Phase Fluctuations Research Articles

Effect of Phase Fluctuation on the Proper Operation of Smart Gear Health Monitoring System.

A smart gear sensor system has been developed for the condition monitoring of gear. This system includes a smart gear—the operation gear and a monitoring antenna. The analysis of the return loss of the monitoring antenna magnetically coupled with the smart gear gives the health condition of the gear. This research considers the effects of the distance and phase fluctuations between two components on the magnetic resonant return loss. The impacts of phase fluctuations include both static and high-speed conditions. Two experimental rigs have been built for the two cases. The coupling distance and static phase fluctuation are conducted via the first experimental rig. The second experimental rig performs both the coupling distance and phase fluctuation effect simultaneously while the smart gear rotates at high speed. During each test, the monitoring antenna return loss is captured thanks to a network analyzer. Analysis of the return loss data demonstrates that both the coupling distance and the change of the phase angle at the static condition and high speed have influenced the resonant return loss of the monitoring antenna. These findings are meaningful to the authors for evaluating and improving the accuracy of this gear health monitoring technique.

Quantum phase transition in a clean superconductor with repulsive dynamical interaction

We consider a model of electrons at zero temperature, with a repulsive interaction which is a function of the energy transfer. Such an interaction can arise from the combination of electron–electron repulsion at high energies and the weaker electron–phonon attraction at low energies. As shown in previous works, superconductivity can develop despite the overall repulsion due to the energy dependence of the interaction, but the gap Δ(ω) must change sign at some (imaginary) frequency ω0 to counteract the repulsion. However, when the constant repulsive part of the interaction is increased, a quantum phase transition towards the normal state occurs. We show that, as the phase transition is approached, Δ and ω0 must vanish in a correlated way such that 1/| log [{{Delta }}(0)]| sim {omega }_{0}^{2}. We discuss the behavior of phase fluctuations near this transition and show that the correlation between Δ(0) and ω0 locks the phase stiffness to a non-zero value.

Integrated photonic metasystem for image classifications at telecommunication wavelength

Miniaturized image classifiers are potential for revolutionizing their applications in optical communication, autonomous vehicles, and healthcare. With subwavelength structure enabled directional diffraction and dispersion engineering, the light propagation through multi-layer metasurfaces achieves wavelength-selective image recognitions on a silicon photonic platform at telecommunication wavelength. The metasystems implement high-throughput vector-by-matrix multiplications, enabled by near 103 nanoscale phase shifters as weight elements within 0.135 mm2 footprints. The diffraction manifested computing capability incorporates the fabrication and measurement related phase fluctuations, and thus the pre-trained metasystem can handle uncertainties in inputs without post-tuning. Here we demonstrate three functional metasystems: a 15-pixel spatial pattern classifier that reaches near 90% accuracy with femtosecond inputs, a multi-channel wavelength demultiplexer, and a hyperspectral image classifier. The diffractive metasystem provides an alternative machine learning architecture for photonic integrated circuits, with densely integrated phase shifters, spatially multiplexed throughput, and data processing capabilities.

Controlling Nonlinear Interaction in a Many-Mode Laser by Tuning Disorder.

A many-mode laser with nonlinear modal interaction could serve as a model system to study many-body physics. However, precise and continuous tuning of the interaction strength over a wide range is challenging. Here, we present a unique method for controlling lasing mode structures by introducing random phase fluctuation to a nearly degenerate cavity. We show numerically and experimentally that as the characteristic scale of phase fluctuation decreases by two orders of magnitude, the transverse modes become fragmented and the reduction of their spatial overlap suppresses modal competition for gain, allowing more modes to lase. The tunability, flexibility, and robustness of our system provides a powerful platform for investigating many-body phenomena.

Improved stabilization scheme for extreme ultraviolet quantum interference experiments

Interferometric pump–probe experiments in the extreme ultraviolet (XUV) domain are experimentally very challenging due to the high phase stability required between the XUV pulses. Recently, an efficient phase stabilization scheme was introduced for seeded XUV free electron lasers (FELs) combining shot-to-shot phase modulation with lock-in detection Wituschek et al (2020 Nat. Commun. 11 883). This method stabilized the seed laser beampath on the fundamental ultraviolet wavelength to a high degree. Here, we extend this scheme including the stabilization of the XUV beampath, incorporating phase fluctuations from the FEL high gain harmonic generation process. Our analysis reveals a clear signal improvement with the new method compared to the previous stabilization scheme.

