429 research outputs found
Generalized ladder operators for the perturbed harmonic oscillator
No full textIn this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our formalism to a couple of examples, namely q and p4 perturbations, and obtain the explicit form of those operators. We also compute the expectation values of position and momentum for the above perturbations. This construction is essential for defining coherent and squeezed states for the perturbed oscillator. Furthermore, this is the first time that corrections to ladder operators for a harmonic oscillator with a generic perturbation and to an arbitrary order of perturbation theory have been constructed
Generalized Uncertainty Principle and angular momentum
No full textVarious models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems. (C) 2017 Elsevier Inc. All rights reserved
Numerical modeling of the dynamic behavior of shredder hammers and correlation with material damage
No full textDynamic behavior and prevention of the damage of material of the massive hammer of the scrap shredding machine
No full textShredders are used for comminuting the metallic scrap fed to the electric arc furnace and consist of a set of hammers connected to a main rotor, whose rotation converts the kinetic energy into a strong impact. Design of the hammer is still based on some daily practice, but often it looks insufficient to predict the effects of wear and the cracks monitored in service. To reduce costs and improve the product quality manufacturers of shredders urgently need for a design tool suitable to predict the hammer dynamic behavior, the damage of material and to locate the stress concentration. Unfortunately no comprehensive design approach was yet proposed in the literature. This paper investigates the behavior of an industrial prototype of shredder to develop such as design tool. A first rotor-dynamic analysis was combined with a numerical investigation, performed through the Multi Body Dynamics and Finite Element Method, respectively. Results were then compared to some experimental evidences. Damage effects were tentatively related to some design parameters, the material properties and the loading conditions of the hammer. Results were used to increase the performance of a new shredder hammer being designed by refining the cutting edge profile and by selecting a different material
Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics
No full textContinuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory
Relativistic generalized uncertainty principle
No full textThe Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies. In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein–Gordon, Schrödinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator
Response to Comments on the paper “Relativistic generalized uncertainty principle”
No full textWe address the comments on our paper (Todorinov et al., 2019) presented in Chargui (2020). We show that the points raised in Chargui (2020) do not contain any new results or valid criticisms
Global Frequency Synchronization over Networks of Uncertain Second-Order Kuramoto Oscillators via Distributed Adaptive Tracking
No full textIn this work, we consider the problem of global frequency synchronization of a network of second-order Kuramoto oscillators, cast as a distributed tracking problem, in the sense that the reference synchronization frequency for the network is generated by an autonomous leader. The main contribution of this paper is to develop a novel control strategy for the problem of leader-follower frequency synchronization, by exploiting the adaptive control framework to cope with parametric uncertainties in the oscillators. These adaptive controllers (one for each system) are interconnected with a distributed observer, used to reconstruct the reference signal for the systems not directly connected to the leader. Adopting the Lie Groups formalism for the unit circle to globally characterize the phase dynamics, we show that synchronization is not hindered if the physical couplings are in part preserved. Stability of the closed-loop interconnection is analyzed with Lyapunov-like arguments and verified in a numerical simulation
Potential tests of the generalized uncertainty principle in the advanced LIGO experiment
No full textThe generalized uncertainty principle and a minimum measurable length arise in various theories of gravity and predict Planck-scale modifications of the canonical position-momentum commutation relation. Postulating a similar modified commutator between the canonical variables of the electromagnetic field in quantum optics, we compute Planck-scale corrections to the radiation pressure noise and shot noise of Michelson–Morley interferometers, with particular attention to gravity wave detectors such as LIGO. We show that advanced LIGO is potentially sensitive enough to observe Planck-scale effects and thereby indirectly a minimal length. We also propose estimates for the bounds on quantum gravity parameters from current and future advanced LIGO experiments
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