Time-dependent Phase Research Articles

Simultaneous path weak-measurements in neutron interferometry

The statistical properties of the detection events constituting the interference fringes at the output of an interferometer are well-known. Nevertheless, there is still no unified view of what is happening to a quantum system inside an interferometer. Strong measurements of path operators destroy the interference effect. In weak measurements, an observable is weakly coupled to a pointer system and the resulting weak values quantify the observable by minimally disturbing the system. Previous which-way experiments with weak measurements could extract either the real or imaginary part of a single weak value with each ensemble. Here, we present the simultaneous full complex quantification of two path weak values with a single ensemble in a Mach–Zehnder neutron interferometer. Magnetic fields, oscillating with different frequencies, change the energy state in each interferometer path. The time-dependent phase between the energy states distinctly marks each path. The resulting beating intensity modulation at the interferometer output gives both path weak values. For the present experiment, the weak values’ absolute value and phase directly describe the observed amplitude and phase of the intensity modulation.

Emergence of the Molecular Geometric Phase from Exact Electron-Nuclear Dynamics.

Geometric phases play a crucial role in diverse fields. In molecules, they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wave function experiences quantum-mechanical interference effects. This intriguing effect, closely resembling the magnetic Aharonov-Bohm effect, crucially relies on the adiabatic description of the dynamics, and it is an open issue whether and how it persists in an exact quantum dynamical framework. Recent works suggest that the molecular geometric phase is an artifact of the adiabatic approximation, thereby challenging the entire concept. Here, building upon a recent investigation (Martinazzo, R.; Burghardt, I. Phys. Rev. Lett. 2024, 132, 243002), we address this issue using the exact factorization of the total wave function. We introduce instantaneous gauge-invariant phases separately for the electrons and nuclei and use them to monitor the phase difference between the trailing edges of a wavepacket encircling a conical intersection between adiabatic surfaces. The transition from the time-dependent open-path phase differences to the closed-path limit is examined, revealing how the phase differences in the electronic and nuclear subspaces compensate for each other upon path closure. In this way, we unambiguously demonstrate the role of the geometric phase in the interference process and shed light on its persistence beyond the adiabatic approximation.

Experimental investigation on vortex-induced vibration characteristics of the dual parallel suspenders

This study investigates vortex-induced vibrations (VIVs) on dual parallel suspenders using wind tunnel experiments and employs a two-degree-of-freedom setup for each circular cylinder to closely simulate actual structural conditions. The VIV responses of dual cylinders exhibit notable deviations and complexity due to aerodynamic interaction. Results indicate a significant shift in the VIV lock-in range towards higher values for dual cylinders, compared to single ones. Both upstream and downstream cylinders demonstrate lower maximum VIV amplitudes than the single-cylinder. The cylinders exhibit effects of negative aerodynamic damping within the VIV process, with the aerodynamic damping becoming more pronounced as amplitude increases. Additionally, the time-dependent phase relationship between the cylinders contributes to these variations in response. Further analysis of surface wind pressure distribution reveals that aerodynamic interference in dual-cylinder systems leads to intricate pressure patterns and modal behaviors.

Fisher–KPP-type models of biological invasion: open source computational tools, key concepts and analysis

This review provides open-access computational tools that support a range of mathematical approaches to analyse three related scalar reaction–diffusion models used to study biological invasion. Starting with the classic Fisher–Kolomogorov (Fisher–KPP) model, we illustrate how computational methods can be used to explore time-dependent partial differential equation (PDE) solutions in parallel with phase plane and regular perturbation techniques to explore invading travelling wave solutions moving with dimensionless speed c ≥ 2 . To overcome the lack of a well-defined sharp front in solutions of the Fisher–KPP model, we also review two alternative modelling approaches. The first is the Porous–Fisher model where the linear diffusion term is replaced with a degenerate nonlinear diffusion term. Using phase plane and regular perturbation methods, we explore the distinction between sharp- and smooth-fronted invading travelling waves that move with dimensionless speed c ≥ 1 / 2 . The second alternative approach is to reformulate the Fisher–KPP model as a moving boundary problem on 0 < x < L ( t ) , leading to the Fisher–Stefan model with sharp-fronted travelling wave solutions arising from a PDE model with a linear diffusion term. Time-dependent PDE solutions and phase plane methods show that travelling wave solutions of the Fisher–Stefan model can describe both biological invasion ( c > 0 ) and biological recession ( c < 0 ) . Open source Julia code to replicate all computational results in this review is available on GitHub; we encourage researchers to use this code directly or to adapt the code as required for more complicated models.

