Related papers: On symmetries and conserved quantities in Nambu me…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…
I describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics (MD) steps utilize Nambu generalized Hamiltonian dynamics. Characterized by multiple Hamiltonian functions, this formalism allows me to…
We discuss the relation between string quantization based on the Schild path integral and the Nambu-Goto path integral. The equivalence between the two approaches at the classical level is extended to the quantum level by a saddle--point…
In this paper we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of [1,3]. We illustrate the theory with classical examples describing the dynamics of…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
We show that a topological Nambu monopole exists as a regular solution for a large range of parameters in two Higgs doublet models, contrary to the standard model admitting only non-topological Nambu monopoles. We analyze a Higgs potential…
In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the ground state. In the traditional Landau theory, a symmetry…
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…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector…
We show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal metric dt^2 locally satisfy Hamilton's…
We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single…
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…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a…
We study numerically classical 1-dimensional Hamiltonian lattices involving inter-particle long range interactions that decay with distance like 1/r^alpha, for alpha>=0. We demonstrate that although such systems are generally characterized…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the…