Adiabatic Approximation Condition Research Articles

Entropic stochastic resonance for a confined system driven by two constant forces and multiplicative noise

The entropic stochastic resonance (ESR) phenomenon for a confined system driven by two constant forces, by two periodic forces and multiplicative noise is studied. The Fokker-Planck equation corresponding to the confined structure is obtianed applying Fick-Jacob approximation. The transition rates from the stable states are derived under the adiabatic approximation condition. The signal-to-noise ratios (SNRs) for the fundamental and higher harmonics are derived by virtue of two-state theory. Analysis result indicates that the SNR for fundamental harmonic decreases as increasing the constant force along x-direction, while the SNR for fundamental harmonic can obtain one maxmimum value with the increment of the constant force along y-direction. Each of the SNRs for higher harmonics can get one resonance peak as increasing the two constant forces. Two peaks appear when the SNRs vary with the multiplicative noise intensity, while only one peak value takes place when the SNRs change with the additive noise strength. The influence of the boundary parameters of the confined system on the SNRs is discussed.

Accelerated Quantum Adiabatic Transfer in Superconducting Qubits

Quantum adiabatic transfer is widely used in quantum computation and quantum simulation. However, the transfer speed is limited by the quantum adiabatic approximation condition, which hinders its application in quantum systems with a short decoherence time. Here we demonstrate quantum adiabatic state transfers that jump along geodesics in one-qubit and two-qubit superconducting transmons. This approach possesses the advantages of speed, robustness, and high-fidelity compared with the usual adiabatic process. Our protocol provides feasible strategies for improving state manipulation and gate operation in superconducting quantum circuits.

Phenomenon of double entropic stochastic resonance with recycled noise

The double entropic stochastic resonance (DSR) phenomenon for a Brown particle moving in a confined geometry driven by a time-dependent force in the declining direction subject to additive master noise and recycled noise is investigated in this paper. Under the adiabatic approximation condition, based on two-state theory and linear response theory, the expression for the system linear response (LR) is derived. Stochastic resonance (SR) and periodic SR behavior is observed when the LR changes with the feedback coefficient and with the time-delay of the recycled noise. DSR phenomenon appears when the LR varies with the constant component and with the fluctuation noise intensity of the force in the declining direction. Tradition SR occurs on the curve of the LR when the LR varies with the intensity of the master noise. The non-monotonous effect of the parameters of the confined structure on the LR is discussed.

Piecewise unsaturated multi-stable stochastic resonance under trichotomous noise and its application in bearing fault diagnosis

The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application.

Polarized Antenna Aided Spectrum Sensing Based on Stochastic Resonance

Wireless communications is one of the most rapidly developing segments of the telecommunications industry. A large amount of intelligent terminal occupying the spectrum results in the reduction of radio spectrum resources. Cognitive radio is considered to be the most effective approach to solve this problem, which required rapid and exact spectrum sensing. This paper proposes a novel polarized antenna method based on likelihood ratio test and stochastic resonance. In the condition of adiabatic approximation, the stochastic resonance can increase signal to noise ratio, and adequately transfer the energy of noise to original signal. The proposed method applies the stochastic resonance to each polarized component. The experiments show that the proposed spectrum sensing method is suitable for generalized likelihood ratio test in additional white Gussion noise and lower signal to noise ratio, rather than polarized channel matrix and idealistic likelihood ratio test.

An adaptive smooth unsaturated bistable stochastic resonance system and its application in rolling bearing fault diagnosis

An adaptive smooth unsaturated bistable stochastic resonance (ASUBSR) system for bearing fault signal detection is established. Based on the problem of output saturation and poor low-frequency suppression performance of classical bistable stochastic resonance (CBSR) system, an SUBSR with unsaturated characteristics is proposed. An ASUBSR system is designed by extracting the envelope spectrum of the input signal and resampling it to satisfy the adiabatic approximation condition, combining high-pass filter to filter out low-frequency interference, and using genetic algorithm to select the optimal system parameters. Through simulations and experiments, we found that the system can effectively suppress the interference of low-frequency and high-frequency, indicates that the system performs like a band-pass filter, and the output signal-to-noise ratio is better than that of the CBSR system. The proposed ASUBSR system has great application in the field of fault detection of rolling bearings.