Cholecystokinin receptor type A are involved in the circadian rhythm of the mouse retina

The retina is the only organ projecting external light to the suprachiasmatic nucleus. Cholecystokinin receptor type A (Cckar/Cckar) is one of the essential factors for light reception in retinal cells. As there was a lack of literature on the matter, we aimed to elucidate the cause of the time-dependent phase change in clock gene expression. We found that Cckar mRNA expression in retinal cells exhibited diurnal variations. The rhythm of expression of the clock gene Per1/Per2 in retinal cells was altered in Cckar−/− mice. The light sensitivity of retinal cells was evaluated in wild-type mice, which showed c-Fos was activated in the ganglion cell layer more than in the inner granular layer. This increase in the number of c-Fos-positive cells was suppressed by lorglumide, a Cckar antagonist. Treatment of rat retina primary cells with lorglumide suppressed Per2 transcription, which was altered in a time-dependent manner relative to the Per2 expression. Light irradiation studies in Cckar−/− mice did not exhibit an increase in Period expression in the suprachiasmatic nucleus. These results indicate that Cckar is among the factors that regulate the cycle of clock genes on the retina. Cckar knockout attenuates the light responsiveness of suprachiasmatic nucleus and reduces the expression amplitude of Period genes in the retina. Thus, Cckar may contribute to entrainment of the light environment and maintenance of the expression cycle of Period gene, which is one of the core clock genes.

Investigating the sorption behavior of selenite on commercial partially oxidized magnetite nanopowder under aerobic conditions: Characterization and mechanisms

Selenium, which belongs to essential elements, has a narrow margin between necessity and toxicity. Anthropogenic activities may lead to its elevated concentrations in aquatic ecosystems, particularly in the undesirable form of toxic selenite, due to its high environmental mobility. Hence, it is imperative to devise effective technologies to limit its potential migration through the environment. Therefore, the development and evaluation of new adsorbents for its effective removal from selenium-contaminated waters are crucial for both human health and environmental stability in affected areas. Specifically, magnetite-based nanomaterials showed promise as sorbents due to their capacity to immobile contaminants through reductive transformation or adsorption, but there is a lack of comprehensive understanding regarding the sorption mechanisms and the factors influencing the efficiency of this process. A deeper understanding of these factors is crucial for developing sustainable and efficient water treatment strategies. This study focuses on magnetite nanopowder’s sorptive properties, examining critical factors such as pH, ionic strength, and competing anions that affect selenite removal. Sorption kinetics revealed an initial rapid selenite removal followed by a slower, time-dependent phase, suggesting a complex sorption mechanism. Chemisorption was considered the primary sorptive interaction, with diffusion playing a minor role, and was best described by the pseudo-second order kinetic model. Notably, pH significantly affected sorption efficiency and the suggested sorptive mechanism. Acidic conditions favored selenite removal due to formation of inner-sphere complexes, while alkaline conditions reduced efficiency due to repulsive interactions. Equilibrium sorption data were best fitted by the Langmuir model, with maximum sorption at pH 3, indicating that acidic conditions favor selenite removal. X-ray photoelectron spectroscopy (XPS) analysis ruled out the formation of reduced selenium compounds on the magnetite nanopowder surfaces. Additionally, Mössbauer spectrometry revealed that the nanopowder is not homogeneous and contains both magnetite and maghemite phases. Ionic strength and co-occurring ions showed minimal chloride impact but significant phosphate competitiveness due to its affinity for iron oxides. In conclusion, this study sheds light on the complex selenite sorptive interactions with magnetite nanopowder, emphasizing the dominance of chemisorption, especially in acidic solutions.

