Related papers: Contact reductions, mechanics and duality
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
This article sketches various ideas in contact geometry that have become useful in low-dimensional topology. Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact…
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…
Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For…
Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…
A general property of the relation between the dynamics of the reduced purity and correlations is investigated in quantum mechanical systems. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of…
In this paper we exploit the use of symmetries of a physical system so as to characterize algebraically the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
This paper is devoted to study the vanishing contact structure problem which is a generalization of the vanishing discount problem. Let $H^\lambda(x,p,u)$ be a family of Hamiltonians of contact type with parameter $\lambda>0$ and converges…
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations,…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
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…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
Motivated by a geometric decomposition of the vector field associated with the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…
Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian…