Linear Ramp Research Articles

Exact dynamics of the Tomonaga-Luttinger liquid and shortcuts to adiabaticity

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an arbitrary interaction quench, making use of the SU(1,1) dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, which cancels the final nonadiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols. Published by the American Physical Society 2024

A method for design a linear heat rate ramp limit curve for thermal reactor fuel rods

A method for design a linear heat rate ramp limit curve for thermal reactor fuel rods

Numerical appraisal of the role of heat transfer regimes on transient response of carbon dioxide based supercritical natural circulation loop during power upsurge

Appearance of steep property gradients with change in temperature is a fascinating feature of any supercritical fluid, which can instigate intricate dynamics in supercritical natural circulation loops by modulating the effective forces. While most of the relevant literature focuses on stability evaluation, anticipation regarding the transient response of the system during power transition is of utmost significance, especially in high-power applications. Present study aims at furnishing insight on the same by developing a one-dimensional numerical model of a rectangular loop with supercritical CO2 as the working medium, and characterizing the temporal trends over a wide range of heating power. Two different profiles of power upsurge have been tested for different regimes of heat transfer, unearthing intriguing characteristics. The combination of initial and final regimes during any transformation is found to be the most crucial factor. Single-step rise in power, in general, is the most vulnerable one, specifically during large-scale change of the order of 1000 W, and better be employed only at low-power regime. Even single-step change ∼ 25 W can inflict instability and flow transition within the transition regime. Power transformation following linear ramp profile with transition periods of 5, 10 and 20 s is identified to be the most suitable one across all the regimes. It can successfully mitigate instability even in the later parts of the transition regime, albeit at the expense of greater time requirement to attain the final stable state and possibly a greater period of transformation. Change through multiple small steps (about 250 W for large change in low power regime and 15 W within transition regime) can also be a feasible option for avoiding the growth of unstable oscillations at higher powers.

A novel methodology for the selection of the optimal velocity profile for planned point-to-point trajectories in 1-DoF manipulators

In this work, an approach based on velocity profile selection is developed and validated to decrease forces, acceleration, velocity, mechanical power, and energy consumption in 1 DOF Cartesian manipulators. Initially, a mathematical modeling of the kinematic and kinetic variables rising in linear, exponential, parabolic, sinusoidal, and s-curve ramp velocity profiles is proposed for different load conditions and saturation values of the velocity profiles, focusing on generic Cartesian manipulators moving a constant inertia load and not equipped with regenerative devices. Lastly, a summary table outlining the benefits and drawbacks of each velocity profile in relation to the relevant variables is given to the reader, along with a set of recommendations for selecting the best velocity profile in accordance with the load conditions and optimization goals. It was shown that, depending on the load conditions, the inappropriate choice of one type of speed profile can increase the required forces by up to 400%, the required maximum power by more than 88%, and the energy consumption by up to 77% with respect to the optimal speed profile.

Square Wave Electrogravimetry Monitors Transient Submonolayer Adsorption of Redox-Active Molecules with a Precision of Less Than 1% of a Monolayer

Square wave voltammetry on electrolytes containing the reversible redox pairs flavin adenine dinucleotide (FAD) and methyl viologen (MV) was complemented by a new form of acoustic microgravimetry. The analytes FAD and MV have promising applications in bacterial fuel cells and redox flow batteries. The instrument operates similarly to a quartz crystal microbalance with dissipation monitoring (EQCM-D). It reports shifts in resonance frequency and half bandwidth on several overtones. Compared to the existing instruments, the time resolution was improved by a factor of 40 down to 2.5 ms by multifrequency lockin amplification, which is important for the analysis of the transients in electrochemistry. The frequency noise after accumulation was reduced below 10 mHz ≙ 0.12 ng/cm2 ≙ 1.2 pm (assuming ρ = 1 g/cm3) by employing modulation and averaging. Square wave modulation of the electrode potential is superior to linear ramps (cyclic voltammetry) because it reduces the contribution of non-Faraday currents and, also, improves sensitivity. The shifts of frequency,Δf, and half bandwidth, ΔΓ, are in line with the Sauerbrey prediction (Δf/n ≈const. and ΔΓ/n < -Δf/nwith n the overtone order). Small deviations (Figure B and D) presumably are caused by the layer’s softness. The apparent shear modulus, G app, of this layer is in the GPa range. The frequency difference, Δf/n|CT (Figure E), amounts to an apparent mass transfer rate. Plots of Δf/n|CT versus potential sometimes show curves similar to the electric current as observed for e. g. MV. For FAD, the results obtained depended on pH and the apparent mass transfer rates are much different from the current (Figure C and E). This difference is most likely caused by adsorbed molecules that are intermediates of the underlying two-electron process. The explanation is further corroborated by the response time of the QCM signals being much larger than the RC time of double layer recharging as determined with EIS. An interpretation in terms of adsorption/desorption is more plausible than an interpretation in terms of changed viscosity in the diffuse double layer.[1] Caption: Currents and frequency shifts obtained on a solution containing FAD. Df/n|av evidences the preferred adsorption of the intermediate state (FADH).

