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At least 325 records · Page 18

Elastic Changepoint Detection for Globally-indexed Functional Time Series Data with Climate Applications

Changepoint detection is a vital tool in the application of climate data analysis. Numerous types of climate observation data are most properly represented by functional time series, implying a need for accurate changepoint detection methods applicable to functional time series data. Such data taken at a global scale often contain both spatial heterogeneity and dependence as well as phase (time) misalignment. In this report, we present methods which can detect spatially-dependent changepoints while allowing different estimates of change time and change strength depending on location. Additionally, we provide extensions to this spatially-predicted model which controls for phase variability among observations. Our methods provide the ability to detect a single change, or control for epidemic changes (where a “return-to-normal” change is more likely to be detected than the initial change). We showcase results analyzing the June 1991 eruption of Mt. Pinatubo, where our methods demonstrate the ability to accurately detect both single and epidemic changepoints even in the presence of strong seasonal variability. We find that our spatially-predicted model improves the detection of relevant changepoints versus methods which do not take spatial information into account, and we find that controlling for phase variability helps to control the false discovery rate during the detection process.

54 ENVIRONMENTAL SCIENCES↗

Identification and overexpression of endogenous transcription factors to enhance lipid accumulation in the biotechnologically relevant species Chlamydomonas pacifica

Sustainable low-carbon energy solutions are critical to mitigating global carbon emissions. Algae-based platforms offer potential by converting carbon dioxide into valuable products while aiding carbon sequestration. However, scaling algae cultivation faces challenges like contamination in outdoor systems. Previously, our lab evolved Chlamydomonas pacifica, an extremophile green alga, which tolerates high temperature, pH, salinity, and light, making it ideal for large-scale bioproduct production, including biodiesel. Here, we enhanced lipid accumulation in evolved C. pacifica by identifying and overexpressing key endogenous transcription factors through genome-wide in-silico analysis and in-vivo testing. These factors include Lipid Remodeling Regulator 1 (CpaLRL1), Nitrogen Response Regulator 1 (CpaNRR1), Compromised Hydrolysis of Triacylglycerols 7 (CpaCHT7), and Phosphorus Starvation Response 1 (CpaPSR1). Under nitrogen deprivation, CpaLRL1, CpaNRR1, and CpaCHT7 overexpression enhanced lipid accumulation compared to wild-type. However, CpaPSR1 increased lipid accumulation compared to wild-type in normal media and did not increase further under nitrogen deprivation, highlighting the difference in function based on media conditions. Notably, lipid analysis of CpaPSR1 under normal media conditions revealed a 2.4-fold increase in triglycerides (TAGs) compared to the wild-type, highlighting its potential for biodiesel production. This approach provides a framework for transcription factor-focused metabolic engineering in algae, advancing bioenergy and biomaterial production.

Biofuels↗

A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data

Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.

Astronomy & Astrophysics↗

The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics

The current generation of large galaxy surveys will test the cosmological model by combining multiple types of observational probes. Realising the statistical promise of these new datasets requires rigorous attention to all aspects of analysis including cosmological measurements, modelling, covariance and parameter likelihood. In this paper we present the results of an end-to-end simulation study designed to test the analysis pipeline for the combination of the Dark Energy Spectroscopic Instrument (DESI) Year 1 galaxy redshift dataset and separate weak gravitational lensing information from the Kilo-Degree Survey, Dark Energy Survey and Hyper-Suprime-Cam Survey. Our analysis employs the 3x2-pt correlation functions including cosmic shear and galaxy-galaxy lensing, together with the projected correlation function of the spectroscopic DESI lenses. We build realistic simulations of these datasets including galaxy halo occupation distributions, photometric redshift errors, weights, multiplicative shear calibration biases and magnification. We calculate the analytical covariance of these correlation functions including the Gaussian, noise and super-sample contributions, and show that our covariance determination agrees with estimates based on the ensemble of simulations. We use a Bayesian inference platform to demonstrate that we can recover the fiducial cosmological parameters of the simulation within the statistical error margin of the experiment, investigating the sensitivity to scale cuts. This study is the first in a sequence of papers in which we present and validate the large-scale 3x2-pt cosmological analysis of DESI-Y1.