Resonance behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise

The stochastic resonance (SR) behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise is investigated. Under the adiabatic approximation condition, the expression for the system output signal-to-noise ratio (SNR) is obtained. The analysis results show that stochastic multi-resonance phenomenon occurs when the SNR varies with the intensities of the multiplicative and additive noise. SR phenomenon can be observed on the curves of the SNR versus the system bias, versus the amplitude of the dichotomous noise and versus the amplitude of the square-wave signal. Moreover, the SNR varies non-monotonously with the variety of other system parameters.

Validation of quantum adiabaticity through non-inertial frames and its trapped-ion realization

Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several relevant adiabatic approximation conditions previously derived and show that all of them fail by introducing a suitable oscillating Hamiltonian for a single quantum bit (qubit). Then, by evaluating the adiabatic condition in a rotated non-inertial frame, we show that all of these conditions, including the standard adiabatic condition, can correctly describe the adiabatic dynamics in the original frame, either far from resonance or at a resonant point. Moreover, we prove that this validation mechanism can be extended for general multi-particle quantum systems, establishing the conditions for the equivalence of the adiabatic behavior as described in inertial or non-inertial frames. In order to experimentally investigate our method, we consider a hyperfine qubit through a single trapped Ytterbium ion 171Yb+, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system. By monitoring the quantum evolution, we explicitly show the consistency of the adiabatic conditions in the non-inertial frame.

Theory and method for weak signal detection in engineering practice based on stochastic resonance

In this paper, the Kramers rate was derived using the Fokker–Planck (FP) equation with the condition of adiabatic approximation (the amplitude and frequency of signal detected are small [Formula: see text]) and the signal-to-noise ratio (SNR) was proved by means of Fourier transform and the power spectrum in bistable system. This is a concise and superior method to demonstrate the Kramers rate and SNR compared to the past methods. It is convenient for readers to understand. The SNR of the bistable system obtained shows that stochastic resonance (SR) can be used to realize energy transition from noise to a periodic signal under the adiabatic approximation condition. Therefore, SR could enhance the SNR of the output signal. The signal modulation technique was employed to transform the large frequency components into a small parameter signal to meet the adiabatic approximation requirement. Furthermore, we have designed the model of modulator. The simulation results show that the modulation method can generate SR in a bistable system and detect weak signals with large parameters from strong noise background.

Parameter allocation of parallel array bistable stochastic resonance and its application in communication systems**Project supported by the National Natural Science Foundation of China (Grant No. 61179027), the Qinglan Project of Jiangsu Province of China (Grant No. QL06212006), and the University Postgraduate Research and Innovation Project of Jiangsu Province (Grant Nos. KYLX15_0829, KYLX15_0831).

In this paper, we propose a parameter allocation scheme in a parallel array bistable stochastic resonance-based communication system (P-BSR-CS) to improve the performance of weak binary pulse amplitude modulated (BPAM) signal transmissions. The optimal parameter allocation policy of the P-BSR-CS is provided to minimize the bit error rate (BER) and maximize the channel capacity (CC) under the adiabatic approximation condition. On this basis, we further derive the best parameter selection theorem in realistic communication scenarios via variable transformation. Specifically, the P-BSR structure design not only brings the robustness of parameter selection optimization, where the optimal parameter pair is not fixed but variable in quite a wide range, but also produces outstanding system performance. Theoretical analysis and simulation results indicate that in the P-BSR-CS the proposed parameter allocation scheme yields considerable performance improvement, particularly in very low signal-to-noise ratio (SNR) environments.

Stochastic multiresonance induced by correlated noise from a gene transcriptional regulatory system driven by amplitude-modulated signal

We analyzed the signal-to-noise ratio (SNR) theoretically by studying a gene transcriptional regulatory model driven by additive amplitude modulation signal and cross-correlated noises. By using the general two-state approach for this model, we obtained the analytic expression of SNR under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the periodic signal. More interestingly, the phenomenon of stochastic multiresonance can be observed in the curve of the SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation coefficient for controlling the SNR under fixed noise intensity, as well as a guidance in the design for the related experiments.

