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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Molten‐Salt‐Mediated Chemical Looping Oxidative Dehydrogenation of Ethane with In‐Situ Carbon Capture and Utilization

Abstract The molten‐salt‐mediated oxidative dehydrogenation (MM‐ODH) of ethane (C 2 H 6 ) via a chemical looping scheme represents an effective carbon capture and utilization (CCU) method for the valorization of ethane‐rich shale gas and concurrent mitigation of carbon dioxide (CO 2 ) emissions. Here, stepwise experimentation with Li 2 CO 3 ‐Na 2 CO 3 ‐K 2 CO 3 (LNK) ternary salts (i) assessed how each component of the LNK mixture impacted ethane MM‐ODH performance and (ii) explored physicochemical and thermodynamic mechanisms behind melt‐induced changes to ethylene (C 2 H 4 ) and carbon monoxide (CO) yields. Of fifteen screened LNK compositions, nine exhibited ethylene yields greater than 50 % at 800 °C while maintaining C 2 H 4 selectivities of 85 % or higher. LNK salts rich in Li 2 CO 3 content yielded more ethylene and CO on average than their counterparts, and net CO 2 capture per cycle reached a maximum of ~75 %. Extended MM‐ODH cycling also demonstrated long‐term stability of a high‐performing LNK medium. Density functional theory (DFT) calculations andab initiomolecular dynamics (AIMD) simulations suggested that the molten salt does not directly activate C 2 H 6 . Meanwhile, an empirical model informed by experimental data and reaction thermodynamics adequately predicted overall MM‐ODH performance from LNK composition and provided insights into the system′s primary drivers.

Chemistry↗
DOE OSTI2012

IPET and FETR: Experimental Approach for Studying Molecular Structure Dynamics by Cryo-Electron Tomography of a Single-Molecule Structure

The dynamic personalities and structural heterogeneity of proteins are essential for proper functioning. Structural determination of dynamic/heterogeneous proteins is limited by conventional approaches of X-ray and electron microscopy (EM) of single-particle reconstruction that require an average from thousands to millions different molecules. Cryo-electron tomography (cryoET) is an approach to determine three-dimensional (3D) reconstruction of a single and unique biological object such as bacteria and cells, by imaging the object from a series of tilting angles. However, cconventional reconstruction methods use large-size whole-micrographs that are limited by reconstruction resolution (lower than 20 Å), especially for small and low-symmetric molecule (,400 kDa). In this study, we demonstrated the adverse effects from image distortion and the measuring tilt-errors (including tilt-axis and tilt-angle errors) both play a major role in limiting the reconstruction resolution. Therefore, we developed a ‘‘focused electron tomography reconstruction’’ (FETR) algorithm to improve the resolution by decreasing the reconstructing image size so that it contains only a single-instance protein. FETR can tolerate certain levels of image-distortion and measuring tilt-errors, and can also precisely determine the translational parameters via an iterative refinement process that contains a series of automatically generated dynamic filters and masks. To describe this method, a set of simulated cryoET images was employed; to validate this approach, the real experimental images from negative-staining and cryoET were used. Since this approach can obtain the structure of a single-instance molecule/particle, we named it individual-particle electron tomography (IPET) as a new robust strategy/approach that does not require a pre-given initial model, class averaging of multiple molecules or an extended ordered lattice, but can tolerate small tilt-errors for high-resolution single ‘‘snapshot’’ molecule structure determination. Thus, FETR/IPET provides a completely new opportunity for a single-molecule structure determination, and could be used to study the dynamic character and equilibrium fluctuation of macromolecules.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Molecular Dynamics Modeling of PPTA Crystals in Aramid Fibers