Investigation of the Influence of Machining Parameters and Surface Roughness on the Wettability of the Al6082 Surfaces Produced with WEDM.

Electrical Discharge Machining (EDM) is a non-conventional machining technique, capable of processing any kind of conductive material. Recently, it has been successfully utilized for producing hydrophobic characteristics in inherently hydrophilic metallic materials. In this work, Wire Electrical Discharge Machining (WEDM) was utilized for producing hydrophobic characteristics on the surface of the aluminum alloy 6082, and various parameters that can affect wettability were investigated. Adopting an orthogonal Taguchi approach, the effects of the process parameter values of peak current, pulse-on time, and gap voltage on the contact angles of the machined surfaces were investigated. After machining, all samples were observed to have obtained hydrophobic properties, reaching contact angles up to 132°. The peak current was identified as the most influential parameter regarding the contact angle, while the gap voltage was the less influential parameter. A contact angle variation of 30° was observed throughout different combinations of machining parameters. Each combination of the machining parameters resulted in a distinct surface morphology. The samples with moderate roughness values (3.4 μm > Sa > 5.7 μm) were found to be more hydrophobic than the samples with high or low values, where the contact angle was measured under 115°. In addition, the finite element modeling of the experimental setup, with parametric surfaces of uniform random and Perlin noise types of roughness, was implemented. Time dependent simulations coupling phase field and laminar flow for the modelingof the wetting of surfaces with different surface roughness characteristics showed that an increase in the Sa roughness and total wetted area can lead to an increase in the contact angle. The combination of experimental and computational results suggests that the complexity of the wettability outcomes of aluminum alloy surfaces processed with WEDM lies in the interplay between variations of the surface chemical composition, roughness, micro/nano morphology, and the surface capability of forming a composite air/water interface.

Dynamic behavior of mixed convection heat transfer among horizontal co-axial fixed pipes at varying temperatures: Efficiency of cylindrical heat sink

The aim of the current research is to highlight the time-dependent properties of laminar convective thermal transmission inside a semi-infinite pipe, with an emphasis on flow frequencies that impact inter-fluid momentum and energy. The implicit finite difference approach is used to solve two-dimensional mathematical model composed of nonlinear partial differential equations. The research includes forecasting thermal performance of time-dependent flow in a pipe over several parameter ranges relevant to the flow model. The obtained forecasts were emphasized graphically. The numerical solutions were separated into steady and unsteady components, with the steady component yielding findings that were then used to determine the time dependent surface shearness and energy shearness in the time dependent phase. The stable component of the investigation revealed that raising the buoyancy force parameter and the impact of viscous dissipation significantly improved the flow velocity pattern and heat distributions throughout the flow domain. While the amplitude of time dependent surface shearness varied somewhat across various buoyancy force parameter values, the amplitude of time dependent heat transmission rates varied significantly. This study sheds light on the interaction of several characteristics, such as buoyancy force effects and internal energy loss, on time-dependent thermal energy flow inside a semi-infinite pipe subjected to laminar convective flow. It is worth noting that the amplitude of the time dependent rate of heat transmission shows more noticeable variations with different values of the buoyancy force parameter, in contrast to the minute change in the amplitude of the time dependent surface sheerness.

Controlling the charge-transfer dynamics of two-level systems around avoided crossings.

Two-level quantum systems are fundamental physical models that continue to attract growing interest due to their crucial role as a building block of quantum technologies. The exact analytical solution of the dynamics of these systems is central to control theory and its applications, such as that to quantum computing. In this study, we reconsider the two-state charge transfer problem by extending and using a methodology developed to study (pseudo)spin systems in quantum electrodynamics contexts. This approach allows us to build a time evolution operator for the charge transfer system and to show new opportunities for the coherent control of the system dynamics, with a particular emphasis on the critical dynamic region around the transition state coordinate, where the avoided crossing of the energy levels occurs. We identify and propose possible experimental implementations of a class of rotations of the charge donor (or acceptor) that endow the electronic coupling matrix element with a time-dependent phase that can be employed to realize controllable coherent dynamics of the system across the avoided level crossing. The analogy of these rotations to reference frame rotations in generalized semiclassical Rabi models is discussed. We also show that the physical rotations in the charge-transfer systems can be performed so as to implement quantum gates relevant to quantum computing. From an exquisitely physical-mathematical viewpoint, our approach brings to light situations in which the time-dependent state of the system can be obtained without resorting to the special functions appearing in the Landau-Zener approach.