STOCHASTIC MULTIRESONANCE INDUCED BY ADDITIVE AMPLITUDE MODULATION SIGNAL AND NOISE IN A GENE TRANSCRIPTIONAL REGULATORY MODEL

We investigate the stochastic resonance (SR) and stochastic multiresonance phenomena in a gene transcriptional regulatory system driven by additive amplitude modulation signal and cross-correlated noise. By using the general two-state approach, we obtained the analytic expression of signal-to-noise ratio (SNR) under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the signal. More interestingly, stochastic multiresonance can be observed in the curve of SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation noise for controlling SNR under fixed noise intensity in the study of stochastic gene transcriptional regulatory process.

До теорії силових сталих багатоатомних систем у моделі сильного зв’язку (частина ІІ)

An approximate expression for the Coulomb interaction energy in solids has been obtained in the framework of the tight-binding model. The condition of adiabatic approximation and the procedure of quantum statistical averaging for the first (static) term in the expansion of the average potential energy in small nuclear shifts are analyzed, which allowed the electron contribution to the thermal expansion of solids to be calculated. An equation of state for a solid is obtained in the harmonic approximation by analyzing the internal energy and the thermal properties of the solid. A relationship between the specific heats Cv and Cp, which agrees with the Gr¨uneisen law, is found.

Adiabatic tunneling of Bose—Einstein condensates with modulated atom interaction in a double-well potential

We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.

Stochastic Resonance in FitzHugh-Nagumo Neural Model

Stochastic resonance is a non-linear phenomenon where the output response of the dynamic system reaches the maximum value under the joint action of a certain intensity of noises and external incentives. In this paper, the phenomenon of stochastic resonance in a FitzHugh-Nagumo neural (FHN) model is studied. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that, the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with increasing the intensities of the multiplicative and additive noise, with increasing the delayed-time as well as increasing the system parameters of the FHN model. The influence of the correlation time of the colored multiplicative noise and the influence of the coupling strength between the multiplicative and additive noise on the SNR is discussed.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance (ESR) in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio (SNR) is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.

Phenomenon of entropic stochastic resonance with asymmetric dichotomous noise and white noise

The entropic stochastic resonance (ESR) in a confined system subject to asymmetric dichotomous noise, white noise, and a periodic square-wave signal is investigated. Under the adiabatic approximation condition, by use of the properties of the dichotomous noise, we obtain the expression of the output signal-to-noise ratio (SNR) based on two-state theory. The SNR is shown to be a nonmonotonic function of the strength and asymmetry of the dichotomous noise, the intensity of the white noise, and the amplitude of the square-wave signal. The SNR varies non-monotonically with increases in the parameters of the confined structure. The influence of the correlation rate of the dichotomous noise and the frequency of the external constant force on the SNR is also discussed.

Vibrational and Stochastic Resonance in the FitzHugh—Nagumo Neural Model with Multiplicative and Additive Noise

The vibrational resonance and stochastic resonance phenomena in the FitzHugh—Nagumo (FHN) neural model, driven by a high-frequency (HF) signal and a low-frequency (LF) signal and by coupled multiplicative and additive noises, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with the increasing intensities of the multiplicative and additive noise as well as with the increasing system parameters of the FHN model. The influence of the coupling strength between the multiplicative and additive noises on the SNR is discussed.

Vibrational and Stochastic Resonance in FitzHugh-Nagumo Neural Model with Time-Delay and Colored Additive Noise

The vibrational resonance (VR) and stochastic resonance (SR) phenomena in time-delayed FitzHugh-Nagumo (FHN) neural model, driven by one high-frequency (HF) signal and one low-frequency (LF) signal, with coupled multiplicative and colored additive noise, is investigated. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that, the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with increasing the intensities of the multiplicative and additive noise, with increasing the delayed-time as well as increasing the system parameters of the FHN model. The influence of the correlation time of the colored additive noise and the coupling strength between the multiplicative and additive noise on the SNR is discussed.

Effect of White Noise and Dichotomous Noise in a Bistable System

The stochastic resonance in a bistable system subject to asymmetric dichotomous noise and multiplicative and additive white noise is investigated. By using the properties of the dichotomous noise, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) is obtained. It is found that the SNR is a non-monotonic function of the asymmetry of the dichotomous noise, and it varies non-monotonously with the intensities of the multiplicative and additive noise as well as with the system parameters. Moreover, the SNR depends on the correlation rate of the dichotomous noise.