79 ASTRONOMY AND ASTROPHYSICS↗

Defect-Limited Mobility and Defect Thermochemistry in Mixed A-Cation Tin Perovskites: (CH3NH3)1-xCsxSnBr3

Hybrid organic-inorganic semiconductors crystallizing in the perovskite structure present a significant opportunity for realizing defect-tolerant semiconductors. In this work, we examine the solid solution, (CH3NH3)1-xCsxSnBr3, and identify the thermochemistry dictating the intrinsic carrier concentrations and how local structural distortions influences this electronic behavior. This family of compounds exhibits the expected systematic trend in decreasing optical gap with the cesium to methylammonium A-site mixing ratio, x, in the visible region. However, the carrier mobility, as determined from time-resolved microwave conductivity measurements, trends opposite to that expected from first-principles calculations combined with Boltzmann scattering theory calculations of the carrier mobility. We propose that this is a result of increasing carrier scattering with x in (CH3NH3)1-xCsxSnBr3 due to a significant increase in the carrier density with x. By examining the dependence of the carrier density as a function of x, we infer the compositional-dependence of the average enthalpy and nonconfigurational entropy per defect. While diffraction reveals a cubic aristotypic perovskite structure as a function of x at room temperature, the pair distribution functions obtained from synchrotron X-ray total scattering from these materials are better described by symmetry-adapted displacement modes of the Pm3m crystal structure, which we attribute to a large degree of anharmonic dynamics of the atom positions. This analysis shows that CH3NH3+-rich compositions retain mostly linear Sn-Br-Sn bonding environments through the displacements, while Cs+-rich compositions lead to more significantly bent Sn-Br-Sn environments. We propose that these bent bonding arrangements in Cs-rich compositions yield a higher propensity for defect formation. This also provides a rationale for carrier trapping that gives rise to anomalous microwave transients. Together, these results provide insight into the structure-dynamics-properties relationships in this highly anharmonic system with high amplitude atomic motions and low defect formation energies.

defect thermochemistry↗

An Analytical Tool to Evaluate Defect Thermodynamics of (La,Ba)Fe1-xMxO3-δ Perovskites for Solid-Oxide Cell Applications

A modeling tool of the defect thermodynamics of (La,Ba)Fe1-xMxO3-δ perovskites which includes energetic information about oxygen vacancy formation, hydration, hydride formation, and charge disproportionation reactions has been developed1. This tool incorporates defect energies and entropies expressed as sixth order polynomial functions to allow refinements of the defect reaction equilibrium constants in the thermodynamic analysis. Calculation of (La,Ba)Fe1-xMxO3-δ Brouwer diagrams as a function of pO2/pH2O and pH2/H2O in a range of temperatures of interest is facilitated by this modeling tool. The results obtained can provide direct guidance how the electronic and ionic defect concentrations of the triple conducting perovskite materials can be used to optimize performance of solid oxide cells for energy applications. The impact of magnetic and electronic structures of the perovskites on the defect reaction energies and entropies as obtained from density function theory modeling and the role played by hydride defect species will also be discussed.

