Related papers: Symmetry in linear physical systems

It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…

This paper contains results on geometric Routh reduction and it is a continuation of a previous paper where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…

Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.

It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…

Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…

The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by ways…

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…

We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…

This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…

Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algebraic and differential-geometric properties. We apply our…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological…

Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…

There are many notions of symmetry for state space models. They play a role in understanding when systems are time reversible, provide a system theoretic interpretation of thermodynamics, and have applications in certain stabilization and…

The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of…