Magnifying Quantum Phase Fluctuations with Cooper-Pair Pairing

Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. The inductive wires contribute a parabolic confinement, while the tunnel junctions add a cosinusoidal corrugation. Usually, the ground state wavefunction is localized within a single potential well -- that is, quantum phase fluctuations are small -- although entering the regime of delocalization holds promise for metrology and qubit protection. A direct route is to loosen the inductive confinement and let the ground state phase spread over multiple Josephson periods, but this requires a circuit impedance vastly exceeding the resistance quantum and constitutes an ongoing experimental challenge. Here we take a complementary approach and fabricate a generalized Josephson element that can be tuned in situ between one- and two-Cooper-pair tunneling, doubling the frequency of the corrugation and thereby magnifying the number of wells probed by the ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy, implying a twofold increase in the vacuum phase fluctuations.

Performance analysis of spatial multiplexing MIMO-MFSK based on energy detection for fast-fading environments

In fast-fading scattering environments such as high-speed rail and low-altitude communications, mobile communication systems need to quickly and robustly estimate and equalize fast-fading, time-varying channels. Under these circumstances, noncoherent multiple-input multiple-output (MIMO) has received attention in recent years, since it is less influenced by factors such as phase fluctuations and has fewer requirements for channel estimation and synchronization. Spatial multiplexing MIMO-MFSK based on energy detection is different from conventional noncoherent MIMO in that it can achieve higher spatial multiplexing gain in the independent distribution of channel fading statistics. At the receiver, partial real channel state information (CSI) is available, which can improve the capacity while ensuring the reliability of the link. With partial real CSI replacing instantaneous CSI, the system performance is inferior to conventional coherent MIMO under the influence of noise. As a result, it is necessary to analyze its theoretical detection performance. By energy detection, the noise of the MIMO-MFSK system conforms to the generalized gamma distribution. On the basis of this distribution, the optimal decision rule of the system and the symbol error rate (SER) formula are derived. Additionally, we investigate the signal-dependent noise problem of minimum Euclidean distance detection. Numerical results show that the SER formula fits well with the simulation results under the condition of a high signal-to-noise ratio.

Oxidation-reduction effects in the flotation of copper sulfide minerals and molybdenite – A proof of concept at industrial scale

Redox potential (Eh) control plays a significant role during sulfide mineral flotation by influencing the reactions on the surface of the minerals and accordingly the flotation behaviour. In this study, the metallurgical performance of typical copper sulfide minerals, molybdenite as well as gangue minerals (e.g., pyrite, tennantite, and enargite) under different pH and Eh conditions of the flotation cell were investigated. The copper and molybdenum processing plant at the Sungun complex-Iran were selected as a case study. For this purpose, Eh of flotation cells of phases 1 and 2 of copper and molybdenum processing circuits – Sungun complex – were measured by off-line method. After performing chemical analysis, the mineralogical study of the input load and products of each of the aforementioned flotation circuits in the rougher, cleaner, re-cleaner, and scavenger stages was performed. Based on the results, the potential in cells of phases 1 and 2 of copper concentration plants is in the range of −60 to −100 mV; and for the molybdenum plant, is in the range of −500 to −700 mV. The potentials of more than −100 mV in the phases of copper concentration plants have created suitable conditions for the separation of copper sulfide and molybdenite minerals from gangue minerals, especially pyrite. Adjustment of Eh in the range of −500 to −700 mV in the molybdenum processing plant has also led to the depression of copper minerals and the flotation of molybdenite, resulting in the effective separation of these minerals. However, grade analysis and mineralogical studies indicate the misplaced copper minerals into tailings, the passage of chalcopyrite and pyrite to molybdenum concentrate, the misplaced molybdenite to copper concentrate, and also the presence of minerals containing harmful elements such as arsenic in copper concentrate. Eh fluctuations in phase 1 and 2 of copper plants, the interaction of copper sulfide minerals, especially chalcopyrite with pyrite (and the depression of pyrite in Eh more than −100 mV), are reasons for the misplaced copper minerals into tailings. The interaction of chalcopyrite and pyrite with molybdenite and the high flotation tendency of molybdenite at the potential of +600 mV is the main factor in increasing the Cu and Fe grade in molybdenite concentrate. The interaction of copper minerals with arsenic-bearing minerals and the similar flotation behavior of these minerals in the potential of the rougher cells of the molybdenum processing plant has increased the arsenic grade in the copper concentrate or molybdenum tailings.

Analogue gravitational field from nonlinear fluid dynamics

The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts on the definition of the background providing the effective space-time metric. Subsequently, we use the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose–Einstein condensates in the ultracold gas laboratory.

Optical response of the Leggett mode in multiband superconductors in the linear response regime

We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of superconducting orders for different bands. We use the Ginzburg-Landau (GL) description to study the collective modes in multiband systems. We find that multiband superconductors generally allow a linear coupling between the Leggett mode and external electric fields due to the presence of a cross term between different components of superconducting orders in the GL theory. The presence of a linear coupling for the Leggett mode is in sharp contrast with the absence of that for Higgs (amplitude) modes in single-band superconductors that only support nonlinear optical responses such as third harmonic generation (THG). We further confirm such a linear coupling in multiband superconductors by a more microscopic description based on a diagrammatic approach. We study the collective modes within the random phase approximation (RPA) and compute their contribution to the linear optical conductivity. These findings suggest a new route to observe the Leggett mode by optical absorption.