In this work, molecular dynamics modeling is used to study the mechanical properties of PPTA crystallites, which are the fundamental microstructural building blocks of polymer aramid bers such as Kevlar. Particular focus is given to constant strain rate axial loading simulations of PPTA crystallites, which is motivated by the rate-dependent mechanical properties observed in some experiments with aramid bers. In order to accommodate the covalent bond rupture that occurs in loading a crystallite to failure, the reactive bond order force eld ReaxFF is employed to conduct the simulations. Two major topics are addressed: The rst is the general behavior of PPTA crystallites under strain rate loading. Constant strain rate loading simulations of crystalline PPTA reveal that the crystal failure strain increases with increasing strain rate, while the modulus is not a ected by the strain rate. Increasing temperature lowers both the modulus and the failure strain. The simulations also identify the C N bond connecting the aromatic rings as weakest primary bond along the backbone of the PPTA chain. The e ect of chain-end defects on PPTA micromechanics is explored, and it is found that the presence of a chain-end defect transfers load to the adjacent chains in the hydrogen-bonded sheet in which the defect resides, but does not in uence the behavior of any other chains in the crystal. Chain-end defects are found to lower the strength of the crystal when clustered together, inducing bond failure via stress concentrations arising from the load transfer to bonds in adjacent chains near the defect site. The second topic addressed is the nature of primary and secondary bond failure in crystalline PPTA. Failure of both types of bonds is found to be stochastic in nature and driven by thermal uctuations of the bonds within the crystal. A model is proposed which uses reliability theory to model bonds under constant strain rate loading as components with time-dependent failure rate functions. The model is shown to work well for predicting the onset of primary backbone bond failure, as well as the onset of secondary bond failure via chain slippage for the case of isolated non-interacting chain-end defects.

36 MATERIALS SCIENCE↗
DOE OSTI2010

Lectures on the gauge/string duality with emphasis on spectroscopy

I review recent progress on the connection between string theory and quantum chromo-dynamics in the context of the gauge/string duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics covered include the large-N{sub c} limit of gauge theories, the gravitational description of gauge theory thermodynamics and hydrodynamics, and the physics of quarks and mesons in the quark-gluon plasma.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Selected topics on parton distribution functions

We report recent studies on structure functions of the nucleon and nuclei. First, clustering effects are investigated in the structure function F{sub 2} of {sup 9}Be for explaining an unusual nuclear correction found in a JLab experiment. We propose that high densities created by formation of clustering structure like 2{alpha}+neutron in {sup 9}Be is the origin of the unexpected JLab result by using the antisymmetrized molecular dynamics (AMD). There is an approved proposal at JLab to investigate the structure functions of light nuclei including the cluster structure, so that much details will become clear in a few years. Second, tensor-polarized quark and antiquark distributions are obtained by analyzing HERMES measurements on the structure function b{sub 1} for the deuteron. The result suggests a finite tensor polarization for antiquark distributions, which is an interesting topic for further theoretical and experimental investigations. An experimental proposal exists at JLab for measuring b{sub 1} of the deuteron as a new tensor-structure study in 2010's. Furthermore, the antiquark tensor polarization could be measured by polarized deuteron Drell-Yan processes at hadron facilities such as J-PARC and GSI-FAIR. Third, the recent CDF dijet anomaly is investigated within the standard model by considering possible modifications of the strange-quark distribution. We find that the shape of a dijet-mass spectrum changes depending on the strange-quark distribution. It indicates that the CDF excess could be partially explained as a PDF effect, particularly by the strangeness in the nucleon, within the standard model if the excess at m{sub jj}{approx_equal}140 GeV is not a sharp peak.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

The non-random walk of chiral magnetic charge carriers in artificial spin ice

The flow of magnetic charge carriers (dubbed magnetic monopoles) through frustrated spin ice lattices, governed simply by Coulombic forces, represents a new direction in electromagnetism. Artificial spin ice nanoarrays realise this effect at room temperature, where the magnetic charge is carried by domain walls. Control of domain wall path is one important element of utilizing this new medium. By imaging the transit of domain walls across different connected 2D honeycomb structures we contribute an important aspect which will enable that control to be realized. Although apparently equivalent paths are presented to a domain wall as it approaches a Y-shaped vertex from a bar parallel to the field, we observe a stark non-random path distribution, which we attribute to the chirality of the magnetic charges. These observations are supported by detailed statistical modelling and micromagnetic simulations. The identification of chiral control to magnetic charge path selectivity invites analogy with spintronics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Kinetic Growth of Multicomponent Microcompartment Shells

