Related papers: Dynamical Symmetries and Beyond: Lessons and Advan…
Detailed description of nuclei necessitates model Hamiltonians which break most dynamical symmetries. Nevertheless, generalized notions of partial and quasi dynamical symmetries may still be applicable to selected subsets of states, amidst…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
The concept of partial symmetry is introduced for an interacting fermion system. The associated Hamiltonians are shown to be closely related to a realistic nuclear quadrupole-quadrupole interaction. An application to $^{12}$C is presented.
The notion of symmetry is shown to be at the heart of all error correction/avoidance strategies for preserving quantum coherence of an open quantum system S e.g., a quantum computer. The existence of a non-trivial group of symmetries of the…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
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…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
Spatial symmetries of quantum systems leads to important effects in spectroscopy, such as selection rules and dark states. Motivated by the increasing strength of light-matter interaction achieved in recent experiments, we investigate a set…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial $SU(3)$ symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…