Harmonic Oscillator Research Articles

Quantum versus classical quenches and the broadening of wave packets

The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed, but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes, the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented, which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks.

Разработка методики диагностирования и определения остаточного ресурса механических демпферов крутильных колебаний машинно-движительных комплексов судов

Import substitution issues in modern conditions remain an urgent topic today, especially in terms of periodic maintenance of mechanical torsional vibration dampers of foreign manufacture (they are also called spring dampers). Diagnostics of such devices is impossible due to the influence of sanctions against Russia, namely, in the absence of the possibility of the arrival of defect specialists from leading specialized organizations and manufacturing plants. A method for developing a model mechanical damper is presented, taking into account all conditions of similarity: geometric, kinematic and dynamic. Through the use of modern Autodesk Fusion 360 software, a digital model of a real Geislinger marine damper model D90/37 (Austria) has been developed. The results of diagnostics of the Kogalym and Langepas ship propulsion systems, which include mechanical dampers, are also reflected, and the dynamics of changes in torsional vibration parameters is analyzed. It is noted that non-selective diagnostics (torsiography procedure) is possible only in coordination with the supervisory authorities, usually with a small operating time of the damper. All further diagnostics are allowed only if there is an approved standard methodology, which currently does not exist, which confirms the relevance of the chosen research topic. An initial version of the methodology for diagnosing and determining the residual life of mechanical torsional vibration dampers of ship propulsion systems is presented.

Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises

We study the generalised Langevin equation (GLE) approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalised versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalised displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped GLEs for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviours.

Vibration assisted electron tunnelling in COVID-19 infection using quantum state diffusion.

The spread of the COVID-19 virus has become a global health crisis, and finding effective treatments and preventions is a top priority. The field of quantum biology primarily focuses on energy or charge transfer, with a particular emphasis on photosynthesis. However, there is evidence to suggest that cellular receptors such as olfactory or neural receptors may also use vibration-assisted electron tunnelling to enhance their functions. Quantum tunnelling has also been observed in enzyme activity, which is relevant to the invasion of host cells by the SARS-CoV-2 virus. Additionally, COVID-19 appears to disrupt receptors such as olfactory receptors. These findings suggest that quantum effects could provide new insights into the mechanisms of biological systems and disease, including potential treatments for COVID-19. We have applied the open quantum system approach using Quantum State Diffusion to solve the non-linear stochastic Schrödinger equation (SSE) for COVID-19 virus infection. Our model includes the mechanism when the spike protein of the virus binds with an ACE2 receptor is considered as dimer. These two entities form a system and then coupled with the cell membrane, which is modelled as a set of harmonic oscillators (bath). By simulating the SSE, we find that there is vibration-assisted electron tunnelling happening in certain biological parameters and coupling regimes. Furthermore, our model contributes to the ongoing research to understand the fundamental nature of virus dynamics. It proposes that vibration-assisted electron tunneling could be a molecular phenomenon that augments the lock-and-key process for olfaction. This insight may enhance our understanding of the underlying mechanisms governing virus-receptor interactions and could potentially lead to the development of novel therapeutic strategies.

Ultra‐Narrow Linewidth Polariton Lasing in Optically Trapped Bose‐Einstein Condensates at Room Temperature

AbstractPolariton lasing via Bose‐Einstein condensation (BEC) provides a peculiar method to achieve low threshold coherent light sources. Until now, the cryogenic operating temperature required for polariton lasers has hampered the development of polaritonics. Here, a novel approach is first reported to realize the ultra‐narrow linewidth polariton lasing under quasi‐3D quantum confinement at room‐temperature (RT). The potential trap landscape is constructed by ring‐shaped optical excitation, wherein the continuum polariton dispersion is modulated into discrete simple harmonic oscillator (SHO) states. The coherent condensation lasing of trapped polaritons occurs beyond the threshold power. Benefiting from the horizontal quantum confinement, the trapped polariton lasing exhibits an ultra‐narrow linewidth (0.7 meV) and excellent quality factor (Q = 3510). Moreover, the second‐order quantum coherence properties of trapped polariton condensation are determined to reveal the quantum phase transition of Bosonic system. The results offer a feasible route for realizing a low‐threshold ultra‐narrow linewidth polariton laser at RT, which significantly facilitates the fabrication of polariton laser and switches on opportunities for future applications.

