Related papers: Hamilton-Jacobi approach to Potential Functions in…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
Hamilton-Jacobi (HJ) Reachability is widely used to compute value functions for states satisfying specific control objectives. However, it becomes intractable for high-dimensional problems due to the curse of dimensionality. Dimensionality…
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the…
We use the Liouville eigenfunctions to define a classical version of the geometric tensor and study its relationship with the classical adiabatic gauge potential (AGP). We focus on integrable systems and show that the imaginary part of the…
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact…
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…
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is…
In this work, an efficient method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups of motions is suggested. The method is based on using a special…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…
In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme chosen, and monotone quantum metrics on the…
The paper is concerned with the properties of the distance function from a closed subset of a Riemannian manifold, with particular attention to the set of singularities.
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…
The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
Cylindrically symmetric vacuum spacetimes are of immense interest in theoretical physics due to its connection to cosmic strings hypothesized in quantum field theory. In this article, we explore the properties of such spacetime and provide…
Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the…
We present the analytic solution for the stationary quantum HamiltonJacobi equation. Knowing the strong relation between the Riccati and quantum Hamilton-Jacobi equations, we develop a simple method to obtain the exact solution. Then, in…