A homogenization model for the rheology and local field statistics of suspensions of particles in yield stress fluids

We investigate the rheological behavior of athermal particle suspensions using experiments and theory. A generalized version of the homogenization estimates of Ponte Castañeda and Willis [J. Mech. Phys. Solids, 43(12), 1919–1951 (1995)] is presented for the effective viscosity of athermal suspensions accounting for additional microstructural features (e.g., polydispersity) via an empirical parameter, λ. For the case of identically sized spheres dispersed with statistical isotropy in a Newtonian fluid, the parameter λ is estimated from the results of Batchelor and Green [J. Fluid Mech. 56(2), 375–400 (1972)] for the Huggins coefficient. Predictions for the macroscopic viscosity are found to be in good agreement with measurements for monodisperse polymethyl methacrylate (PMMA) spheres in glycerol, as well as for the empirical Krieger–Dougherty equation for the shear viscosity. The proposed estimates have the added benefit that they can also be used to get information on the statistics of the stress and strain-rate fields in the fluid and particle phases. In addition, results for the effective shear viscosity are used in combination with the linear comparison method of Ponte Castañeda [J. Mech. Phys. Solids 39(1), 45–71 (1991)] to generate the corresponding estimates for the effective macroscopic behavior and field statistics of particle suspensions in (viscoplastic) yield stress fluids. Good agreement is also found between the theoretical estimates and experimental results for the effective yield and flow stress of suspensions with monodisperse PMMA spheres in Carbopol. Finally, it is argued that the results for the phase averages and fluctuations of the stress and strain-rate fields can be used to provide a physical interpretation for the parameter λ in terms of the polydispersity of the suspension and its implications for the percolation threshold.

Characterization of collective excitations in weakly coupled disordered superconductors

Isolated islands in two-dimensional strongly-disordered and strongly-coupled superconductors become optically active inducing sub-gap collective excitations in the ac conductivity. Here, we investigate the fate of these excitations as a function of the disorder strength in the experimentally relevant case of weak electron-phonon coupling. An explicit calculation of the ac conductivity, that includes vertex corrections to restore gauge symmetry, reveals the existence of collective sub-gap excitations, related to phase fluctuations and therefore identified as the Goldstone modes, for intermediate to strong disorder. As disorder increases, the shape of the sub-gap excitation transits from peaked close to the spectral gap to a broader distribution reaching much smaller frequencies. Phase-coherence still holds in part of this disorder regime. The requirement to observe sub-gap excitations is not the existence of isolated islands acting as nano-antennas but rather the combination of a sufficiently inhomogeneous order parameter with a phase fluctuation correlation length smaller than the system size. Our results indicate that, by tuning disorder, the Goldstone mode may be observed experimentally in metallic superconductors based for instance on Al, Sn, Pb or Nb.

Non-Markov behavior of acoustic phase variance in the atmospheric boundary layer

The Markov approximation is widely used in wave propagation in random media. This approximation is valid if the propagation path length is greater than the scale of the medium inhomogeneities affecting a particular statistical moment of a wave field and the moment changes insignificantly over this scale. These conditions might be violated for the variance of the phase fluctuations and other statistical moments of acoustic signals that have propagated through atmospheric turbulence: the scale of the largest eddies can be hundreds of meters, and fluctuations in the acoustic refractive index are relatively strong. In the current article, the phase variance of a spherical sound wave in statistically inhomogeneous turbulence is formulated without the Markov approximation. For propagation ranges smaller than the scale of the largest eddies, the phase variance without the Markov approximation is significantly smaller than when this approximation is employed. As the range increases, the difference between the two results tends toward a constant value (a ‘memory’ effect), which might be significant in many applications. The phase variance without the Markov approximation agrees better with the experimental data on sound propagation through the atmosphere, while the variance calculated with this approximation significantly overpredicts the data.

Impact of FBG feedback phase on laser dynamics

Fiber Bragg gratings (FBGs) have been advantageously used to improve the chaotic properties of semiconductor lasers. Though these components are known to be highly sensitive to environmental conditions, feedback phase fluctuations are often neglected. In this work, we experimentally demonstrate that the small variations of the propagation time induced by a simple thermal tuning of the FBG are sufficient to induce significant changes of the laser behavior. We report periodic stability enhancements linked with phase variations and highlight that both phase variation and phase offsets play an important role. Last, we show a good qualitative agreement with simulations based on an expanded version of the Lang-Kobayashi model.