Comments to ‘Stability of traveling waves for deterministic and stochastic delayed reaction-diffusion equation based on phase shift’

In Liu et al. (2023), the authors set out to prove orbital stability for traveling waves in a (stochastic) delay reaction–diffusion equation. For the deterministic proof, they follow a phase-tracking technique as developed by Zumbrun and Howard (1998) [1] and for the stochastic version, they use a stochastic phase-tracking technique as developed by Hamster and Hupkes (2019, 2020a,b) [2,3] (which in turn is based on the aforementioned technique by Howard and Zumbrun). Note that the authors do not acknowledge the origins of their techniques.In the deterministic case, stability results are known (Mei, 2009) [4], but the application of phase-tracking to this problem appears to be new. However, there is a very subtle interplay between the time-dependent phase and the delay in the delay equation which is not accounted for, nor is explained or proved if the chosen phase has the same properties in the general framework of delay semigroups as for regular semigroups.The proof of the stochastic case of course has the same issues, but let us assume that the issues can be resolved, then there are still several issues with the proof. Especially, the phase tracking introduces terms that depend on the gradient of the solution which must be bounded in the H1 norm. This introduces singularities in the bounds that do not show in these proofs.

HyBench: A New Benchmark for HTAP Databases

In this paper, we propose, HyBench, a new benchmark for HTAP databases. First, we generate the testing data by simulating a representative HTAP application. We particularly develop a time-dependent generation phase and an anomaly generation phase for testing HTAP with large cardinality and various anomalies. Second, we propose a set of hybrid workloads. Specifically, we design 18 read/write transactions, 13 analytical queries, and a mix workload of 6 analytical transactions and 6 interactive queries. We also develop a graph-based parameter curation method to control the access patterns including skew access and data contention of the hybrid workload. Third, we propose a unified metric for quantifying the overall HTAP performance. Particularly, we introduce a query-driven method that evaluates the data freshness (lag time between analytics and transactions). Then we introduce a three-phase execution rule to compute a unified metric, combining the performance of OLTP (TPS), OLAP (QPS), and OLXP (XPS) and data freshness. To verify the effectiveness of HyBench and to debunk the myth of different HTAP architectures, extensive experiments have been conducted over five HTAP databases.

Scattering of a wave packet by the Pöschl-Teller potential well

We investigate the scattering of a wave packet by the Pöschl-Teller potential in momentum representation. The scattering dynamics of the wave packet for a long-time evolution is feasible in this representation. With the wave function in momentum space, we can construct the time-dependent phase space Wigner function. The corresponding density function in coordinate space is then calculated through the Wigner function. The reflectionless wave packet for integer ν and partially reflected for non-integer ν are demonstrated by analyzing the Wigner function.

Lipids with negative spontaneous curvature decrease the solubility of the cancer drug paclitaxel in liposomes.

