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The response field and the saddle points of quantum mechanical path integrals

Highlights: • Moyal quantum mechanics and Marinov’s path integral. • Classical and semiclassical limits of Marinov’s path integral. • Oscillating functional integrals. • Instantons of the Marinov’s path integral. In quantum statistical mechanics, Moyal’s equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal’s equation is given by Marinov’s path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov’s integral, plays for pure states even. The discussion focuses on how the integral’s semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov’s integral based upon the concept of “Airy averaging”, a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued (“Wick rotated”) response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Understanding the transient large amplitude oscillatory shear behavior of yield stress fluids

A full understanding of the sequence of processes exhibited by yield stress fluids under large amplitude oscillatory shearing is developed using multiple experimental and analytical approaches. A novel component rate Lissajous curve, where the rates at which strain is acquired unrecoverably and recoverably are plotted against each other, is introduced and its utility is demonstrated by application to the analytical responses of four simple viscoelastic models. Using the component rate space, yielding and unyielding are identified by changes in the way strain is acquired, from recoverably to unrecoverably and back again. The behaviors are investigated by comparing the experimental results with predictions from the elastic Bingham model that is constructed using the Oldroyd–Prager formalism and the recently proposed continuous model by Kamani, Donley, and Rogers in which yielding is enhanced by rapid acquisition of elastic strain. The physical interpretation gained from the transient large amplitude oscillatory shear (LAOS) data is compared to the results from the analytical sequence of physical processes framework and a novel time-resolved Pipkin space. The component rate figures, therefore, provide an independent test of the interpretations of the sequence of physical processes analysis that can also be applied to other LAOS analysis frameworks. Each of these methods, the component rates, the sequence of physical processes analysis, and the time-resolved Pipkin diagrams, unambigiously identifies the same material physics, showing that yield stress fluids go through a sequence of physical processes that includes elastic deformation, gradual yielding, plastic flow, and gradual unyielding.

Kamani, Krutarth M. (ORCID:0000000338975420)↗

The Electromagnetic Characteristics of the Tianlai Cylindrical Pathfinder Array

A great challenge for 21 cm intensity mapping experiments is the strong foreground radiation which is orders of magnitude brighter than the 21 cm signal. Removal of the foreground takes advantage of the fact that its frequency spectrum is smooth while the redshifted 21 cm signal spectrum is stochastic. However, a complication is the non-smoothness of the instrument response. This paper describes the electromagnetic simulation of the Tianlai cylinder array, a pathfinder for 21 cm intensity mapping experiments. Due to the vast scales involved, a direct simulation requires a large amount of computing resources. We have made the simulation practical by using a combination of methods: first simulate a single feed, then an array of feed units, finally with the feed array and a cylindrical reflector together, obtain the response for a single cylinder. We studied its radiation pattern, bandpass response and the effects of mutual coupling between feed units, and compared the results with observation. Many features seen in the measurement result are reproduced well in the simulation, especially the oscillatory features which are associated with the standing waves on the reflector. The mutual coupling between feed units is quantified with S-parameters, which decrease as the distance between the two feeds increases. Based on the simulated S-parameters, we estimate the correlated noise which has been seen in the visibility data, and the results show very good agreement with the data in both magnitude and frequency structures. These results provide useful insights on the problem of 21 cm signal extraction for real instruments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE↗

Rheology guiding the design and printability of aqueous colloidal composites for additive manufacturing

Vat photopolymerization (VP) and direct ink write (DIW) additive manufacturing (AM) provide complex geometries with precise spatial control employing a vast array of photo-reactive polymeric systems. Although VP is recognized for superior resolution and surface finish, DIW provides versatility for higher viscosity systems. However, each AM platform presents specific rheological requirements that are essential for successful 3D printing. First, viscosity requirements constrain VP polymeric materials to viscosities below 10 Pa s. Thus, this requirement presents a challenging paradox that must be overcome to attain the physical performance of high molecular weight polymers while maintaining suitable viscosities for VP polymeric materials. Second, the necessary rheological complexity that is required for DIW pastes requires additional rheological measurements to ensure desirable thixotropic behavior. Further, this manuscript describes the importance of rheological measurements when designing polymeric latexes for AM. Latexes effectively decouple the dependency of viscosity on molecular weight, thus enabling high molecular weight polymers with low viscosities. Photo-crosslinking of water-soluble monomers and telechelic oligomeric diacrylates in the presence of the latex enables the fabrication of a scaffold, which is restricted to the continuous aqueous phase and effectively surrounds the latex nanoparticles enabling the printing of otherwise inaccessible high molecular weight polymers. Rheological testing, including both steady and oscillatory shear experiments, provides insights into system properties and provides predictability for successful printing. This perspective article aims to provide an understanding of both chemical functionality (photo- and thermal-reactivity) and rheological response and their importance for the successful design and evaluation of VP and DIW processable latex formulations.