An important goal of systems and synthetic biology is to produce high value chemical species in large quantities. Microcompartments, which are protein nanoshells encapsulating catalytic enzyme cargo, could potentially function as tunable nanobioreactors inside and outside cells to generate these high value species. Modifying the morphology of microcompartments through genetic engineering of shell proteins is one viable strategy to tune cofactor and metabolite access to encapsulated enzymes. However, this is a difficult task without understanding how changing interactions between the many different types of shell proteins and enzymes affect microcompartment assembly and shape. Here, we use multiscale molecular dynamics and experimental data to describe assembly pathways available to microcompartments composed of multiple types of shell proteins with varied interactions. As the average interaction between the enzyme cargo and the multiple types of shell proteins is weakened, the shell assembly pathway transitions from (i) nucleating on the enzyme cargo to (ii) nucleating in the bulk and then binding the cargo as it grows to (iii) an empty shell. Atomistic simulations and experiments using the 1,2-propanediol utilization microcompartment system demonstrate that shell protein interactions are highly varied and consistent with our multicomponent, coarse-grained model. Furthermore, our results suggest that intrinsic bending angles control the size of these microcompartments. Altogether, our simulations and experiments provide guidance to control microcomparmtent size and assembly by modulating the interactions between shell proteins.

defects↗
DOE OSTI2020

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗
DOE OSTI2025

Extending JuTrack’s capabilities to the FRIB accelerator to enhance online modeling

JuTrack is a Julia-based accelerator modeling and tracking package that utilizes compiler-level automatic differentiation (AD) to enable fast and accurate derivative calculations. While JuTrack provides a solid foundation for beam dynamics simulations, its capabilities must be extended to support the Facility for Rare Isotopes (FRIB) linac. This includes modeling heavy-ion linac accelerator components such as the liquid-lithium charge stripper, which facilitates efficient acceleration by remove electrons from heavy isotopes, and incorporating multi-charge state acceleration tracking, which allows for charge-dependent beam dynamics. These extensions address challenges such as the beam matching and optimization of multi charge state through various accelerating structures and beam-material interaction modeling while maintaining the auto differentiation capability. This work focuses on adapting JuTrack to incorporate these elements, enhancing its online modeling abilities. We present modifications to JuTrack’s framework and demonstrate their performance in FRIB simulations.

Accelerator Physics↗
DOE OSTI2019

Two-phase equation of state for lithium fluoride

Here, we present an equation of state for the solid and liquid phases of lithium fluoride that covers a wide range of conditions from ambient pressure and temperature to the high pressures and temperatures exhibited in shock- and ramp-compression studies. The particular solid phase we have focused on in this work is the B1 phase. We have followed an approach where the pressure and heat-capacity functions of both phases are fit to experimental data and our own quantum molecular dynamics simulations and are then integrated in a thermodynamically consistent way to obtain the corresponding free-energy functions. This approach yields a two-phase equation of state that provides better overall agreement with experimental data than other equations of state for lithium fluoride, such as SESAME 7271v3, LEOS 2240, and the model presented by Smirnov. The last of these is a three-phase equation of state that predicts a B1–B2 transition along the shock Hugoniot at a pressure of about 140 GPa. This solid–solid transition has been a topic of speculation and debate in the literature for over 50 years, culminating in the work of Smirnov, who has developed the only potentially viable equation of state that allows for this transition. We explain why the proposed B1–B2 transition at 140 GPa is not consistent with recent velocimetry data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Cyberattack Detection for Cyber Physical Systems Security–A Preliminary Study.

Cyber-physical systems (CPS) security has become an increasingly important research topic in recent years. Geared towards more advanced cyberattack detection techniques as part of strategies for enhancing the security of CPS, in this paper we propose a machine learning based cyber-attack detection scheme. The proposed scheme is a physical-domain technique; specifically, it assumes the physical measurements of the system carry sufficient information for capturing the system behavior, thus can be used for differentiating normal operation and attacks. CPS are complex in nature and the number of physical measurements available for CPS is often overwhelmingly high. Thus, accurately modeling CPS’ dynamic behavior, more importantly, distinguishing normal and adversary activities based on the large number of physical measurements, can be challenging. To address the challenge, we have focused our research effort on feature engineering, that is, to intelligently derive a set of salient signatures or features from the noisy measurements. We make sure the derived features are more compact and, more importantly, have more discriminant power than the original physical measurements, thus enabling us to achieve more accurate and robust detection performance. To demonstrate the effectiveness of the proposed scheme, in our experimental study we consider gas turbines of combined cycle power plants as the cyberphysical system. Using the data from the high-fidelity simulation we show that our proposed cyberattack detection scheme is able to achieve high detection performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Summary report of the 4th IAEA Technical Meeting on Fusion Data Processing, Validation and Analysis (FDPVA)

