Search NASA⌕ Search

SEARCH · Search NASA

Results for “harmonic oscillator”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Wideband Impedance Passivation of MMCs for Suppressing Harmonic Oscillations

Harmonic instability and associated oscillation events have become one of the main concerns in MMC-based HVdc systems. These oscillations can appear in the range from a few hundred hertz to several kilohertz, and the root cause is identified as delay-induced negative damping of MMC impedance appearing at the system resonance frequency. Here, this paper introduces a wideband impedance reshaping method through MMC control to eliminate such negative damping for both grid-following (GFL) and grid-forming (GFM) MMCs, which makes the MMC impedance completely passive from the second harmonic frequency upward, thus preventing all harmonic oscillations. First, simplified impedance models of MMCs are derived for the harmonic stability analysis and the impedance reshaping control design. Next, a passivity-based impedance reshaping method is presented, as well as practical considerations for its implementation. In addition, to maintain the MMC's disturbance ride-through capability, an adaptive activation scheme is developed, which enables the wideband impedance reshaping control only in the presence of harmonic oscillation events. The effectiveness of the proposed method is validated by frequency domain analysis and by electromagnetic transient (EMT) simulations of two typical MMC-based power systems.

17 WIND ENERGY↗
DOE OSTI2015

Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D [Microwave Imaging Reflectometry (MIR) for the study of Edge Harmonic Oscillations (EHOs) on DIII-D]

Quiescent H-mode (QH) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation which can help to explain the physics behind EHO modes. MIR data sometimes indicates a counter-propagation between higher (n>1) and dominant (n=1) harmonics of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical misalignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-uniform rotation of the EHO structure, which induces multiple harmonics that are properly characterized in the synthetic diagnostic. Excluding these possible explanations for the data, the counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. Furthermore, the identification of a non-ideal structure motivates further exploration of nonlinear models of this instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The multi-faceted inverted harmonic oscillator: Chaos and complexity

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) from the Hamiltonian for two, coupled QHOs and provide a physical picture for the Kravchuk function eigenstates of the oscillator. The familiar $\mathfrak{su}(2)$ structure of the coupled QHO Hamiltonian divides its spectrum into sets corresponding to the DQHO at different resolutions. In addition to energy ladder operators, the formulation allows for the introduction of resolution ladder operators connecting all DQHOs with different resolutions, thus enabling the dynamic scaling of the resolution of finite degree-of-freedom quantum simulations. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator. The DQHO coherent state recovers that of the quantum harmonic oscillator at large resolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Pisot q-coherent states quantization of the harmonic oscillator

We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0<q<1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which q{sup -1} is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0<q<1 these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. Black-Right-Pointing-Pointer q-Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). Black-Right-Pointing-Pointer We examine the main physical characteristics of the corresponding quantum oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Angular momentum eigenstates of the isotropic 3-D harmonic oscillator: Phase-space distributions and coalescence probabilities

The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into angular momentum eigenstates in such a potential has interesting applications. Here we compute the probabilities for coalescence of two distinguishable, non-relativistic particles into such a bound state, where the initial particles are represented by generic wave packets of given average positions and momenta. We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators. These distribution functions have been discussed in the literature before but we utilize an alternative approach to obtain these functions. Along the way, we derive a general formula that expands angular momentum eigenstates in terms of products of 1-dimensional harmonic oscillator eigenstates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Coherent states for the nonlinear harmonic oscillator

Wave packets for the quantum nonlinear oscillator are considered in the generalized coherent state framework. To first order in the nonlinearity parameter the coherent state behaves very similar to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features (such as the squeezed state nature) of the coherent state have been discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Experimental characterization of the effect of E×B shear on edge-harmonic oscillation mode structure

The Edge Harmonic Oscillation (EHO) mode is one of the characteristic modes that provides an edge transport channel during high-confinement ELM-free phase (the so-called Quiescent High confinement phase). Recent theoretical work and extensive experimental observations have suggested that the large rotational E×B shear is the key to destabilize an EHO. As the eigenmode grows to large amplitude, it will exert a drag on the rotation, resulting in EHO's saturation. However, detailed mechanisms concerning this process remain vague. We have performed here continuous tracking on how the E×B shear affects the EHO mode structure to search for a possible explanation of the saturation mechanism. Two edge density fluctuation diagnostics are employed to observe the eigenmode structure evolution of EHO in the pedestal region in the radial and poloidal directions, respectively. Our results show that the EHO mode's radial wavenumber is strongly correlated with the E×B shear rate, while the poloidal wavenumber is unaffected by the E×B shear rate. During the EHO existence, with the E×B shearing rate ramping down, the radial wavenumber is also observed to be decreasing.