Monoreactive multimass oscillator of non-fixed frequency

Introduction. The work relates to the field of mechanical engineering, namely to oscillating mechanical systems. The relevance of the study is determined by the fact that vibrations of inertial masses occur everywhere.Target. Development of a mathematical model of a monoreactive multimass oscillator of non-fixed frequency.Research methods. It is proved that the points that are the coordinates of the end of an arbitrary vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector, i.e. unchangeable. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which oscillating loads of masses m are located, lies in the Z plane. In technical applications, the loads should not interfere with each others movements, therefore, each load should have its own plane, and all planes should be parallel (like multi-piston mechanism).Results. The condition for the occurrence of free harmonic oscillations is the equality to zero of the total energy of the system, which in the case under consideration is exclusively kinetic, which determines the monoreactive nature of the oscillator. In the considered multidimensional flat monoreactive oscillator, free harmonic linear oscillations of weights can occur.Conclusion. Only kinetic energy is involved in energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural frequency of oscillation. The frequency depends on the initial speeds and positions of the weights. A regular polygon undergoes a double rotation - around point 0 and around point r. At the same time, the loads carry out linear harmonic oscillations with amplitude . The use of a crank-slider or crank-rod mechanism will allow for parallel movement of loads.

Evaluation of the single-frequency variometric approach based on low-cost GNSS observations and different satellite combinations for detecting short-term dynamic behaviors

This study presents the capability of the single-frequency (SF) variometric approach (VA) technique with low-cost GNSS observations to detect short-term dynamic behaviors. Harmonic oscillations with amplitudes between 5 and 20 mm and frequencies between 0.3 and 5.0 Hz were generated employing a single-axis shake table to investigate the performance of the SF-VA technique in the structural health monitoring (SHM) system. Besides, a Mw 6.9 Kobe, 1995 earthquake simulation was generated using the shake table to analyze the SF-VA performance for the earthquake early warning (EEW) system. A low-cost u-blox ZED-F9P GNSS receiver and ANN-MB-00 patch antenna were used to collect GNSS observations at a 20 Hz sampling rate during the experiments. The observations were processed using the MATLAB-based open-source PPPH-VA software in real-time (RT) mode, considering eight different satellite combinations. The capability of the SF-VA technique to detect horizontal dynamic behaviors in RT mode was investigated in the frequency and time domains, accepting the displacements from the linear variable differential transformer sensor as a reference. The results in the frequency domain demonstrate that the SF-VA technique with low-cost GNSS observations can successfully detect the peak frequency value of short-term harmonic oscillations up to 5 Hz. Moreover, time domain findings emphasize that the short-time dynamic oscillations can be determined with the SF-VA technique with an accuracy ranging from 0.8 to 6.4 mm. Earthquake simulation experiment results demonstrate that the strong ground motions caused by mega earthquakes can be determined at mm-level by the SF-VA method. The results of both experiments show that multi-GNSS observations contribute to the SF-VA technique considerably. Overall, the findings reveal that the SHM and EEW systems can be operated with low-cost GNSS receivers, and the natural frequency of the man-made structures and accurate displacement values of seismic waveforms can be determined in RT with the SF-VA technique.

Casimir–Onsager matrix for weakly driven processes

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are the Casimir–Onsager ones. The result is verified in paradigmatic models of the overdamped and underdamped white noise Brownian motions. Finally, an extension to thermally isolated systems is made by using the time-averaged Casimir–Onsager matrix, in which the example of the harmonic oscillator is presented.

A carbon nanotube metamaterial sensor showing slow light properties based on double plasmon-induced transparency.

In this study, we proposed a bifunctional sensor of high sensitivity and slow light based on carbon nanotubes (CNTs). An array of left semicircular ring (LSR), right semicircular ring (RSR), and circular ring (CR) resonators are utilized to form the proposed metamaterial. The proposed structure can achieve double plasmon-induced transparency (PIT) effects under the excitation of a TM-polarization wave. The double PIT originated from the destructive interference between two bright modes and a dark mode. A coupled harmonic oscillator model is used to describe the destructive interference between the two bright modes and a dark mode, and the simulation results agree well with the calculated results. Moreover, we investigate the influence of the coupling distance, period, and flare angle on the PIT spectra. The relationship between the resonant frequencies, full width at half maximum (FWHM), amplitudes, quality factors (Q), and the coupling distance is also studied. Finally, a high sensitivity of 1.02 THz RIU-1 is obtained, and the transmission performance can be maintained at a good level when the incident angle is less than 40°. Thus, the sensor can cope with situations where electromagnetic waves are not perpendicular to the structure's surface. The maximum figure of merit (FOM) can reach about 8.26 RIU-1; to verify the slow light property of the device, the slow light performance of the proposed structure is investigated, and a maximum time delay (TD) of 22.26 ps is obtained. The proposed CNT-based metamaterial can be used in electromagnetically induced transparency applications, such as sensors, optical memory devices, and flexible terahertz functional devices.