36 MATERIALS SCIENCE↗

Additive friction stir deposition induced stress ripples in aluminum alloy

In additive manufacturing, modification of the viscosity of softened or molten metal plays a significant role in the development of mechanical properties distribution. Similar to soft polymers, molten or softened metal usually exhibits vastly different viscoelastic properties. During scratching tests, viscoelastic polymers undergo spatiotemporal stress development and relaxation, causing stress ripples to form on their surfaces. Here, it is observed that friction stir-based solid-state manufacturing can yield similar stress ripples on softened aluminum alloys due to the linear motion of the deposition tool. Softened aluminum alloys exhibit viscoelastic and viscoplastic responses similar to polymeric material during the solid-state deposition process. In the final product, residual stress ripples appear on the surface of the metal alloy due to periodic residual stress relaxation, leading to oscillatory behavior from the bulk mechanical properties of the material. The orientation of the in-built stress pattern formed in the bulk of the additively manufactured metal alloy underneath the visually evident onion ring-like surface pattern formation is diametrically in the opposite direction. The experimentally observed results are consistent with analytical calculation and numerical simulations in terms of behaviors.

36 MATERIALS SCIENCE↗

Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current

ABSTRACT Nonlinear responses of superconductors to intense terahertz radiation has been an active research frontier. Using terahertz pump-terahertz probe spectroscopy, we investigate the c-axis nonlinear optical response of a high-temperature superconducting cuprate. After excitation by a single-cycle terahertz pump pulse, the reflectivity of the probe pulse oscillates as the pump-probe delay is varied. Interestingly, the oscillatory central frequency scales linearly with the probe frequency, a fact widely overlooked in pump-probe experiments. By theoretically solving the nonlinear optical reflection problem on the interface, we show that our observation is well explained by the Josephson-type third-order nonlinear electrodynamics, together with the emission coefficient from inside the material into free space. The latter results in a strong enhancement of the emitted signal whose physical frequency is around the Josephson plasma edge. Our result offers a benchmark for and new insights into strong-field terahertz spectroscopy of related quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Extracting the Frequency-Dependent Dynamic Stokes Shift from Two-Dimensional Electronic Spectra with Prominent Vibrational Coherences

The dynamic Stokes shift is a common means for characterizing ultrafast solvation dynamics of electronically excited states. Here we extract the excitation frequency-dependent dynamic Stokes shift from two-dimensional electronic spectra (2DES) of cresyl violet, a molecule with a well-defined vibronic progression. The extracted dynamic Stokes shift function, S(t), exhibits oscillatory behavior, and the oscillatory components are assigned to intramolecular vibrational modes through DFT and TD-DFT calculations. Here, the well-characterized oscillations are incorporated into the fitting procedure of S(t). The excitation frequency dependence of the ultrafast response is examined through the analysis of S(t) obtained from slices taken at different excitation frequencies of the 2DES spectra. The extracted ultrafast timescales range from 36 to 98 fs, and we interpret the frequency dependence of the timescales in the context of other dynamic processes that also lead to lineshape changes in the 2DES spectrum, such as vibrational energy relaxation and spectral diffusion. Through comparison of the extracted timescales, we find that the fastest timescales are extracted over a range of excitation frequencies, where contributions from vibrational relaxation and spectral diffusion can be minimized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Driven responses of periodically patterned superconducting films

Here, we simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density J c , the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f 0 , which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Distributed Acoustic Sensing as a Distributed Hydraulic Sensor in Fractured Bedrock

Distributed acoustic sensing (DAS) was originally intended to measure oscillatory strain at frequencies of 1 Hz or more on a fiber optic cable. Recently, measurements at much lower frequencies have opened the possibility of using DAS as a dynamic strain sensor in boreholes. A fiber optic cable mechanically coupled to a geologic formation will strain in response to hydraulic stresses in pores and fractures. A DAS interrogator can measure dynamic strain in the borehole, which can be related to fluid pressure through the mechanical compliance properties of the formation. Because DAS makes distributed measurements, it is capable of both locating hydraulically active features and quantifying the fluid pressure in the formation. We present field experiments in which a fiber optic cable was mechanically coupled to two crystalline rock boreholes. The formation was stressed hydraulically at another well using alternating injection and pumping. The DAS instrument measured oscillating strain at the location of a fracture zone known to be hydraulically active. Rock displacements of less than 1 nm were measured. Laboratory experiments confirm that displacement is measured correctly. These results suggest that fiber optic cable embedded in geologic formations may be used to map hydraulic connections in three-dimensional fracture networks. A great advantage of this approach is that strain, an indirect measure of hydraulic stress, can be measured without beforehand knowledge of flowing fractures that intersect boreholes. The technology has obvious applications in water resources, geothermal energy, CO 2 sequestration, and remediation of groundwater in fractured bedrock.