42 ENGINEERING↗
DOE OSTI2021

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

Highlights: • Equivalence of a harmonic oscillator to a free particle is considered. • The Eisenhart lift is applied to most general harmonic and linear potentials. • In geometric language, equivalence is the result of the conformal flatness of the Eisenhart metric. It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein’s principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Macroscopic detection of deformed QM by the harmonic oscillator

Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations (to the first order in deformation parameter as it has been pointed out in Bawaj et al. (2015)). For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics. - Highlights: • The classical motion of harmonic oscillator is derived from deformed QM. • The classical limit is obviously inconsistent with observations. • The reason for this inconsistency is explained. • An alternate estimate of the effect is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Generalized ladder operators for the perturbed harmonic oscillator

In 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 p{sup 4} 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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials

A simple discrete model of the two-dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier polynomials. This adds to the other discrete superintegrable models of the oscillator based on Krawtchouk and Meixner orthogonal polynomials in several variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Franck-Condon factors perturbed by damped harmonic oscillators: Solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene

Damped harmonic oscillators are utilized to calculate Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling unperturbed Hessian matrix that represents local modes of force constants for molecule in gaseous phase, and then by diagonalizing perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. Scaling parameters are empirically introduced for simulating absorption and fluorescence spectra of an isolated solute molecule in solution. The present method is especially useful for simulating vibronic spectra of polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in solution can be scaled equally, namely the same scaling factor being applied to all hydrogen atoms in polycyclic aromatic hydrocarbons. The present method is demonstrated in simulating solvent enhanced X {sup 1}A{sub g} ↔ A{sup 1}B{sub 1u} absorption and fluorescence spectra of perylene (medium-sized polycyclic aromatic hydrocarbon) in benzene solution. It is found that one of six active normal modes v{sub 10} is actually responsible to the solvent enhancement of spectra observed in experiment. Simulations from all functionals (TD) B3LYP, (TD) B3LYP35, (TD) B3LYP50, and (TD) B3LYP100 draw the same conclusion. Hence, the present method is able to adequately reproduce experimental absorption and fluorescence spectra in both gas and solution phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Generation of high power sub-terahertz radiation from a gyrotron with second harmonic oscillation

New power records of second harmonic gyrotron oscillation have been demonstrated in the sub-THz band. The first step gyrotron of demountable type had succeeded in oscillation with power more than 50 kW at 350 GHz and nearly 40 kW at 390 GHz [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009)]. Then, the second step gyrotron of sealed-off type was manufactured. A cavity mode was carefully selected to avoid mode competition with a neighboring fundamental harmonic mode. Matching of the selected mode with the electron gun was also circumspectly considered. The second step gyrotron has attained higher power radiation than the first gyrotron. The maximum single mode power was 62 kW at 388 GHz. Then, the electron gun was modified for use of a different cavity mode with a higher coupling coefficient than that for the 62 kW mode. The new mode proved single mode oscillation power of 83 kW at about 389 GHz. These results are new second-harmonic-oscillation power records for sub-THz gyrotrons. The present study constitutes foundations of development of high power second harmonic sub-THz gyrotron for application to collective Thomson scattering measurement on fusion plasmas, especially on high-density plasmas such as those produced in LHD [N. Ohyabu et al., Phys. Rev. Lett. 97, 055002 (2006)]. This paper reports the design consideration to realize high power single mode gyrotron oscillation at second harmonic and the examination of oscillation characteristics of the gyrotron.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

The harmonic oscillator in a space with a screw dislocation

Highlights: •Quantum-mechanical systems with screw dislocation are receiving considerable interest. •The harmonic oscillator with screw dislocation is not completely separable. •The screw dislocation removes the degeneracy. •The variational method is useful for obtaining eigenvalues and eigenfunctions. •The spectrum exhibits a rich structure of avoided crossings. -- Abstract: We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of values of the space-deformation parameter. The energies exhibit a rich structure of avoided crossings in terms of such model parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX

A new n =1 dominated edge harmonic oscillation (EHO) has been found in NSTX. The new EHO, rotating toroidally in the counter-current direction and the opposite direction of the neutral beam, was observed during certain inter-ELM and ELM-free periods of H-mode operation. This EHO is associated with a significant broadening of the integral heat flux width (${{\lambda}_{\operatorname{int}}}$ ) by up to 150%, and a decrease in the divertor peak heat flux by >60%. An EHO induced filament was also observed by the gas puff imaging diagnostic. The toroidal rotating filaments could change the edge magnetic topology resulting in toroidal rotating strike point splitting and heat flux broadening. Finally, experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking–Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantum harmonic oscillator with superoscillating initial datum

In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