Related papers: Dynamical Symmetries and Beyond: Lessons and Advan…
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
In this contribution to the proceedings of a conference honoring the career of Francesco Iachello, two applications of symmetry principles to neutrino physics are described. These applications are the connection between fermion pairing in…
Partial dynamical symmetry is shown to be relevant for describing the anharmonicity of excited bands in $^{196}$Pt while retaining solvability and good SO(6) symmetry for the ground band.
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Explicit forms of IBM Hamiltonians with a generalized partial dynamical O(6) symmetry are presented and compared with empirical data in $^{162}$Dy.
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
We show that the dynamical symmetry exists in dissipative quantum many-body systems. Under constraints on both Hamiltonian and dissipation parts, the time evolution of particular observables can be symmetric between repulsive and attractive…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
Recently, consensus-type problems have been formulated in the quantum domain. Obtaining average quantum consensus consists in the dynamical symmetrization of a multipartite quantum system while preserving the expectation of a given global…
Polynomial dynamical systems (DSs) can model a wide range of physical processes. A special subset of these DSs that can model chemical reactions under mass-action kinetics is called chemical dynamical systems (CDSs). A fundamental problem,…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…