Lee, Yueh-Lin↗

Network analysis of memristive device circuits: dynamics, stability and correlations

Abstract Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the information-processing of neurons. The resistance in a memristive device depends on the history of the applied bias and thus displays a type of memory. The interplay of this memory with the dynamic properties of the network can give rise to new behavior, offering many fascinating theoretical challenges. But methods to analyze general memristive circuits are not well described in the literature. In this paper we develop a general circuit analysis for networks that combine memristive devices alongside resistors, capacitors and inductors and under various types of control. We derive equations of motion for the memory parameters of these circuits and describe the conditions for which a network should display properties characteristic of a resonator system. For the case of a purely memresistive network, we derive Lyapunov functions, which can be used to study the stability of the network dynamics. Surprisingly, analysis of the Lyapunov functions show that these circuits do not always have a stable equilibrium in the case of nonlinear resistance and window functions. The Lyapunov function allows us to study circuit invariances, wherein different circuits give rise to similar equations of motion, which manifest through a gauge freedom and node permutations. Finally, we identify the relation between the graph Laplacian and the operators governing the dynamics of memristor networks operators, and we use these tools to study the correlations between distant memristive devices through the effective resistance.

97 MATHEMATICS AND COMPUTING↗

Exploring the effects of molecular beam epitaxy growth characteristics on the temperature performance of state-of-the-art terahertz quantum cascade lasers

This study conducts a comparative analysis, using non-equilibrium Green’s functions (NEGF), of two state-of-the-art two-well (TW) Terahertz Quantum Cascade Lasers (THz QCLs) supporting clean 3-level systems. The devices have nearly identical parameters and the NEGF calculations with an abrupt-interface roughness height of 0.12 nm predict a maximum operating temperature (T max ) of ~ 250 K for both devices. However, experimentally, one device reaches a T max of ~ 250 K and the other a T max of only ~ 134 K. Both devices were fabricated and measured under identical conditions in the same laboratory, with high quality processes as verified by reference devices. The main difference between the two devices is that they were grown in different MBE reactors. Our NEGF-based analysis considered all parameters related to MBE growth, including the maximum estimated variation in aluminum content, growth rate, doping density, background doping, and abrupt-interface roughness height. From our NEGF calculations it is evident that the sole parameter to which a drastic drop in T max could be attributed is the abrupt-interface roughness height. We can also learn from the simulations that both devices exhibit high-quality interfaces, with one having an abrupt-interface roughness height of approximately an atomic layer and the other approximately a monolayer. However, these small differences in interface sharpness are the cause of the large performance discrepancy. This underscores the sensitivity of device performance to interface roughness and emphasizes its strategic role in achieving higher operating temperatures for THz QCLs. We suggest Atom Probe Tomography (APT) as a path to analyze and measure the (graded)-interfaces roughness (IFR) parameters for THz QCLs, and subsequently as a design tool for higher performance THz QCLs, as was done for mid-IR QCLs. Our study not only addresses challenges faced by other groups in reproducing the record T max of ~ 250 K and ~ 261 K but also proposes a systematic pathway for further improving the temperature performance of THz QCLs beyond the state-of-the-art.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Multilabel proportion prediction and out-of-distribution detection on gamma spectra of short-lived fission products

In the machine learning problem of multilabel classification, the objective is to determine for each test instance which classes the instance belongs to. In this work, we consider an extension of multilabel classification, called multilabel proportion prediction, in the context of radioisotope identification (RIID) using gamma spectra data. We aim to not only predict radioisotope proportions, but also identify out-of-distribution (OOD) spectra. We achieve this goal by viewing gamma spectra as discrete probability distributions, and based on this perspective, we develop a custom semi-supervised loss function that combines a traditional supervised loss with an unsupervised reconstruction error function. Our approach was motivated by its application to the analysis of short-lived fission products from spent nuclear fuel. In particular, we demonstrate that a neural network model trained with our loss function can successfully predict the relative proportions of 37 radioisotopes simultaneously. The model trained with synthetic data was then applied to measurements taken by Pacific Northwest National Laboratory (PNNL) to conduct analysis typically done by subject-matter experts. Here, we also extend our approach to successfully identify when measurements are OOD, and thus should not be trusted, whether due to the presence of a novel source or novel proportions.