54 ENVIRONMENTAL SCIENCES↗

Lattice-scale variations in viscosity are correlated with solution structure at mineral-water interfaces

At solid-liquid interfaces, the viscosity increases markedly from the bulk due to the collective interactions of ions and water molecules, influencing phenomena relevant to nanofluidics, colloidal dynamics, and electrochemistry. Here, in this study, we investigated dissipative forces at the boehmite-water interface using 3D atomic force microscopy. We observed an increase in interfacial solution viscosity, η, by 10-100-fold as the nanoprobe approached the surface in normal direction, with up to four oscillatory features showing average peaks of η/η bulk = 44-71. Moreover, the viscosity showed sub-nanometer variations within 0.5 nm from the interface, templated by the underlying crystal lattice and correlated with the interfacial solution structure. Beyond a near-wall region of approximately 1.2 nm, the dissipative response was comparable to that in bulk solution. Molecular dynamics simulations, along with statistical mechanical analyses, provided details on hydrodynamic structures near the interface. Specifically, the lattice-dependent dissipative responses are correlated with extensive hydrogen bonding by interfacial water molecules, which increased friction, particularly along the [001] direction. These results demonstrate how solution viscosity at mineral-water interfaces is anisotropic and correlated with the local solution structure, providing insights into the dynamics of nanocrystal attachment.

Viscosity↗

Ultrafast Dynamics of Excited Electronic States in Nitrobenzene Measured by Ultrafast Transient Polarization Spectroscopy

We investigate ultrafast dynamics of the lowest singlet excited electronic state in liquid nitrobenzene using ultrafast transient polarization spectroscopy, extending the well-known technique of optical Kerr effect spectroscopy to excited electronic states. The third-order nonlinear response of the excited molecular ensemble is measured using a pair of femtosecond pulses following a third femtosecond pulse that populates the S 1 excited state. By measuring this response, which is highly sensitive to details of the excited state character and structure, as a function of time delays between the three pulses involved, we extract the dephasing time of the wave packet on the excited state. The dephasing time, measured as a function of time delay after pump excitation, shows oscillations indicating oscillatory wave packet dynamics on the excited state. Finally, from the experimental measurements and supporting theoretical calculations, we deduce that the wave packet completely leaves the S 1 state potential energy surface after three traversals of the intersystem crossing between the singlet S 1 and triplet T 2 states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TEAMER: Electrically Engaged Undulation (EEL) System

The Electrically Engaged UnduLation (EEL) system is a buoyancy-driven submersible device for powering oceanographic instruments. Physically, EEL is a slender body whose flexible spine is made up of energy units interconnected by uniaxial hinges. Each unit consists of a pair of piezoelectric elements that converts the bending stress into electrical current to a battery charging circuit. An outer plastic skin forms a seal against water and allows for flexibility at hinge locations. At the top is a bluff body with electronics that holds a ballast for buoyancy adjustment. The bluff body is also responsible for creating fluid instabilities in its wake. When gliding through the water (mode 2), the spine will flex in response to the alternating vortices that shed from the head. This "lock-in" phenomenon occurs when the frequency at which vortices shed resonates with the EEL natural frequency, during which the efficient gaits were found in species of sea snake, eels, and fish. For active propulsion, a single motor can be placed at the first segment and provide the oscillatory input for propulsion similar to a dolphin's kick. Such anguilliform swimming is both efficient and nearly silent compared to a spinning propeller. Ultimately, mimicking bio-locomotion provides a viable path to a drag-reduced, self-propelled energy harvesting system for ocean monitoring.

