Chaos and nonlinearities in high harmonic generation

Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term

On the dynamics of confined particles: a laser test

Reduced dimensionality systems (RDS) are materials extending along one or two dimensions much more than the other(s). The degrees of freedom of the small dimension are not explored by the electrons since their energy is very large. The time dependent wave function of a particle in a short nanotube, taken as a paradigm of the RDS family, is calculated by solving the Klein\u2013Gordon equation; the confining condition produces a small change in the mass of the particles and of the energy levels. These changes are of relativistic origin and therefore small, but can be measured by use of a weak resonant laser field which produces cumulative effects in the time development of the wave function. The shift of the energy of the levels are within today\u2019s spectroscopy capacity

The Emergence of Chaos in Quantum Mechanics

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere

Measurement of the Convective Heat-Transfer Coefficient

We propose an experiment for investigating how objects cool down toward the thermal equilibrium with their surroundings. We describe the time dependence of the temperature difference of the cooling objects and the environment with an exponential decay function. By measuring the thermal constant τ, we determine the convective heat-transfer coefficient, which is a characteristic constant of the convection system

The double cone: a mechanical paradox or a geometrical constraint?

In the framework of the Italian National Plan \u2018Lauree Scientifiche\u2019 (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum and a couple of wooden rails

Electrons on a spherical surface: Physical properties and hollow spherical clusters

We discuss thephysical properties of a non interacting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential,and its electric static polarizability. All these properties are discussed analytically as functions of the number N of electrons. The trends obtained with increasing N are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasi spherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the de\ufb01nition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent 120.5. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems

Modifications of high harmonic spectra by ion resonant transitions

High-order harmonic generation is considered in a system consisting of an ion with an internal degree of freedom plus an outer electron. The theoretical treatment is both quantum-mechanical and classical. The emphasis is on the core resonance effects, which can significantly modify the harmonic spectra, with appearance of anomalous peaks. Under some assumptions, the spectral amplitude of the resonant harmonic of the system dipole moment can be obtained by evaluation of such amplitude within a single-electron approximation and multiplication of the result by a correcting factor. The latter depends on the polarizability of the ion and of a free electron at the harmonic frequency. Copyright \ua9 1996 by MAHK Hayka/Interperiodica Publishing

Variation of physical constants and electron–positron oscillations: Zitterbewegung in a plane wave

The space and time dependence of physical constants is currently a debated issue for experimental findings, and theoretical reasons seem to indicate that this is not a mere speculative possibility. The paper provides a relativistic description of a free fermion evolving under the assumption of temporal variation of the physical constants. The assumed generalisation of the Dirac equation is particularly simple and permits a grouping of the constants in one single parameter and a consequent agile treatment of the problem. The form of the equations suggests a rescaling of the temporal coordinate x= ct which allows a plane wave solution. Two are the main results of the treatment. First, the effects of the variation of the constants are better seen in the weak relativistic regime which indicates that experiments can be carried out without having to resort to super accelerators and, second, that a slow particle–antiparticle oscillation occurs in the evolution of a plane wave. This prediction of charge non-conserving oscillation is the analytical outcome of the generalised Dirac equation and appears to be a necessary consequence of the variation of the physical constants

Time variability of low-temperature fumaroles at Stromboli island (Italy) and its application to volcano monitoring

The constant and mild activity of Stromboli volcano (Italy) is occasionally interrupted by effusive events and/or more energetic explosions, referred to as major explosions and paroxysms, which are potentially dangerous for the human community. Although several premonitory signals for effusive phases have been identified, precursors of major explosions and paroxysms still remain poorly understood. With the aim of contributing to the identification of possible precursors of energetic events, this work discusses soil temperature data acquired in low-temperature fumaroles at Stromboli in the period 2006–2010. Data analysis revealed that short-term anomalies recorded in the thermal signal are potentially useful in predicting state changes of the volcano. In particular, sudden changes in fumarole temperatures and their hourly gradients were observed from several days to a few hours prior to fracturing and paroxysmal events, heralded by peculiar waveforms of the recorded signals. The qualitative interpretation is supported by a quantitative, theoretical treatment that uses circuit theory to explain the time dependence of the short-period temperature variations, showing a good agreement between theoretical and observational data

Defects in quantum ring to control high-harmonic spectrum

The high-harmonic generation from a structured quantum ring (SQR) driven by an intense laser field is presented within the single active electron approximation. The spectrum is studied by varying the symmetry of the physical system. The standard SQR (six identical and equidistant dots in a ring) presents a 60\ub0 rotational symmetry, that in this work is broken, moving or changing only one potential hole. We find that careful designed breaking of the geometrical symmetry of the SQR opens the possibility of controlling the characteristics of the harmonic lines such as intensity and polarization. HHG analysis of the emission spectrum performed through a Morlet wavelet, shows that the high-frequency emission occurs during short time intervals