Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well

Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential

For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, H_{2}, N_{2}, Cl_{2}, I_{2}, O_{2}, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation.

Stochastic resonance noise modified decision solution for binary hypothesis-testing under minimax criterion

In this paper, on the premise that the prior probability is unknown, a noise enhanced binary hypothesis-testing is investigated under the Minimax criterion for a general nonlinear system. Firstly, for lowering the decision risk, an additive noise is intentionally injected to the input and a decision is made under Minimax criterion based on the noise modified output. Then an optimization problem for minimizing the maximum of Bayesian conditional risk under an equality constraint is formulated via analyzing the relationship between the additive noise and the optimal noise modified Minimax decision rule. Furthermore, lemma and theorem are proposed to prove that the optimal noise is a constant vector, which simplifies the optimization problem greatly. An algorithm is also developed to search the optimal constant and the key parameter of detector, and further to determine the decision rule and the Bayes risk. Finally, simulation results about the original (in the absence of additive noise) and the noise-modified optimal decision solutions under Minimax criterion for a sine transform system are provided to illustrate the theoretical results.

Improvement of signal propagation in the optoelectronic artificial spiking neuron by vibrational resonance

Experimental evidence of vibrational resonance (VR) in the optoelectronic artificial spiking neuron based on a single photon avalanche diode and a vertical cavity laser driven by two periodic signals with low and high frequencies is reported. It is shown that a very weak subthreshold low-frequency (LF) periodic signal can be greatly amplified by the additional high-frequency (HF) signal. The phenomenon shows up as a nonmonotonic resonant dependence of the LF response on the amplitude of the HF signal. Simultaneously, a strong resonant rise of the signal-to-noise ratio is also observed. In addition, for the characterization of VR an area under the first LF period in the probability density function of interspike intervals for the LF signal and the maximal amplitude in this area were used, both of which also demonstrate a resonant behavior depending on the amplitude of the HF signal.

Ultrasensitive vibrational resonance induced by small disturbances

We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

Effect of a modulated acoustic field on the dynamics of a vibrating charged bubble

We investigate the effect of amplitude-modulated acoustic irradiation on the dynamics of a charged bubble vibrating in a liquid. We show that the potential V(x) of the bubble, and the number and stability of its equilibria, depend on the magnitude of the charge it carries. Under high-frequency amplitude-modulation, a modulation threshold, Gth, was found for the onset of increased bubble amplitude oscillations. For some pressure field values, charge can facilitate the control of chaotic dynamics via reversed period-doubling bifurcation sequences. There is evidence for peak-shouldering and shock waves. The Mach number increases rapidly with the drive amplitude G. In the supersonic regime, for G>1.90Pa, the high-frequency modulation raises both Blake's and the transient cavitation thresholds. We found a decrease in the bubble's maximum charge threshold, and threshold modulation amplitude for the occurrence Vibrational resonance (VR). VR occurs due to the modulated oscillatory pressure field, and the influence on VR of the electrostatic charge, and other parameters of the system are investigated. In contrast to the cases of VR reported earlier, where the amplitude G of the high-frequency driving is typically much higher than the amplitude of the low-frequency driving (Ps), the VR resonance peaks occur here at relatively low G values (0 Collapse

Key Words

• Acoustic waves
• Amplitude modulation
• Bubble oscillator
• Electrostatic charges
• Vibrational resonance

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Affiliation(s)

O T Kolebaje Department of Physics, Adeyemi Federal University of Education, Ondo, Ondo State, Nigeria; Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria
U E Vincent Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria; Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
B E Benyeogor Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria
P V E McClintock Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom

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The Impurity and Decay-Magnetic Polaron Effects in III–V Compound Gaussian Quantum Wells

The effects of a decay magnetic field and hydrogen-like impurities on the ground-state binding energy (GSBE) and ground-state energy (GSE) of weak-coupling bound polarons in asymmetrical Gaussian potential (AGP) III–V compound quantum wells (QWs) were studied based on unitary transformation methods and linear combination operators. By numerical calculation, we found that the polarons were affected by the AGP, the decay magnetic field, Coulomb impurities, and the type of crystal, which led to a series of interesting phenomena, such as changes in the ground-state energy and the ground-state binding energy. The results obtained provide good theoretical guidance for optoelectronic devices and quantum information.

Subharmonics and superharmonics of the weak field in a driven two-level quantum system: Vibrational resonance enhancement

We consider a quantum two-level system in bichromatic classical time-periodic fields, the frequency of one of which far exceeds that of the other. Based on systematic separation of timescales and averaging over the fast motion a reduced quantum dynamics in the form of a nonlinear forced Mathieu equation is derived to identify the stable oscillatory resonance zones intercepted by unstable zones in the frequency-amplitude plot. We show how this forcing of the dressed two-level system may generate the subharmonics and superharmonics of the weak field in the stable region, which can be amplified by optimization of the strength of the high frequency field. We have carried out detailed numerical simulations of the driven quantum dynamics to corroborate the theoretical analysis.

Energy and frequency ripple in devices with inertial excitation of oscillations

We consider vibration devices that consist of softly vibration-isolated rigid bodies subjected to vibrations transmitted by means of inertial vibration exciters (unbalanced rotors) driven into rotation by electric motors. Typically, when designing such devices, it is assumed that the rotors rotate uniformly with a certain circular frequency and the body performs small harmonic oscillations with the same frequency. The present work, using a second-order approximation of their nonlinear coupled differential equations, shows that the rotor and the oscillating body keep exchanging energy. At the same time, the angular velocity of the rotor oscillates with the working frequency as well as with its multiple frequencies during each revolution. As a result, the acceleration of the oscillating body also acquires harmonics with multiple frequencies. This may cause both unwanted and beneficial resonance phenomena. We obtain formulae describing the magnitudes of these ripples. We show that the magnitude of oscillations of the angular frequency can also be estimated using energy considerations. Such estimates are provided for the three most common schemes of dynamic devices. Available experimental data confirm the main conclusions of the theory. We discuss both the harmful effects of these phenomena as well as their possible applications. The latter include design of bi-harmonic vibration exciters and exciters based on vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Vibrational resonance in a driven two-level quantum system, linear and nonlinear response

We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Vibrational and stochastic resonances in driven nonlinear systems

Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties-one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances-addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Vibrational resonances in driven oscillators with position-dependent mass

The vibrational resonance (VR) phenomenon has received a great deal of research attention over the two decades since its introduction. The wide range of theoretical and experimental results obtained has, however, been confined to VR in systems with constant mass. We now extend the VR formalism to encompass systems with position-dependent mass (PDM). We consider a generalized classical counterpart of the quantum mechanical nonlinear oscillator with PDM. By developing a theoretical framework for determining the response amplitude of PDM systems, we examine and analyse their VR phenomenona, obtain conditions for the occurrence of resonances, show that the role played by PDM can be both inductive and contributory, and suggest that PDM effects could usefully be explored to maximize the efficiency of devices being operated in VR modes. Our analysis suggests new directions for the investigation of VR in a general class of PDM systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.