16 TIDAL AND WAVE POWER↗

Quasi-1D Coulomb Drag in the Nonlinear Regime

One-dimensional Coulomb drag has been an essential tool to probe the physics of interacting Tomonaga-Luttinger liquids. To date, most experimental work has focused on the linear regime while the predictions for Luttinger liquids beyond the linear response theory remain largely untested. In this Letter, we report measurements of reciprocal momentum transfer induced Coulomb drag between vertically coupled quasi-one-dimensional quantum wires in the nonlinear regime. Measurements were performed at ultralow temperatures between wires only 15 nm apart. Our results reveal a nonlinear dependence of the drag voltage as a function of the drive current superimposed with an oscillatory contribution, in agreement with theoretical predictions for Coulomb drag between Tomonaga-Luttinger liquids. Additionally, the observed current-voltage characteristics exhibit a nonmonotonic temperature dependence, further corroborating the presence of non-Fermi-liquid behavior in our system. In conclusion, these findings are observed both in the single and in the multiple subband regimes and in the presence of disorder, extending the onset of this behavior beyond the clean single channel Tomonaga-Luttinger regime where the predictions were originally formulated.

1-dimensional systems↗

A Parametric Reduced-Order Model for Inverter Short-Circuit Response in Protection Studies

This paper presents a reduced-order model (ROM) for grid-following (GFL) inverters that reproduces inverter fault current trajectories, including sub transients, transient, and steady-state phases, across a range of fault types, locations, and pre-fault operating points. . The proposed model is developed by: Constructing the positive- and negative-sequence current with parameterization fitted by large data training and fitting Validating using EMT simulation against EMT full model and demonstrating the ROM's capability to capture fault current magnitude, phase angle, and oscillatory transients. Building a standard EMT simulation platform library component for easy configuration and application.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The relaxation behavior of supercooled and glassy imidacloprid

Employing dielectric spectroscopy, oscillatory shear rheology, and calorimetry, the present work explores the molecular dynamics of the widely used insecticide imidacloprid above and below its glass transition temperature. In its supercooled liquid regime, the applied techniques yield good agreement regarding the characteristic structural (alpha) relaxation times of this material. In addition, the generalized Gemant–DiMarzio–Bishop model provides a good conversion between the frequency-dependent dielectric and shear mechanical responses in its viscous state, allowing for an assessment of imidacloprid’s molecular hydrodynamic radius. In order to characterize the molecular dynamics in its glassy regime, we employ several approaches. These include the application of frequency–temperature superposition (FTS) to its isostructural dielectric and rheological responses as well as use of dielectric and calorimetric physical aging and the Adam–Gibbs–Vogel model. While the latter approach and dielectric FTS provide relaxation times that are close to each other, the other methods predict notably longer times that are closer to those reflecting a complete recovery of ergodicity. In conclusion, this seemingly conflicting dissimilarity demonstrates that the molecular dynamics of glassy imidacloprid strongly depends on its thermal history, with high relevance for the use of this insecticide as an active ingredient in technological applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shear-Induced Conformations of Salt-Free Polyelectrolytes in Semidilute Solutions

Here, we present coarse-grained molecular dynamics simulations of salt-free polyelectrolyte chains in semidilute solutions under simple shear flow, with full hydrodynamic interactions and explicit dipolar solvent. At equilibrium, chain orientation statistics follow a pseudo-Voigt distribution, and the structural correlation length and chain end-to-end vector autocorrelation function exhibit scaling behavior consistent with theoretical predictions for polyelectrolytes. Under shear, chains transition from coiled to stretched states and the end-to-end vector autocorrelation function reveals oscillatory dynamics at high Weissenberg numbers. Analysis of the gyration tensor and shear strain distributions identified three distinct chain populations with directional alignment along and against the shear gradient. Compared with their neutral polymer counterparts, polyelectrolytes exhibit stronger shear thinning and enhanced chain alignment under the same Weissenberg number, which is attributed to electrostatic interactions and shear-induced counterion release. These findings provide molecular insight into the distinct flow response of charged polymers and have implications for tailoring the rheological properties of polyelectrolyte-based materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photoresponsive polymers for carbodiimide-fueled transient hydrogels

Light- and carbodiimide-responsive hydrogels were synthesized. An “AND” gate was developed using ortho-nitrobenzyl (ONB) protected carboxylic acids in the polymer backbone. Crosslinking was only realized in the presence of both UV stimulus to photocleave the ONB group and carbodiimide fuels to induce anhydride bonds. In the presence of water, the anhydride bonds eventually hydrolyze to carboxylic acids and the system returns to the solution state. The mechanical properties of the out-of-equilibrium hydrogels were investigated using oscillatory rheology to examine the effects of deprotection efficiency, carbodiimide concentration and chain architecture on the hydrogels’ moduli and decrosslinking time. Higher moduli and longer decrosslinking times were found with increased carbodiimide concentration and deprotection efficiency. These discoveries unveil new possibilities for photoresponsive chemically fueled soft materials.

36 MATERIALS SCIENCE↗