Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach and the WKB approximation. Unlike other similar studies, in the present work we consider arbitrary bounded potentials and obtain exact solutions for the thresholds, and for the transverse modes in the form of power series of the spectral parameter. Our approach leads to an effective numerical method for the analysis of such quantum waveguides and for the tunnel effect observed in sections of the waveguide that shrink or widen too much. Several examples of interest show the applicability of the method.

A novel non-adiabatic approach to transition crossing in a circular hadron accelerator

Crossing the transition energy is always a delicate process, representing a potential source of strong perturbations of the dynamics of charged particle beams in a hadron circular accelerator. Since the first generation of multi-GeV rings, intense studies have been devoted to understanding the possible harmful mechanisms involved in transition crossing and to devise mitigation measures. Nowadays, several circular particle accelerators are successfully operating across the transition energy and this process is well mastered. In a completely different context, stable resonances of the traverse phase space have been proposed as new means of manipulating charged particle beams. While the original aim of such a proposal was multi-turn extraction from the CERN Proton Synchrotron to the Super Proton Synchrotron, many more applications have been proposed and studied in detail. In this paper, the two topics, i.e. transition crossing and stable resonances, have been brought together with the goal of providing a novel and non-adiabatic approach to perform a clean transition crossing. The idea presented here is that by judiciously using sextupoles and octupoles it is possible to generate stable islands of the horizontal phase space. These islands represent a second closed orbit whose properties can be selected independently of those of the standard, i.e. central, closed orbit. This provides a means of performing a non-adiabatic change of the transition energy experienced by the charged particles by displacing the beam between the two closed orbits.

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

On the Role of Local Many-Body Interactions on the Thermoelectric Properties of Fullerene Junctions

The role of local electron–vibration and electron–electron interactions on the thermoelectric properties of molecular junctions is theoretically analyzed focusing on devices based on fullerene molecules. A self-consistent adiabatic approach is used in order to obtain a non-perturbative treatment of the electron coupling to low frequency vibrational modes, such as those of the molecule center of mass between metallic leads. The approach also incorporates the effects of strong electron–electron interactions between molecular degrees of freedom within the Coulomb blockade regime. The analysis is based on a one-level model which takes into account the relevant transport level of fullerene and its alignment to the chemical potential of the leads. We demonstrate that only the combined effect of local electron–vibration and electron–electron interactions is able to predict the correct behavior of both the charge conductance and the Seebeck coefficient in very good agreement with available experimental data.

Numerical assessment of miniaturized cold spray nozzle for additive manufacturing

Purpose Application of cold spray technology may exhibit significant benefits for the additive manufacturing process, particularly for producing intricate objects. To ascertain the feasibility of such an application, this paper aims to present a numerical investigation of the effect of scaling down a convergent-divergent (de Laval) nozzle, which is typically used in the cold spray industry, on the compressible flow parameters and thermal characteristics. Design/methodology/approach The Navier–Stokes equations and energy equation governing compressible flow are numerically solved using a finite volume method with a coupled solver. The conjugate heat transfer technique is used to couple fluid and solid heat transfer domains and predict the local heat transfer coefficient between the solid and fluid. The use of various RANS turbulence models has also been investigated to quantify the effect of the turbulence model on the simulation. Findings The numerical results reveal that the flow and thermal characteristics are altered as the convergent-divergent nozzle is scaled down. The static pressure and temperature profiles at any section in the nozzle are shifted toward higher values, while the Mach number profile at any section in the nozzle is shifted toward a lower Mach number. The turbulent kinetic energy at the nozzle exit increases with the scaling down of the nozzle geometry. This study also provides convincing evidence that the adiabatic approach is still suitable even though the temperature of the nozzle wall is extremely high, as required for industrial application. Results indicate that it is feasible to use the available capabilities of the cold spray technology for additive manufacturing after scaling down the nozzle. Originality/value The idea of adopting cold spray technology for additive manufacturing is new and innovative. To develop this idea into a viable commercial product, a thorough understanding of the flow physics within a cold spray nozzle is required. The simulation results discussed in this paper demonstrate the effect that scaling down of a convergent-divergent nozzle has on the flow characteristics in the nozzle.

Electron Cyclotron collisionless interaction during EC-assisted tokamak start-up

In the initial phase of a plasma discharge with EC-assisted breakdown, the wave-particle interaction is nonlinear and wave trapping provides the mechanism for transition from a very low energy state to a much larger energy state. A Hamiltonian adiabatic approach provides the condition for the energy variation to occur in a rigorous way, together with quantitative estimate as a function of the wave frequency, harmonic number, polarisation and EC power and beam width, for the first, and second cyclotron harmonic. The interaction is highly localized in space close to the EC resonance. The spatial profile of the energy gain are reported together with the estimates of the width of the radial region where the interaction takes place in the case of a tokamak configuration. The analysis provides a physics based description of the process as well as indications for an optimized experimental setup.