Damping Optimization Method of Combine Harvester Frame Undergoing Multi-Source Excitation

The complex mechanical system of a rice combine harvester not only has various excitation sources, but also, the vibration transmission path between each working device and the vibration contribution characteristics to the frame are not clear, so it is difficult to perform a reduction vibration design for the sharp vibration of the rice combine harvester frame. Therefore, based on the comparison and improvement of multiple classical transfer path analysis methods, this paper analyzed the vibration transfer characteristics and transfer characteristics of each harvester by the discrete time matrix method and operating path method. In the Experimental section, through the vibration characteristic experiment firstly, this paper obtained the power spectrum variation and the most needed optimized path in the transmission path of each device under each operating condition. Secondly, through frame simulation analysis under the exciting force, we obtained the vibration damping areas that needs to be optimized. Finally, the damping optimization experiment connected with the vibration characteristic experiment, and the excitation force simulation analysis was performed. The results of the damping optimization experiment displayed that the maximum change value of the vibration acceleration of the cutting table decreased from 7.862 m·s−2 to 3.522 m·s−2, decreasing by 55.2%, and the peak amplitude of the multipoint test in the cab was 5.4, 5.3, 1.7 and 2.0 μm, respectively, which was significantly reduced, so the optimization effect was significant. This study provides theoretical support for the vibration reduction optimization of a rice combine harvester frame.

Exact prime density reproduced through resonant tunneling across a doublebarrier system

Abstract A solid-state experiment based on quantum tunneling is proposed
to reproduce the natural numbers and prime numbers as resonant
tunneling energies in a double barrier system (DBS). For getting
the prime numbers as eigenvalues the well potential is considered
as the superposition of a smooth potential which is estimated using
semi-classical approach and a weak local fluctuating potential. We
use the transfer matrix approach and finite element method by
taking only the smooth part of the potential to obtain resonant
energies which reproduces the local average prime density and the
local average prime gap exactly. The methodology when applied
to a quadratic potential of the well, produces whole numbers as
eigenvalues except for a constant zero-point energy-the energy
levels of a simple harmonic oscillator.

Observation of a phase space horizon with surface gravity water waves

In 1974, Stephen Hawking predicted that quantum effects in the proximity of a black hole lead to the emission of particles and black hole evaporation. At the very heart of this process lies a logarithmic phase singularity which leads to the Bose-Einstein statistics of Hawking radiation. An identical singularity appears in the elementary quantum system of the inverted harmonic oscillator. In this Letter we report the observation of the onset of this logarithmic phase singularity emerging at a horizon in phase space and giving rise to a Fermi-Dirac distribution. For this purpose, we utilize surface gravity water waves and freely propagate an appropriately tailored energy wave function of the inverted harmonic oscillator to reveal the phase space horizon and the intrinsic singularities. Due to the presence of an amplitude singularity in this system, the analogous quantities display a Fermi-Dirac rather than a Bose-Einstein distribution.

Heat Bath in a Quantum Circuit.

We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.

Fractional particle and sigma model

We introduce a classical fractional particle model in ℝn, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum and kinetic energy, is provided. We further derive the equations of motion and discuss the symmetries of the system. The Green’s function method is employed to solve the equations of motion in a general case. We illustrate the theory with three important examples: the free fractional particle, the fractional harmonic oscillator, and the charged fractional particle that interacts locally with the electromagnetic field. We use the results of the extension problem by Caffarelli and Silvestre, to construct the associated classical local sigma model for the fractional particle. The sigma model is then quantized using the canonical quantization method, and we compute the vacuum energy at the boundary.

Identifying factors influencing the properties of vibroacoustic metamaterials using three different acoustic methods

Vibroacoustic metamaterials offer an approach for the targeted damping of unwanted structural vibrations and noise by integrating periodically arranged resonators into a matrix of bulk material. Fabrication using the Laser Bed Powder Fusion (L‐PBF) process allows the targeted integration of bulk resonators and powder depots, leading to an extension of the designable damping properties. In this work, we focus on the adaptation of acoustic methods to characterize the properties of metamaterial plates. The investigated vibroacoustic metamaterial plates are made of nylon PA 1.2, combining material and structural damping. We investigated the vibration behavior of the plates over a range of frequencies using acoustic impedance measurements in a custom‐built measurement tube and compared it with structural dynamics experiments using an electrodynamic shaker. The measurements allow for the identification of stop bands (frequency range with high damping) and influencing factors such as metamaterial design, mass, powder amount and surface on the frequency dependent damping properties. The adapted technique investigated in this work provides an experimental platform to characterize the complex interplay of acoustic metamaterial design and holds promise for scaling up metamaterial technology for industrial applications due to its simplicity, small space requirement, and low cost.This article is protected by copyright. All rights reserved.