The objective of the Fourth Technical Meeting on Fusion Data Processing, Validation and Analysis was to provide a platform during which a set of topics relevant to fusion data processing, validation and analysis are discussed with the view of extrapolating needs to next step fusion devices such as ITER. The validation and analysis of experimental data obtained from diagnostics used to characterize fusion plasmas are crucial for a knowledge-based understanding of the physical processes governing the dynamics of these plasmas. This paper presents the recent progress and achievements in the domain of plasma diagnostics and synthetic diagnostics data analysis (including image processing, regression analysis, inverse problems, deep learning, machine learning, big data and physics-based models for control) reported at the meeting. The progress in these areas highlight trends observed in current major fusion confinement devices. A special focus is dedicated on data analysis requirements for ITER and DEMO with a particular attention paid to artificial intelligence for automatization and improving reliability of control processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Social-ecological network analysis for sustainability sciences: a systematic review and innovative research agenda for the future

Social-ecological network (SEN) concepts and tools are increasingly used in human-environment and sustainability sciences. We take stock of this budding research area to further show the strength of SEN analysis for complex human-environment settings, identify future synergies between SEN and wider human-environment research, and provide guidance about when to use different kinds of SEN approaches and models. We characterize SEN research along a spectrum specifying the degree of explicit network representation of system components and dynamics. We then systematically review one end of this spectrum, what we term ‘fully articulated SEN’ studies, which specifically model unique social and ecological units and relationships. Results show a larger number of papers focus on methodological advancement and applied ends. While there has been some development and testing of theories, this remains an area for future work and would help develop SENs as a unique field of research, not just a method. Authors have studied diverse systems, while mainly focusing on the problem of social-ecological fit alongside a scattering of other topics. There is strong potential, however, to engage other issues central to human-environment studies. Analyzing the simultaneous effects of multiple social, environmental, and coupled processes, change over time, and linking network structures to outcomes are also areas for future advancement. This review provides a comprehensive assessment of (fully articulated) SEN research, a necessary step that can help scholars develop comparable cases and fill research gaps.

environmental governance↗
DOE OSTI2024

Slow thermalization and subdiffusion in $U$(1) conserving Floquet random circuits

Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random U(1) charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin-1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates, (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Furthermore, our results should inform future studies of charge conserving circuits, which are relevant for a wide range of topical theoretical questions.

1-dimensional spin chains↗
DOE OSTI2016

Sanibel Symposium in the Petascale-Exascale Computational Era

The 56 th Sanibel Symposium was held February 14-19 2016 at the King and Prince Hotel, St. Simons Island, GA. It successfully brought quantum chemists and chemical and condensed matter physicists together in presentations, posters, and informal discussions bridging those two communities. The Symposium has had a significant role in preparing generations of quantum theorists. As computational potency and algorithmic sophistication have grown, the Symposium has evolved to emphasize more heavily computationally oriented method development in chemistry and materials physics, including nanoscience, complex molecular phenomena, and even bio-molecular methods and problems. Given this context, the 56 th Sanibel meeting systematically and deliberately had sessions focused on exascale computation. A selection of outstanding theoretical problems that need serious attention was included. Five invited sessions, two contributed sessions (hot topics), and a poster session were organized with the exascale theme. This was a historic milestone in the evolution of the Symposia. Just as years ago linear algebra, perturbation theory, density matrices, and band-structure methods dominated early Sanibel Symposia, the exascale sessions of the 56 th meeting contributed a transformative influence to add structure and strength to the computational physical science community in an unprecedented way. A copy of the full program of the 56 th Symposium is attached. The exascale sessions were Linear Scaling, Non-Adabatic Dynamics, Interpretive Theory and Models, Computation, Software, and Algorithms, and Quantum Monte Carlo. The Symposium Proceedings will be published in Molecular Physics (2017). Note that the Sanibel proceedings from 2015 and 2014 were published as Molecular Physics vol. 114, issue 3-4 (2016) and vol. 113, issue 3-4 (2015) respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Combustion energy frontier research center (CEFRC) final report (August 1, 2009 – July 31, 2016)