Design of shortcuts to adiabaticity for Bose-Einstein condensates dynamics in soliton Josephson junctions

Abstract This article primarily establishes a two-soliton system and employs the Lewis-Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study on the atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions (BJJs). Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.

Rheology of automotive adhesives during dispensing: A direct comparison of epoxy and rubber based systems via drag and pressure driven flows

Construction of vehicles requires adhesive dispensing for body-in-white assembly, hemming of closure panels, decking of windshields and the manufacture of battery packs. Knowledge of the rheological properties of adhesives applied using common dispensing systems is important for optimization of dispensing and application conditions. However, flow behavior of adhesives at shear rates used in dispensing is not well understood. Therefore, this study combines parallel plate and capillary rheology techniques to directly compare the rheological properties of an epoxy structural adhesive used in hemming applications and a rubber ‘topical sealer’ used to seal water leak paths across the range of shear rates observed in dispensing. Shear viscosity (η) and complex viscosity (η*) master curves were created from time-temperature-superposition (TTS) of steady shear and dynamic oscillatory data. Both adhesives did not follow the Cox-Merz rule. It was found that the Carreau-Yasuda model fit the steady shear viscosity master curve of the epoxy structural adhesive, while a simpler power law model fit the steady shear viscosity master curve of the rubber topical sealer. An inexpensive capillary rheometer was developed to simulate the adhesive dispensing process. Viscosity data was corrected for entrance pressure losses and a non-Newtonian flow front using Bagley and Weissenberg-Rabinowitsch corrections, respectively. It was observed that complex viscosity master curves better predicted viscosity during dispensing, as compared to steady shear viscosity master curves. Linear stress ramp measurements showed that the adhesives have widely different yield stresses, while the capillary rheometry measurements showed they have similar viscosities during dispensing. Furthermore, the capillary rheometer ‘shot meter’ pressures were related to the apparent and doubly corrected viscosity values through power law functions. A new quality control method based on the capillary rheology data is proposed.

Practical Guide to Large Amplitude Fourier-Transformed Alternating Current Voltammetry-What, How, and Why.

Fourier-transformed alternating current voltammetry (FTacV) is a technique utilizing a combination of a periodic (frequently sinusoidal) oscillation superimposed onto a staircase or linear potential ramp. The advanced utilization of a large amplitude sine wave induces substantial nonlinear current responses. Subsequent filter processing (via Fourier-transformation, band selection, followed by inverse Fourier-transformation) generates a series of harmonics in which rapid electron transfer processes may be separated from non-Faradaic and competing electron transfer processes with slower kinetics. Thus, FTacV enables the isolation of current associated with redox processes under experimental conditions that would not generate meaningful data using direct current voltammetry (dcV). In this study, the enhanced experimental sensitivity and selectivity of FTacV versus dcV are illustrated in measurements that (i) separate the Faradaic current from background current contributions, (ii) use a low (5 μM) concentration of analyte (exemplified with ferrocene), and (iii) enable discrimination of the reversible [Ru(NH3)6]3+/2+ electron-transfer process from the irreversible reduction of oxygen under a standard atmosphere, negating the requirement for inert gas conditions. The simple, homebuilt check-cell described ensures that modern instruments can be checked for their ability to perform valid FTacV experiments. Detailed analysis methods and open-source data sets that accompany this work are intended to facilitate other researchers in the integration of FTacV into their everyday electrochemical methodological toolkit.

Synthesizing polarization singularity lattices using phase ramps

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

Fast Quantum State Preparation and Bath Dynamics Using Non-Gaussian Variational Ansatz and Quantum Optimal Control.

Fast preparation of quantum many-body states is essential for myriad quantum algorithms and metrological applications. Here, we develop a new pathway for fast, nonadiabatic preparation of quantum many-body states that combines quantum optimal control with a variational Ansatz based on non-Gaussian states. We demonstrate our approach on the spin-boson model, a single spin interacting with the bath. We use a multipolaron Ansatz to prepare near-critical ground states. For one mode, we achieve a reduction in infidelity of up to ≈60 (≈10) times compared to linear (optimized local adiabatic) ramps; for many modes, we achieve a reduction in infidelity of up to ≈5 times compared to nonadiabatic linear ramps. Further, we show that the typical control quantity, the leakage from the variational manifold, provides only a loose bound on the state's fidelity. Instead, in analogy to the bond dimension of matrix product states, we suggest a controlled convergence criterion based on the number of polarons. Finally, motivated by the possibility of realizations in trapped ions, we study the dynamics of a system with bath properties going beyond the paradigm of (sub- and/or super-) Ohmic couplings.