Shell-model representations of the microscopic version of the Bohr-Mottelson collective model

Abstract The structure of the irreducible collective spaces of the group
$Sp(12,R)$, which many-particle nuclear states are classified
according to the chain $Sp(12,R) \supset U(6) \supset SO(6) \supset
SU_{pn}(3) \otimes SO(2) \supset SO(3)$ of the proton-neutron
symplectic model (PNSM), is considered in detail. This chain of the
PNSM was recently shown to correspond to a microscopic shell-model version of
the Bohr-Mottelson collective model. The construction of the
relevant shell-model representations of the $Sp(12,R)$ group along
this chain is considered for three nuclei with varying collective
properties and from different mass regions. It is shown that the
$SU_{pn}(3)$ basis states of the $Sp(12,R)$ representations
belonging to $SO(6)$ irreps with seniority
$\upsilon \geq \upsilon_{0}$, with $v_{0}$ denoting the maximal
seniority $SO(6)$ irrep contained in the $Sp(12,R)$ bandhead, are
always Pauli allowed, but organized in a different way into
different $SO(6)$ shells. This is in contrast to the case of filling
the levels of the standard three-dimensional harmonic oscillator and
using the plethysm operation. Although the $SU_{pn}(3)$ multiplets
with $\upsilon < \upsilon_{0}$ are not all Pauli forbidden, it is
safe to discard them. The results obtained in the present work are
important for the practical application of the microscopic version
of the Bohr-Mottelson collective model.

Single-piston quantum engine

A single-piston quantum engine based on a harmonic oscillator acting as the working fluid is proposed. Using the fact that the interaction between the piston and the oscillator depends on the extent of the oscillator wave function, one can control this interaction by modifying the oscillator temperature. By retracting the piston when the interaction is weak (hot oscillator) and returning it to the original position when the coupling is strong (cold oscillator), useful work can be performed assuming the interaction is attractive. The cycle of the engine is simulated numerically using two different powering protocols: bath and measurement. Using the collision model for the baths, the engine is shown to reach a steady state with positive work output. Published by the American Physical Society 2024

Non‐Markovian Cost Function for Quantum Error Mitigation

Non‐Markovian Cost Function for Quantum Error Mitigation

Frequency dependent polarizability of confined harmonic oscillators

Abstract The D-dimensional Schr ̈odinger equation for a confined harmonic potential perturbed by a time-dependent dipole field is analysed. The model uses exact confined solutions for the harmonic potential whereas the time-dependent field is treated using first-order time-dependent perturbation theory. Exact analytic solutions are obtained in terms of generalised Laguerre functions. This system has applications to nanostructures where there are strong confinement potentials in some dimensions and example calculations are carried out to illustrate the effect of the dimension.

Modulating Nonlinear Acoustic Response of Phospholipid-Coated Microbubbles with pH for Ultrasound Imaging.

Activatable microbubble contrast agents for contrast-enhanced ultrasound have a potential role for measuring physiologic and pathologic states in deep tissues, including tumor acidosis. In this study, we describe a novel observation of increased harmonic oscillation of phosphatidylcholine microbubbles (PC-MBs) in response to lower ambient pH using a clinical ultrasound scanner. MB echogenicity and nonlinear echoes were monitored at neutral and acidic pH using B-mode and Cadence contrast pulse sequencing (CPS), a harmonic imaging technique at 7.0 and 1.5 MHz. A 3-fold increase in harmonic signal intensity was observed when the pH of PC-MB suspensions was decreased from 7.4 to 5.5 to mimic normal and pathophysiological levels that can be encountered in vivo. This pH-mediated activation is tunable based on the chemical structure and length of phospholipids composing the MB shell. It is also reliant on the presence of phosphate groups, as the use of lipids without phosphate instead of phospholipids completely abrogated this phenomenon. The increased harmonic signal likely is the result of increased MB oscillation caused by a decrease of the interfacial tension induced at a lower pH, altering the lipid conformation. While relative signal changes are interpreted clinically as mostly related to blood flow, pH effects could be significant contributors, particularly when imaging tumors. While our observation can be used clinically, it requires further research to isolate the effect of pH from other variables. These findings could pave the way toward for the development of new smart ultrasound contrast agents that expand the clinical utility of contrast-enhanced ultrasound.