Anomaly detection↗

Free Energy and Flexibility Analysis of Autoinhibited Human BRAF

The RAF serine/threonine protein kinases function as direct effectors of RAS in the intracellular transmission of extracellular growth signals, and they are key targets for drug discovery, given the high incidence of oncogenic mutations in RAF and other components of this signaling pathway. In its inactive state, RAF is held in an autoinhibited conformation in the cytosol through a combination of intramolecular interactions and binding to a regulatory 14−3−3 protein dimer. Activation of RAF is initiated by its interaction with membrane-localized GTP-bound RAS, which induces conformational changes that release RAF from its autoinhibited state. However, the molecular mechanisms governing RAF activation remain incomplete, largely due to the challenges in experimentally capturing the intermediate conformational states in this process. To address this gap, we developed a comprehensive all-atom model of BRAF based on existing cryo-EM structures. Using this model, we performed extensive molecular dynamics simulations to evaluate the stability and free energy landscape of autoinhibited BRAF in solution. Our analysis reveals conformational flexibility within the autoinhibited complex, suggesting that this dynamic behavior may play a role in facilitating BRAF activation upon engagement with the membrane-bound RAS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dark Energy Survey: DESI-independent angular BAO measurement

In this work, we present a measurement of the angular baryon acoustic oscillation (BAO) scale from the completed Dark Energy Survey (DES) dataset excluding the area of overlap with the Dark Energy Spectroscopic Instrument (DESI). We follow the same methodology and validation process as in the DES Y6 BAO analysis. We interpret the impact of this measurement in the context of the statistical preference for 𝑤 0 ⁢𝑤 𝑎 cold dark matter (CDM) over Λ⁢CDM when combined with DES Y5 Type Ia supernovae (SN), Planck CMB, and DESI BAO. Based on our previous work, using the full Y6 DES BAO sample, in combination with SN, CMB and DESI data release 1 (DR1) BAO, added 0.3⁢𝜎 in this preference (from 3.7⁢𝜎 to 4.0⁢𝜎), but this ignored possible correlations between datasets. Using our new DESI-independent DES BAO likelihood instead, we find a smaller increase in the statistical preference for 𝑤 0 ⁢𝑤 𝑎 ⁢CDM, from 3.7⁢𝜎 to 3.8⁢𝜎 when using DESI DR1 BAO, and from 4.0⁢𝜎 to 4.1⁢𝜎 when updating to the more recent DESI data release 2 (DR2) BAO. These significances reduce to 3.1⁢𝜎 when using the new calibrated DES SN-Dovekie. Alongside this work, we publicly release baofit_wtheta, the BAO fitting code for the angular correlation function used in the DES Y6 BAO analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

A Principled Framework to Assess the Information-Theoretic Fitness of Brain Functional Sub-Circuits

In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects’ functional connectomes (FCs) without adequately assessing the information-theoretic appropriateness of the partition. Another practice that goes unchallenged is thresholding weighted FCs to remove spurious connections without justifying the chosen threshold. This paper leverages recent theoretical advances in Stochastic Block Models (SBMs) to formally define and quantify the information-theoretic fitness (e.g., prominence) of a predetermined set of FNs when mapped to individual FCs under different fMRI task conditions. Our framework allows for evaluating any combination of FC granularity, FN partition, and thresholding strategy, thereby optimizing these choices to preserve the important topological features of the human brain connectomes. By applying to the Human Connectome Project with Schaefer parcellations at multiple levels of granularity, the framework showed that the common thresholding value of 0.25 was indeed information-theoretically valid for group-average FCs, despite its previous lack of justification. Our results pave the way for the proper use of FNs and thresholding methods, and provide insights for future research in individualized parcellations.