The Strange-Metal Behavior of Cuprates

Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.

Emergence of Lie group symmetric classical spacetimes in the canonical tensor model

AbstractWe analyze a wave function of a tensor model in the canonical formalism, when the argument of the wave function takes Lie group invariant or nearby values. Numerical computations show that there are two phases, which we call the quantum and the classical phases. In the classical phase fluctuations are suppressed, and configurations emerge which are discretizations of classical geometric spaces invariant under Lie group symmetries. This is explicitly demonstrated for emergence of Sn (n = 1, 2, 3) for SO(n + 1) symmetries by checking the topological and geometric (Laplacian) properties of the emerging configurations. The transition between the two phases has the form of splitting/merging of distributions of variables, resembling a matrix model counterpart, namely the transition between one-cut and two-cut solutions. However, this resemblance is obscured by a difference in the mechanism of distribution in our setup from that in the matrix model. We also discuss this transition as a replica symmetry breaking. We perform various preliminary studies of the properties of the phases and the transition for such values of the argument.

Menstrual Cycle-Related Changes in Women with Schizophrenia: A Resting-State fMRI Study

Introduction: Different influences of ovarian hormones in schizophrenia (SCZ) have been reported, but no study to date has assessed their effects on the brain dynamics at rest. The present study aimed to examine the hormonal and clinical changes related to the menstrual cycle and alterations in the resting-state functional connectivity (RS-FC) depending on cycle phase and/or hormonal fluctuations in SCZ. Method: This study was conducted based on both between- and within-subject experimental designs, including 13 clinically stable female patients with SCZ (32 ± 7.7 years) and 13 healthy women (30 ± 7.3 years). RS-functional magnetic resonance imaging (fMRI) scanning, as well as hormonal and clinical assessments, was applied to each participant twice during two cycle phases: early follicular and mid-luteal. Results: A difference in mid-luteal progesterone levels was found between groups, with a large effect size (Cohen’s d) of 0.8 (p < 0.05). Also, the estradiol levels negatively correlated with the negative symptom severity of the patients during their mid-luteal phase. In the patients, estrogen positively correlated with the auditory network connectivity in the left amygdala during the early follicular phase. In the controls, progesterone had positive correlations with the connectivity of the posterior default mode and the left frontoparietal networks in the bilateral precuneus during the early follicular phase and had a negative correlation with the executive control network connectivity in the mid-luteal phase. Conclusion: The present study showed hormonal differences between groups and suggested that the levels of cycle-dependent hormones might be associated with the changes in clinical symptom severity and the RS-FC in the groups. Our RS-fMRI findings warrant further investigation.

Topological phases and collective modes in U(1) and SU(2) sectors of spin-orbit-coupled two-dimensional superfluid Fermi gases

We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive $s$-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.

The quantum phase fluctuation parameters of coherent light coupled to a Harmonically driven quartic anharmonic oscillator

The quantum phase fluctuation parameters of coherent light coupled to a Harmonically driven quartic anharmonic oscillator

Optimal nonlinear filtering of MPSK signals in the presence of a Doppler frequency shift

Objectives . Phase-shift keyed (PSK) signals are widely used in many telecommunication, communication, and cellular information transmission systems. Phase-shift keying provides a higher noise immunity than amplitude and frequency modulations do. An increase in the modulation order of such a signal leads not only to an increase in its spectral efficiency, but also to a certain decrease in the noise immunity of reception. To ensure a high noise immunity of reception of multiple phase-shift keyed (MPSK) signals, a demodulator should provide the coherence of the reference oscillation with the carrier. Ignorance of the frequency and phase of the received signal leads to significant energy losses. The purpose of this work was to synthesize and analyze algorithms for receiving MPSK signals with phase fluctuations caused by changes in the carrier frequency due to the Doppler effect against the background of white Gaussian noise. Methods . The problem was solved using the apparatus of optimal nonlinear filtering and methods of statistical radio engineering. Results . A demodulator was synthesized, which includes two interconnected units. One of them is a discrete symbol estimation unit, at the output of which a decision on the received symbol is issued, and the other is a phase-lock circuit. Analytical expressions were derived to estimate the characteristics of the receiver noise immunity as functions of the signalto-noise ratio and fluctuation parameters. It was shown that the synthesized quasi-coherent algorithm compensates well for the MPSK signal phase fluctuations caused by the instability of the master oscillator and the Doppler effect. Conclusions . Comparison of the results of this work with results obtained in the case of the absence of fluctuations in the initial phase showed that, at a high relative speed of the transmitter and the receiver (satellite radio channel), the energy loss is no more than 1 dB, and at lower speeds of the objects, it is about 0.2 dB and less.