Demonstration of nonlinear tuning curve vibration response using a homemade analog sweep spectrum analyzer

A super-heterodyne sweep spectrum analyzer has been designed (using analog circuitry), built and tested to cover the 5 to 1000 Hz range. The analyzer employs a linear ramp voltage versus time, driving a voltage-controlled oscillator VCO that generates a sweep from 32.768 kHz to 33.768 kHz in 70 s. An analog AD734 multiplies the VCO signal by a sinusoidal signal (generated by a watch crystal 32.768 kHz oscillator). The “mixer” signal is low-pass filtered and amplified to generate a 5-1000 Hz swept tone using a 2-in. speaker. The accelerometer (mounted on a thin circular clamped acrylic plate) vibration response involves multiplying this signal by the VCO, then filtering this “mixer” signal using a 4-stage watch crystal ladder filter with a 1 Hz bandwidth. This signal is squared and low-pass filtered to generate the time (converted to frequency) vs. mean-squared voltage response on an oscilloscope. In the demonstration, 300 g of 6 mm diameter glass beads are supported by the 11.4 cm diam, 3.2 mm thick plate and upper rigid cylindrical wall column. The nonlinear tuning curve vibration response is recorded for various incremental drive amplitudes to demonstrate that the tuning curve resonant frequency significantly decreases with increasing drive amplitude.

Spatially-coded Fourier ptychography: flexible and detachable coded thin films for quantitative phase imaging with uniform phase transfer characteristics.

Fourier ptychography (FP) is an enabling imaging technique that produces high-resolution complex-valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques -- a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non-uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, we present spatially-coded Fourier ptychography (scFP), a new method that synergizes FP with spatial-domain coded detection for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality and corrects refractive index underestimation issues prevalent in conventional FP and related tomographic implementations. The inclusion of the coded thin film further adds a new dimension of measurement diversity in the spatial domain. The development of scFP is expected to catalyse new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response.

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) — a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is En ~ log n. Despite the presence of ramps, these sequences do not exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument s = β + it is the Riemann zeta function ζ(s). An immediate consequence is that the spectral form factor is simply −ζ|(it)|2. Our observation that log spectra have a linear ramp, is closely related to the Lindelöf hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through |ζ(it)|2 on a log-log plot is indeed 1, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer N causes the would-be-eternal ramp to end on a plateau.

An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition.

Using a precise electrochemical quartz crystal microbalance (EQCM), it was shown that electrogravimetry can be carried out with microelectrode arrays (MEAs). MEAs were prepared on the resonator surface by coating it with a thin polymer layer containing holes, where the holes constitute the microelectrodes. The preparation procedures, their benefits, and their limitations are discussed. Microelectrode-based electrogravimetry is challenging because the reduced active area reduces the QCM signal. It is still feasible. This work is limited to linear voltage ramps (as opposed to steps). The processes chosen for demonstration were the electrodeposition/stripping of copper and the redox cycling of methyl viologen dichloride (MVC). The current trace often showed microelectrodic behavior, depending on the sweep rate. For the case of copper deposition, the mass transfer rate was proportional to the electric current. For the case of MVC, the electric current showed a plateau at the ends of the current-voltage diagram, but the mass transfer rate did not change. The difference can be explained by adsorption and desorption going into saturation at the two ends of the voltage range. Based on whether or not a microelectrodic gravimetric signal is seen, it can be stated whether the mass transfer is closely linked to the current. Further advantages of the microelectrode-based EQCM are an improved access to fast processes, reduced effects of double layer recharging, and the possibility to work at a low electrolyte support.

Mechanistic insights into on-surface reactions from isothermal temperature-programmed X-ray photoelectron spectroscopy.

On-surface synthesis often proceeds under kinetic control due to the irreversibility of key reaction steps, rendering kinetic studies pivotal. The accurate quantification of reaction rates also bears potential for unveiling reaction mechanisms. Temperature-Programmed X-ray Photoelectron Spectroscopy (TP-XPS) has emerged as an analytical tool for kinetic studies with splendid chemical and sufficient temporal resolution. Here, we demonstrate that the common linear temperature ramps lead to fitting ambiguities. Moreover, pinpointing the reaction order remains intricate, although this key parameter entails information on atomistic mechanisms. Yet, TP-XPS experiments with a stepped temperature profile comprised of isothermal segments facilitate the direct quantification of rate constants from fitting time courses. Thereby, rate constants are obtained for a series of temperatures, which allows independent extraction of both activation energies and pre-exponentials from Arrhenius plots. By using two analogous doubly versus triply brominated aromatic model compounds, we found that their debromination on Ag(111) is best modeled by second-order kinetics and thus proceeds via the involvement of a second, non-obvious reactant. Accordingly, we propose that debromination is activated by surface supplied Ag adatoms. This hypothesis is supported by Density Functional Theory (DFT) calculations. We foresee auspicious prospects for this TP-XPS variant for further exploring the kinetics and mechanisms of on-surface reactions.