Duong-Tran, Duy (ORCID:0009000944967575)↗

Automated Scoring of Morphological Changes in Images of Pentaerythritol Tetranitrate

Recent advances in characterization techniques that generate large datasets of material microstructure images require robust, automated image-processing. We applied an unsupervised anomaly detection method called feature anomaly detection system (FADS) to automatically detect and quantify microstructure changes in images of the explosive pentaerythritol tetranitrate (PETN) aged at various temperatures. We demonstrated the FADS approach on two-dimensional images extracted from computed tomography scans, but the same technique can be readily applied to other imaging modalities. FADS calculates anomaly scores on the basis of differences in filter activations of nominal and test data in pretrained convolutional neural networks. The FADS scores successfully differentiated between pristine PETN and PETN aged at a temperature where material coarsening occurred. Morphological metric analysis of segmented images verified observed trends in FADS scores as a function of aging temperature and aging time, specifically by calculating volume fractions, specific boundary lengths, two-point correlation functions, and local thicknesses. Here, the FADS technique has two important advantages compared to traditional morphological analysis: First, it uses grayscale images as input, rather than images that are segmented to separate the appropriate phases; and second, FADS scores capture any type of changes among image sets, rather than requiring prior knowledge or selection of a relevant set of metrics.

Accelerated aging↗

DESI DR1 Ly$α$ forest: 3D full-shape analysis and cosmological constraints

We perform an analysis of the full shapes of Lyman-$α$ (Ly$α$) forest correlation functions measured from the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). Our analysis focuses on measuring the Alcock-Paczynski (AP) effect and the cosmic growth rate times the amplitude of matter fluctuations in spheres of $8$$h^{-1}\text{Mpc}$, $fσ_8$. We validate our measurements using two different sets of mocks, a series of data splits, and a large set of analysis variations, which were first performed blinded. Our analysis constrains the ratio $D_M/D_H(z_\mathrm{eff})=4.525\pm0.071$, where $D_H=c/H(z)$ is the Hubble distance, $D_M$ is the transverse comoving distance, and the effective redshift is $z_\mathrm{eff}=2.33$. This is a factor of $2.4$ tighter than the Baryon Acoustic Oscillation (BAO) constraint from the same data. When combining with Ly$α$ BAO constraints from DESI DR2, we obtain the ratios $D_H(z_\mathrm{eff})/r_d=8.646\pm0.077$ and $D_M(z_\mathrm{eff})/r_d=38.90\pm0.38$, where $r_d$ is the sound horizon at the drag epoch. We also measure $fσ_8(z_\mathrm{eff}) = 0.37\; ^{+0.055}_{-0.065} \,(\mathrm{stat})\, \pm 0.033 \,(\mathrm{sys})$, but we do not use it for cosmological inference due to difficulties in its validation with mocks. In $Λ$CDM, our measurements are consistent with both cosmic microwave background (CMB) and galaxy clustering constraints. Using a nucleosynthesis prior but no CMB anisotropy information, we measure the Hubble constant to be $H_0 = 68.3\pm 1.6\;\,{\rm km\,s^{-1}\,Mpc^{-1}}$ within $Λ$CDM. Finally, we show that Ly$α$ forest AP measurements can help improve constraints on the dark energy equation of state, and are expected to play an important role in upcoming DESI analyses.

Cuceu, Andrei [LBL, Berkeley; Chicago U., KICP] (O↗

Joint cosmological fits to DESI-DR1 full-shape clustering and weak gravitational lensing in configuration space

