Related papers: The Phase Space Distance Between Collider Events
For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce…
Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…
We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…
Chemical selectivity is a phenomenon displayed by potential energy surfaces (PES) that is relevant for many organic chemical reactions whose PES feature a valley-ridge inflection point (VRI) in the region between two sequential index-1…
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of…
Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…
The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N greater or equal to 2. Liquid-liquid phase separation is modelled using a virial expansion up to the second order of the…
We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our…
The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure…
Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
There are many cases in collider physics and elsewhere where a calibration dataset is used to predict the known physics and / or noise of a target region of phase space. This calibration dataset usually cannot be used out-of-the-box but…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
The dynamical phase-space of axisymmetric Canham-Helfrich (CH) cells is constructed from a Hamiltonian field recapitulating membrane curvature-elasticity and systemic restrictions. Guiding principles are reparametrization to convert a…
The covariant phase space technique is a powerful formalism for understanding the Hamiltonian description of covariant field theories. However, applications of this technique to problems involving subregions, such as the exterior of a black…
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
The discrete phase space and continuous time representation of relativistic quantum mechanics is further investigated here as a continuation of paper I [1]. The main mathematical construct used here will be that of an area-filling Peano…