Paclitaxel (PTX) is a hydrophobic small-molecule cancer drug that loads into the membrane (tail) region of lipid carriers such as liposomes and micelles. The development of improved lipid-based carriers of PTX is an important objective to generate chemotherapeutics with fewer side effects. The lipids 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) and glyceryl monooleate (GMO) show propensity for fusion with other lipid membranes, which has led to their use in lipid vectors of nucleic acids. We hypothesized that DOPE and GMO could enhance PTX delivery to cells through a similar membrane fusion mechanism. As an important measure of drug carrier performance, we evaluated PTX solubility in cationic liposomes containing GMO or DOPE. Solubility was determined by time-dependent kinetic phase diagrams generated from direct observations of PTX crystal formation using differential-interference-contrast optical microscopy. Remarkably, PTX was much less soluble in these liposomes than in control cationic liposomes containing univalent cationic lipid 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP) and 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC), which are not fusogenic. In particular, PTX was not substantially soluble in GMO-based cationic liposomes. The fusogenicity of DOPE and GMO is related to the negative spontaneous curvature of membranes containing these lipids, which drives formation of nonlamellar self-assembled phases (inverted hexagonal or gyroid cubic). To determine whether PTX solubility is governed by lipid membrane structure or by local intermolecular interactions, we used synchrotron small-angle X-ray scattering. To increase the signal/noise ratio, we used DNA to condense the lipid formulations into lipoplex pellets. The results suggest that local intermolecular interactions are of greater importance and that the negative spontaneous curvature-inducing lipids DOPE and GMO are not suitable components of liposomal carriers for PTX delivery.

Evaluation of Kunkur Fines for Utilization in the Production of Ternary Blended Cements

Ternary blended cements, such as limestone calcined clay cement (LC3), represent a type of strategic binder for the mitigation of environmental impacts associated with cement production. These are estimated to reduce CO2 emissions by about 40% compared to ordinary Portland cement (OPC). In this paper, we explore the possibility of producing such ternary blends by utilizing secondary raw materials that may be locally available. Specifically, the primary limestone that is commonly used in LC3 is herein substituted with quarry dust obtained by sourcing “kunkur”, a carbonate-rich sedimentary rock (also known as caliche) that can be locally utilized for the production of ordinary OPC clinker. To optimize the blending proportions of ternary cement consisting of OPC, calcined clay, and kunkur fines, a “design of experiment” (DoE) approach was implemented with the goal of exploring the possibility of reducing the amount of the OPC fraction to values lower than 50%. The properties of the formulated blends were assessed by a combination of techniques that comprise mechanical strength testing, XRD time-dependent quantitative phase analysis, and SEM–EDS microstructural and microchemical analyses. The results suggest that ternary blended cement based on kunkur fines forms hydration products, such as hemicarboaluminates, which are also observed in LC3. This shows that such waste materials can potentially be used in sustainable cement blends; however, the presence of kaolinite in the kunkur fines seems to affect their strength development when compared to both OPC and conventional LC3.

Attractors for a fluid-structure interaction problem in a time-dependent phase space

This paper is concerned with the long-time dynamics of a fluid-structure interaction problem describing a Poiseuille inflow through a 2D channel containing a rectangular obstacle. Physically, this models the interaction between the wind and the deck of a bridge in a wind tunnel experiment, as time goes to infinity. Due to this interaction, the fluid domain depends on time in an unknown fashion and the problem needs a delicate functional analytic setting. As a result, the solution operator associated to the system acts on a time-dependent phase space, and it cannot be described in terms of a semigroup nor of a process. Nonetheless, we are able to extend the notion of global attractor to this particular setting, and prove its existence and regularity. This provides a strong characterization of the asymptotic behavior of the problem. Moreover, when the inflow is sufficiently small, the attractor reduces to the unique stationary solution of the system, corresponding to a perfectly symmetric configuration.

Noise-resistant phase imaging with intensity correlation.

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.

Unraveling the Ultrafast Coherent Dynamics of Exciton Polariton Propagation at Room Temperature.

Exciton polaritons are widely considered as promising platforms for developing room-temperature polaritonic devices, owing to the high-speed propagation and nonlinear interactions. However, it remains challenging to explore the dynamics of exciton polaritons specifically at room temperature, where the lifetime could be as small as a few picoseconds and the prevailing time-averaged measurement cannot give access to the true nature of it. Herein, by using the time-resolved photoluminescence, we have successfully traced the ultrafast coherent dynamics of a moving exciton polariton condensate in a one-dimensional perovskite microcavity. The propagation speed is directly measured to be ∼12.2 ± 0.8 μm/ps. Moreover, we have developed a time-resolved Michelson interferometry to quantify the time-dependent phase coherence, which reveals that the actual coherence time of exciton polaritons could be much longer (nearly 100%) than what was believed before. Our work sheds new light on the ultrafast coherent propagation of exciton polaritons at room temperature.