AdS3/RMT2 duality

We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS3 quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for chaotic quantum systems, which originates from the SL(2, ℤ) spectral decomposition of the Virasoro primary density of states. An analogy to Berry’s diagonal approximation allows us to extract spectral statistics of individual 2d CFTs by coarse-graining, and to identify signatures of chaos and random matrix universality. This leads to a necessary and sufficient condition for a 2d CFT to display a linear ramp in its coarse-grained spectral form factor.Turning to gravity, AdS3 torus wormholes are cleanly interpreted as diagonal projections of squared partition functions of microscopic 2d CFTs. The projection makes use of Hecke operators. The Cotler-Jensen wormhole of AdS3 pure gravity is shown to be extremal among wormhole amplitudes: it is the minimal completion of the random matrix theory correlator compatible with Virasoro symmetry and SL(2, ℤ)-invariance. We call this MaxRMT: the maximal realization of random matrix universality consistent with the necessary symmetries. Completeness of the SL(2, ℤ) spectral decomposition as a trace formula allows us to factorize the Cotler-Jensen wormhole, extracting the microscopic object ZRMT(τ) from the coarse-grained product. This captures details of the spectrum of BTZ black hole microstates. ZRMT(τ) may be interpreted as an AdS3 half-wormhole. We discuss its implications for the dual CFT and modular bootstrap at large central charge.

Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity.

Optimization of Electron Bunch Characteristics in Bubble Wakefield: Role of Different Linear Upward Density Ramp Profiles

Optimization of Electron Bunch Characteristics in Bubble Wakefield: Role of Different Linear Upward Density Ramp Profiles

Surfactant-free nano-emulsions from two lemongrass essential oils: Investigation of temperature ramp influence

Nano-emulsions are alternatives for incorporation of essential oils in food-products. Despite generation of surfactant-free nano-emulsions is well known (e.g., Ouzo effect) its stabilization is a critical issue. This study shows the behavior of surfactant-free nano-emulsions prepared with two lemongrass essential oils based in dynamic light scattering analysis through exposure to a linear ramp of temperature. The gas-chromatography coupled to mass-spectrometry analysis revealed that β-myrcene was found in the Cymbopogon citratus and absent in C. flexuosus. C. citratus nano-emulsion prepared with deionized water (CCNE-DW) presented initial lower size diameter (208.6 ± 1.9 nm) than C. flexuosus nano-emulsion (245.2 ± 3.1 nm) prepared with deionized water (CFNE-DW), probably due to the presence of β-myrcene capable of avoiding a rapid droplet growth before onset of dynamic light scattering measurements. In silico physicochemical properties suggest that β-myrcene could considered decisive for low size of C. citratus nano-emulsions, since reduction of its concentration may induce destabilization of C. citratus diluted nano-emulsions. Similar initial droplet size was observed for C. citratus nano-emulsion (221.0 ± 1.3 nm) prepared with infusion (CCNE-IN) and C. flexuosus nano-emulsion (215.7 ± 1.7 nm) prepared with infusion (CFNE-IN). The highest droplet reduction was observed for CFNE-DW (DR25–80ºC = 45.9 %; p<0.0001). Distinct phytochemical profile evidenced by 1H NMR, since C. citratus infusion shows an envelope of signals with more overlapped peaks between the chemical shifts at δH 3.5 – 4.0 ppm, may favored solubilization of droplet components by the infusion and responsible by droplet growth of diluted nano-emulsions, in addition to decrease of β-myrcene content. Our results show the feasibility of preparation of surfactant-free nano-emulsions from two lemongrass and contribute to better knowledge related to influence of chemical profiles in natural-product based nano-emulsions.

Electron-beam-driven plasma wakefield acceleration of photons

The paper [R .T. Sandberg and A. G. R. Thomas, Phys. Rev. Lett. 130, 085001 (2023)] proposed a scheme to generate ultrashort, high energy pulses of XUV photons through dephasingless photon acceleration in a beam-driven plasma wakefield. An ultrashort laser pulse is placed in the plasma wake behind a relativistic electron bunch so that it experiences a density gradient and therefore shifts up in frequency. Using a tapered density profile provides phase-matching between the driver and witness pulses. In this paper, we study via particle-in-cell simulation the limits, practical realization, and 3D considerations for beam-driven photon acceleration using the tapered plasma density profile. We study increased efficiency by the use of a chirped drive pulse, establishing the necessity of the density profile shape we derived as opposed to a simple linear ramp, but also demonstrating that a piecewise representation of the profile—as could be experimentally achieved by a series of gas cells—is adequate for achieving phase matching. Scalings to even higher frequency shifts are given.