geometric intuition. In this note, we propose a Bohmian, trajectory-based framework for constructing…