Search results for "harmonic"
showing 10 items of 984 documents
Unitary Representations of Quantum Superpositions of two Coherent States and beyond
2013
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results are briefly outlined.
A Swanson-like Hamiltonian and the inverted harmonic oscillator
2022
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian $H$ of the inverted quantum harmonic oscillator can be deduced from that of $H_\theta$. We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian $H$ of the inverted oscillator.
A tomographic approach to non-Markovian master equations
2010
We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function of some unknown time-independent parameters, we show that these parameters can be reconstructed by means of a finite number of tomograms. Two different approaches towards reconstruction, integral and differential, are presented and applied to a benchmark model made of a harmonic oscillator coupled to a bosonic bath. For this model the number of tomograms needed to retrieve the unknown parameters is explicitly computed.
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…
Effects of 3rd-harmonic voltage content on dielectric losses of solid insulating materials
1981
Dielectric losses in solid insulating materials subjected to voltages containing 3rd harmonics are studied. By simple theoretical analysis, some curves are obtained showing the behaviour of the ratio between the dielectric losses in the distorted steady state and in a reference sinusoidal steady state, against 3rd-harmonic content. The reference sinusoidal voltage amplitudes were selected in two different ways; namely, such as to have either peak value or effective value equal to those of distorted waveform.Separate effects of harmonic content and of effective value of the applied voltage are shown through the correspondence of every 3rd-harmonic phase angle. Percentage differences between …
Thermoelastic Stress Analysis by Means of a Standard Thermocamera and a 2D-Fft Based Lock-In Technique
2007
The thermoelastic effect in a generic orthotropic body under adiabatic and linear elastic stress conditions induces small and reversible temperature changes that can be correlated with the stress field by means of linear relationships. Infrared techniques are mainly used to measure temperature changes on the component surface [1], while adiabatic conditions are generally achieved by applying cyclic loads above a threshold frequency. The resolution resulting from implementing a Thermoelastic Stress Analysis (TSA) technique is a combination of the infrared acquiring system resolution and of the signal post-processing procedure. State of the art infrared detectors have NETD (Noise Equivalent T…
Forced oscillations in a self-oscillating surface reaction model
2004
A microscopic lattice gas model for the catalytic CO + O2 reaction on Pt(110) subject to external periodic forcing is studied by means of cellular automaton simulations. Harmonic resonance, subharmonic and superharmonic entrainment, quasiperiodic as well as chaotic behavior are among the observed phenomena in this model when the gas phase concentration of CO as an external control parameter is periodically varied and interacts with the self-oscillating reaction system.
Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators
1985
Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.
Efficient energy conversion for cubic third-harmonic generation that is phase matched in KTiOPO(4).
2000
We demonstrate, for the first time to our knowledge, that efficient third-harmonic generation can be achieved with a cubic contribution much larger than the quadratic processes. An energy-conversion efficiency of 2.4% is achieved for cubic third-harmonic generation that is phase matched along the x axis of a KTiOPO(4) crystal by use of a picosecond fundamental laser emitting at 1618 nm. The associated cascading processes are only 10% of the pure cubic interaction, which is very suitable for study of the specific quantum optical correlations. Calculations of the third-harmonic generation conversion efficiency with respect to group-velocity dispersion and to the longitudinal Gaussian beam pro…
A set-up for simultaneous measurement of second harmonic generation and streaming potential and some test applications.
2018
We present a measurement cell that allows simultaneous measurement of second harmonic generation (SHG) and streaming potential (SP) at mineral-water interfaces with flat specimen that are suitable for non-linear optical (NLO) studies. The set-up directly yields SHG data for the interface of interest and can also be used to obtain information concerning the influence of flow on NLO signals from that interface. The streaming potential is at present measured against a reference substrate (PTFE). The properties of this inert reference can be independently determined for the same conditions. With the new cell, for the first time the SHG signal and the SP for flat surfaces have been simultaneousl…