Related papers: Lifted tensors and Hamilton-Jacobi separability
We describe how the dynamical system of rolling two $n$-dimensional connected, oriented Riemannian manifolds $M$ and $\hat M$ without twisting or slipping, can be lifted to a nonholonomic system of elements in the product of the oriented…
We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a non-invertible symmetry closely related to T-duality. We also study…
Let $X$ be a smooth projective complex curve, $P\subset X$ a reduced effective divisor, and $X^{0}=X\setminus P$. We study logarithmic $V$-twisted Higgs bundles arising from a logarithmic Hecke compactification of a rank-two bundle on…
We introduce a general framework for detecting genuine multipartite entanglement and non full-separability in multipartite quantum systems of arbitrary dimensions based on correlation tensors. Regarding genuine multipartite entanglement our…
We study bipartite entanglement in systems of N identical bosons distributed in M different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given…
Geometric separability theory of Gel'fand-Zakharevich bi-Hamiltonian systems on Riemannian manifolds is reviewed and developed. Particular attention is paid to the separability of systems generated by the so-called special conformal Killing…
In a number of physically relevant contexts, a quantum system interacting with a decohering environment is simultaneously subjected to time-dependent controls and its dynamics is thus described by a time-dependent Lindblad master equation.…
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal…
In this paper we propose the time & fitness-dependent Hamiltonian form of human biomechanics, in which total mechanical + biochemical energy is not conserved. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian…
Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We…
Holomorphic vector bundles on $\mathbb C\times M$, $M$ a complex manifold, with meromorphic connections with poles of Poincar\'e rank 1 along $\{0\}\times M$ arise naturally in algebraic geometry. They are called $(TE)$-structures here.…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
We introduce the concept of directed orbifold, namely triples (X, V, D) formed by a directed algebraic or analytic variety (X, V), and a ramification divisor D, where V is a coherent subsheaf of the tangent bundle TX. In this context, we…
Interacting systems consisting of two rotators and a pendulum are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of unstable quasi periodic motions in phase space is…
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing…
We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-de Sitter spacetime in all dimensions. Complete separation of both equations is carried out in 2n+1 spacetime dimensions with all n rotation…
In this paper, the Conley conjecture, which were recently proved by Franks and Handel \cite{FrHa} (for surfaces of positive genus), Hingston \cite{Hi} (for tori) and Ginzburg \cite{Gi} (for closed symplectically aspherical manifolds), is…
The present paper reviews recent achievements on the ab initio determination of effective model Hamiltonians aimed at the description of strongly correlated materials. These models (Heisenberg, $t-J$, extended Hubbard, Kondo, etc) are…
The two-jet of the curvature tensor at some point of a pseudo-Riemannian manifold is called Einstein if the Ricci tensor is a multiple of the metric tensor at the given point and additionally its first two covariant derivatives vanish…
We propose a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity $1+m, m\geq 0$. Physically, the model represents a toroidal pendulum, coupled with a…