Related papers: Level dynamics and the ten-fold way

In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…

We briefly show how we can obtain Hamiltonians for spatially compact locally homogeneous vacuum spacetimes. The dynamical variables are categorized into the curvature parameters and the Teichm\"{u}ller parameters. While the Teichm\"{u}ller…

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…

We develop a formalism to study the use of Level Set Method (LSM) in the investigation of evolution of observables in terms of parameters of the Hamiltonian, both of the system itself and the control part. A simple example with an analytic…

In these lecture notes we present different methods and concepts developed in statistical physics to analyze gradient descent dynamics in high-dimensional non-convex landscapes. Our aim is to show how approaches developed in physics, mainly…

In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and…

The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.

This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…

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…

Dynamics of collisionless plasma described by the Poisson-Vlasov equations is connected with the Hamiltonian motions of particles and their symmetries. The Poisson equation is obtained as a constraint arising from the gauge symmetries of…

This paper explores the relationship between Cartan symmetries, dynamical similarities, and dynamical symmetries in contact Hamiltonian mechanics. By introducing an alternative decomposition of vector fields, we characterize these…

We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…

We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of…

Levels densities of independent-particle Hamiltonians can be calculated easily by using the real-time representation of the evolution operator together with the fast Fourier transform. We describe the method and implement it with a set of…

A novel Hamiltonian description of the dynamics of a spherically symmetric, light-like, self-gravitating shell is presented. It is obtained via the systematic reduction of the phase space with respect to the Gauss-Codazzi constraints, model…

For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…

The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…