We present a joint $3\times2$-pt cosmological analysis of auto- and cross-correlations between the Dark Energy Spectroscopic Instrument Data Release 1 (DESI-DR1) Bright Galaxy Survey (BGS) and Luminous Red Galaxy (LRG) samples and overlapping shear measurements from the KiDS-1000, DES-Y3 and HSC-Y3 weak lensing surveys. We perform our analysis in configuration space and, in addition to the cosmic shear correlation functions for each weak lensing dataset, we fit the tangential shear of the weak lensing source galaxies around DESI lens galaxies. Finally, we make use of the anisotropic BGS and LRG clustering information by fitting the full shape of the two-point correlation function multipoles measured over the full DESI-DR1 footprint, presenting the first full-shape analysis of DESI measurements in configuration space. We find that the addition of weak lensing information serves to improve, with respect to the clustering-only case, the measurements of the power spectrum amplitude parameters $\ln(10^{10}A_{\rm{s}})$ and $σ_{12}$ by $15\%$ and $36\%$, respectively. It also improves measurements of the linear bias of the lens galaxies by $15-20\%$, depending on the tracer. Our results show excellent consistency, regardless of the weak lensing survey considered, and are furthermore consistent with a companion analysis that fits $3\times2$-pt correlations including DESI projected clustering measurements, as well as the results published by the weak lensing collaborations themselves. Our measured values for weak lensing amplitude are $S_{8}^{\mathrm{DESI\times HSC}}=0.787\pm0.020$, $S_{8}^{\mathrm{DESI\times DES}}=0.791\pm0.016$, $S_{8}^{\mathrm{DESI\times KiDS}}=0.771\pm0.017$, which are $1.9σ-2.9σ$ below the $S_8$ value preferred by Planck. Finally, our clustering-only results are in good agreement with the Fourier space full-shape analysis of all DESI tracers.

Semenaite, A. [Swinburne U., Ctr. Astrophys. Super↗

Large-signal Stability Analysis of Grid-forming Inverters with Equivalent-circuit Models

Here, this paper proposes an energy function-based direct method for large-signal stability assessment of grid-forming (GFM) inverters leveraging an equivalent-circuit representation of all involved control- and physical-layer dynamics. Three different primary controls, a standard inner-current outer-voltage cascaded-control architecture, output LCL filter, and reference-current saturation limiting are featured in the modeling and analysis framework. A composite energy function for the GFM inverter is obtained by summing up individual energy contributions gleaned from the circuit representation. The approach can readily be generalized to different primary controls, output-filter arrangements, and current limiters since it is based on a circuit-theoretic foundation. Numerical simulations validate the efficacy of the approach in estimating the critical clearing time following a large-signal disturbance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters

Understanding structure-property relationships is foundational to numerous modern chemistries, such as proton-coupled electron transfer (PCET). However, an experimentally measured property is the result of the behavior from an ensemble of molecules. Neglecting ensemble effects, especially under complex chemical environments, may obfuscate these relationships and lead to discrepancies between theory and experiment. In this work, we demonstrate the impact of configurational entropy and local chemical environments on hydroxide bond dissociation free energies [BDFE- (O−H)] for a set of polyoxovanadate nanoclusters, at ambient conditions. The O−H bond strengths are investigated via density functional theory (DFT) coupled with statistical thermodynamic analysis and bilinear modeling, and compared with previous experimental results on the same systems, namely electrochemical solutions of: [V 6 O 13−x (OH) x (TRIOL R ) 2 ] −2 (x = 2, 4, 6; R = NO 2 , Me) and [V 6 O 11−x (OMe) 2 (OH) x (TRIOL NO 2 ) 2 ] −2 (x = 2, 4). Interestingly, we find that ensemble effects, even at room temperature, can account for a significant portion of the BDFE(O−H) trend with the degree of reduction via H atom binding, which cannot be fully captured by single-structure, static DFT calculations. Moreover, we find that the ensemble effects may be replicated statistically, requiring only enumeration of energetically accessible H-binding sites. With the ensemble effects resolved, we present a simple bilinear model to reconcile remaining biases between experiment and ensemble-informed theory, which corelate with clusterspecific electronic environment differences. The bilinear model achieves outstanding accuracy vs experiments with a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical characteristics of hydrogen interaction with polyoxometalates, we present a simple methodology that captures the BDFE(O−H) trend while dramatically reducing required DFT calculations by 98% and achieving accuracy within 1 kcal/mol. Overall, this work elucidates the roles and structural origins of configurational entropy and chemical effects on polyoxometalate hydroxide bond energies, with potential applicability to various atomically precise metal oxide systems. Importantly, it introduces models for rapid and highly accurate property calculations in connection with experiments.

Cluster chemistry↗

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