The Combustion Energy Frontier Research Center (CEFRC) was established to tackle the single overarching grand challenge of energy sustainability, energy security and global warming: to develop a “validated, predictive, multi-scale, combustion modeling capability to optimize the design and operation of evolving fuels in advanced engines for transportation applications,” as identified in the DOE report on “Basic Energy Needs for Clean and Efficient Combustion of 21st Century Transportation Fuels”. The challenge is particularly daunting since energy conversion efficiencies and exhaust emissions are governed by coupled chemical and transport processes at multiple length scales ranging from electron excitation to molecular rearrangements to nanoscale particulate formation to turbulent fuel/air mixing. To tackle this challenge, the CEFRC assembled a world-class team of 15 principal investigators, with the objectives to: 1) develop and test theoretical models to predict elementary reaction rates, molecule thermalization rates, chemical bond dissociation energies, and nonequilibrium transport properties using quantum chemistry calculations that account for strong electron correlation and multiple electronic potential energy surfaces; 2) develop automated kinetic mechanism generation, reduction, and error control methods for predicting alternative fuel including biofuel oxidation, fuel droplet decomposition, and NOx and particulate formation; 3) validate and improve the predictions of these models by measuring ignition delay times, species profiles, flame structures, burning limits, turbulence-kinetic coupling, and NOx and soot emissions at high-pressures and near-limit conditions, by using advanced experimental diagnostic techniques including multiple laser techniques, molecular beam sampling and synchrotron photoionization, and by conducting the measurements in high-pressure shock tubes, jet-stirred and flow reactors, flame bombs, counterflow flames, and advanced-design rapid compression ignition instruments; and 4) develop a suite of validated petascale high-fidelity simulation and modeling capabilities to understand and predict chemistry-turbulence-radiation coupling for new fuels in new regimes, including the high pressure, low-temperature combustion in advanced engine and turbine designs, and 5) establish a knowledge highway between researchers and engineers in academia, national laboratories, and industry to facilitate the dissemination and exchange of knowledge on national and international levels, and enrich the talent pool and capabilities of the next generation of combustion scientists and engineers. The technical activities of the CEFRC were conducted through three Disciplinary Working Groups – Chemistry Theory, Experiment and Mechanism, and Reacting Flows, which coordinated the Center’s research on the development of combustion chemistry of Foundation Fuels (C0–C4 hydrocarbons), Alcohols, and Biodiesel through three corresponding Mechanism Thrust Groups. Such a two-dimensional coordinated and tightly interwoven research structure has been proven to be highly effective in assuring the interplay between the developments of the fundamentals of combustion science and the utilization of the various categories of fuels. The Center has accomplished the above goals over the five year period (August 1, 2009 – July 31, 2014) with appropriated funding, followed by two additional no-cost-extension (NCE) years. The research results are documented in 230 journal publications, with six legacy review papers on the study of combustion chemistry using shock tubes, flow reactors, rapid compression machines, and flames, on uncertainty quantification, and on theoretical reaction dynamics and chemical modeling of combustion. A robust outreach program complemented these PI-led research activities, consisting of: 1) a roving post-doc program comprised of a corps of Center-appointed, co- or multi-sponsored post-doctoral fellows with rotating assignments to conduct seed projects initiated by at least two PIs, in residence with these sponsoring PIs, to rapidly pursue new and high-risk, high-payoff interdisciplinary ideas; 2) an annual summer school on combustion heavily attended (~200) by senior graduate students and practicing researchers covering advanced topics on chemical kinetics, fluid mechanics, turbulent combustion, engine combustion, new technologies, etc.; 3) a robust open web-site providing Center and community information as well as the lecture videos and notes of the summer school; and 4) widely distributed biannual newsletters.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dispersive nonreciprocity between a qubit and a cavity

The dispersive interaction between a qubit and a cavity is ubiquitous in circuit and cavity quantum electrodynamics. It describes the frequency shift of one quantum mode in response to excitations in the other and, in closed systems, is necessarily bidirectional, i.e., reciprocal. Here, we present an experimental study of a nonreciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity, arising from a common coupling to dissipative intermediary modes with broken time reversal symmetry. We characterize the qubit-cavity dynamics, including asymmetric frequency pulls and photon shot noise dephasing, under varying degrees of nonreciprocity by tuning the magnetic field bias of a ferrite component in situ. We introduce a general master equation model for nonreciprocal interactions in the dispersive regime, providing a compact description of the observed qubit-cavity dynamics agnostic to the intermediary system. Our result provides an example of quantum nonreciprocal phenomena beyond the typical paradigms of non-Hermitian Hamiltonians and cascaded systems.

74 ATOMIC AND MOLECULAR PHYSICS↗