Pursuing further the recent methods in the algebraic Hamiltonian approach to gauged WZW models, we apply them to the bosonic SL(2, IR) −k ′ ⊗SU (2) k /(IR⊗˜IR) model recently investigated by Nappi and Witten. We find the global space and compute the conformally exact metric and dilaton fields to all orders in the 1/k expansion. The semiclassical limit k ′ , k → ∞ of our exact results agree with...

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on g...

We investigate the algebraic structure of the Feynman propagator with a general timedependent quadratic Hamiltonian system. Using the Lie-algebraic technique we obtain a normal-ordered form of the time-evolution operator, and then the propagator is easily derived by a simple “Integration Within Ordered Product” (IWOP) technique.It is found that this propagator contains a classical generating fu...

We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision-reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in ...

In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

We characterize stable differential-algebraic equations (DAEs) using a generalized Lyapunov inequality. The solution of this inequality is then used to rewrite DAEs as dissipative Hamiltonian (dH) on the subspace where solutions evolve. Conversely, we give sufficient conditions guaranteeing stability dH DAEs. Further, for stabilizable descriptor systems construct algebraic Bernoulli which can b...

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in fourdimensional space–time represents the relativistic invariance by the equation for four-velocity ulu + c = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in fou...

Abstract Several models of quantum gravity predict the emergence a minimal length at Planck scale. This is commonly taken into consideration by modifying Heisenberg uncertainty principle generalized principle. In this work, we study implications polynomial on harmonic oscillator. We revisit both analytic and algebraic methods, deriving exact form algebra in terms new position momentum operators...

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual sl(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the sl(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is do...