An automated multi-order phase correction routine for processing ultra-wideline NMR spectra

Efficient acquisition of wideline solid-state nuclear magnetic resonance (NMR) spectra with patterns affected by large inhomogeneous broadening is accomplished with the use of broadband pulse sequences. These specialized pulse sequences often use frequency-swept pulses, which feature time-dependent phase and amplitude modulations that in turn deliver broad and uniform excitation across large spectral bandwidths. However, the resulting NMR spectra are often affected by complex frequency-dependent phase dispersions, owing to the interplay between the frequency-swept excitations and anisotropic resonance frequencies. Such phase distortions necessitate the use of multi-order non-linear corrections in order to obtain absorptive, distortion-free patterns with uniform phasing. Performing such corrections is often challenging due to the complex interdependence of the linear and non-linear phase contributions, and how these may affect the NMR signal. Hence, processing of these data usually involves calculating the spectra in magnitude mode wherein the phase information is discarded. Herein, we present a fully automated phasing routine that is capable of processing and phase correcting such wideline NMR spectra. Its performance is corroborated via processing of NMR data acquired using both the WURST-CPMG (Wideband, Uniform-Rate, Smooth Truncation with Carr-Purcell Meiboom-Gill acquisition) and BRAIN-CP (BRoadband Adiabatic Inversion Cross Polarization) pulse sequences for a variety of nuclei (i.e., 119Sn, 195Pt, 35Cl, 87Rb, and 14N). Based on both simulated and experimental NMR datasets, it is demonstrated that automatic phase corrections up to and including second order can be readily achieved without a priori information regarding the nature of the phase-distorted NMR datasets, and independently of the exact manner in which time-domain NMR data are collected and subsequently processed. In addition, it is shown that NMR spectra acquired at both single and multiple transmitter frequencies that are processed with this automated phasing routine have improved signal-to-noise properties than those processed with conventional magnitude calculations, along with powder patterns that better match those of ideal NMR spectra, even for datasets possessing low signal-to-noise ratios and/or affected by spectral artifacts.

Statistical solutions and Liouville theorem for the second order lattice systems with varying coefficients

In this article, we first verify the global well-posedness of the second order lattice systems with varying coefficients. Then we prove that the solution mappings form a continuous process on the time-dependent phase spaces and the process has a time-dependent pullback attractor. Afterwards, we establish that there exists a family of Borel probability measures carried by the time-dependent pullback attractor which possesses invariant property under the action of the process. Further, we formulate the definition of statistical solution for the addressed evolution equations on time-dependent phase spaces and prove its existence. Our results reveal that the statistical solution of the second order lattice systems with varying coefficients satisfies the Liouville theorem in Statistical Mechanics. Finally, we propose some interesting issues concerning the singular limiting behavior as the varying coefficients tend to zero.

Multistate transition dynamics by strong time-dependent perturbation in NISQ era

Abstract We develop a quantum computing scheme utilizing McLachlan variational principle in a hybrid quantum–classical algorithm to accurately calculate the transition dynamics of a closed quantum system with many excited states subject to a strong time-dependent perturbation. A systematic approach for optimal construction of a general N-state ansatz with unary N-qubit encoding is refined. We also use qubit efficient encoding in McLachlan variational quantum algorithm to reduce the number of qubits to log 2 N , simultaneously diminishing depths of the quantum circuits. The significant reduction of the number of time steps is achieved by use of the second order marching method. Instrumental in obtaining high accuracy are adaptations of the circuits to include time-dependent global phase correction. We illustrated, tested and optimized our quantum computing algorithm on a set of 16 bound hydrogenic eigenstates exposed to a strong laser attosecond pulse. Results for transition probabilities are obtained with accuracy better than 1%, as established by comparison to the benchmark data. Use of interaction representation of the Hamiltonian reduces the noise accumulation while the quantum system evolves in time.