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The modeling and simulation of the growth of ducted single-frequency whistler-mode waves through cyclotron resonance with radiation belt electrons are considered. The Siple transmitter and a geomagnetically conjugate receiving station are used for the present study. The results can be applied to slowly varying frequency signals and to broadband 'noiselike' signals.
A miniflare that occurred in active region Hale 16896 on 1980 June 15 was observed in H-alpha, UV lines, and soft X-rays. These data allow us to analyze the flare emission and derive the energetics and dynamics of the chromospheric plasma involved. Our results indicate that the energy released by the miniflare was about 10(exp 28) ergs, about four orders of magnitude smaller than that of a large flare. However, hard X-rays (5.5-8.0 keV) were observed which indicated a plasma with temperature as high as 27 x 10(exp 6) K. The H-alpha wings, C IV, and X-rays all showed a short-lived and compact (3 sec x 3 sec) brightening in a location near the leading sunspot. At this location, small-scale changes in the magnetic field were observed from about 2 hr before to about 6 hr after the miniflare. Only very small velocities seem to have been associated with most of the event in H-alpha. The data are consistent with short and dense loops at temperatures above 10(exp 7) K which lost a large fraction of their energy via downward conduction through regions at the footpoints. Several secondary events appear to have been triggered by the miniflare along an arch filament which itself was not greatly affected. A number of much less energetic (10(exp 25)-10(exp 26) erg) events preceded and followed the mini-flare. One of these occurred 11 minutes after the mini-flare and displayed a highly Doppler-shifted signature from the foot-point of a C IV arch. This arch delineates the connection that existed between the location of the mini-flare and the location of secondary events triggered by the flare.
Heavy ions have gained considerable importance in radiotherapy due to their advantageous dose distribution profile and high Relative Biological Effectiveness (RBE). Heavy ions are difficult to produce on Earth, but they are present in space and it is impossible at this moment to completely shield astronauts from them. The risk of these radiations is poorly understood, which is a concern for a 3-years Mars mission. The effects of radiation are mainly due to DNA damage such as DNA double-strand breaks (DSBs), although non-targeted effects are also very important. DNA can be damaged by the direct interaction of radiation and by reactions with chemical species produced by the radiolysis of water. The energy deposition is of crucial importance to understand biological effects of radiation. Therefore, much effort has been done recently to improve models of radiation tracks.
We report new HST/STIS observations that map the high-ionization forbidden line emission in the inner arc second of Eta Car, the first that fully image the extended wind-wind interaction region of the massive colliding wind binary. These observations were obtained after the 2009.0 periastron at orbital phases 0.084, 0.163, and 0.323 of the 5.54-year spectroscopic cycle. We analyze the variations in brightness and morphology of the emission, and find that blue-shifted emission (-400 to -200 km/s is symmetric and elongated along the northeast-southwest axis, while the red-shifted emission (+ 100 to +200 km/s) is asymmetric and extends to the north-northwest. Comparison to synthetic images generated from a 3-D dynamical model strengthens the 3-D orbital orientation found by Madura et al. (2011), with an inclination i = 138 deg, argument of periapsis w = 270 deg, and an orbital axis that is aligned at the same P A on the sky as the symmetry axis of the Homunculus, 312 deg. We discuss the potential that these and future mappings have for constraining the stellar parameters of the companion star and the long-term variability of the system. Plain-Language Abstract: With HST, we resolved the interacting winds of the binary, Eta Carinae. With a 3-D model, we find the binary orbit axis is aligned to the Homunculus axis. This suggests a connection between the binary and Homunculus ejection mechanism.
We report new HST/STIS observations that map the high-ionization forbidden line emission in the inner arcsecond of Eta Car, the first that fully image the extended wind-wind interaction region of the massive colliding wind binary. These observations were obtained after the 2009.0 periastron at orbital phases 0.084, 0.163, and 0.323 of the 5.54-year spectroscopic cycle. We analyze the variations in brightness and morphology of the emission, and find that blue-shifted emission (-400 to -200 km/s is symmetric and elongated along the northeast-southwest axis, while the red-shifted emission (+ 100 to +200 km/s) is asymmetric and extends to the north-northwest. Comparison to synthetic images generated from a 3-D dynamical model strengthens the 3-D orbital orientation found by Madura et al. (2011), with an inclination i approx. 138deg, argument of periapsis omega approx. 270deg, and an orbital axis that is aligned at the same PA on the sky as the symmetry axis of the Homunculus, 312deg. We discuss the potential that these and future mappings have for constraining the stellar parameters of the companion star and the long-term variability of the system.
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Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.
In this work, we present novel concepts for quantum algorithms to solve transient, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the incompressible Navier-Stokes equations as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts solving nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. We propose a new framework based on matrix product states (MPSs) and matrix product operators (MPOs), in addition to the Krylov subspace methods. For example, the solution variables of the Navier-Stokes equations are represented by MPSs, and the linear and nonlinear terms are processed by MPOs. The time evolution of the operators is attained by a fast-forwarding algorithm using Krylov subspace methods. Furthermore, we discuss various techniques for efficient encoding of MPSs, measurement reduction for MPOs, and use of tensor operations to treat multi-variate, multi-physics characteristics of Navier-Stokes.
In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.
We generalize isometric tensor network states to fermionic systems, paving the way for efficient adaptations of 1D tensor network algorithms to 2D fermionic systems. As the first application of this formalism, we developed and benchmarked a time-evolving block-decimation (TEBD) algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge modes to good accuracy. Here, the real-time TEBD captures the scattering of two fermions and the chiral edge dynamics on the boundary of a Chern insulator.
Many geophysical time series possess nonlinear characteristics that reflect the underlying physics of the phenomena the time series describe. The nonlinear character of times series can change with time, so it is important to quantify time series nonlinearity without assuming stationarity. A common way of quantifying the time evolution of time series nonlinearity is to compute sliding skewness time series, but it is shown here that such an approach can be misleading when time series contain periodicities. To remedy this deficiency of skewness, a new waveform skewness index is proposed for quantifying local nonlinearities embedded in time series. A waveform skewness spectrum is proposed for determining the frequency components that are contributing to time series waveform skewness. The new methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to test a recently proposed hypothesis that states that changes in the ENSO–Indian monsoon relationship are related to ENSO nonlinearity. We show that the ENSO–Indian rainfall relationship weakens during time periods of high ENSO waveform skewness. The results from two different analyses suggest that the breakdown of the ENSO–Indian monsoon relationship during time periods of high ENSO waveform skewness is related to the more frequent occurrence of strong central Pacific El Niño events, supporting arguments that changes in the ENSO–Indian rainfall relationship are not solely related to noise.
We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), which is a central object in quantum statistical mechanics. We introduce several key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS only for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since both canonical and grand canonical ensemble thermal equilibrium properties depend on subspaces of fixed number. Second, in our approach, by time evolving very simple, random initial states, such as randomly chosen computational basis states, we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window—thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons, we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics can yield a semiquantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault-tolerant devices will likely enable higher-resolution DOS reconstruction through longer time evolutions. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and indeed find that our approach is highly robust against algorithmic errors in the time evolution and against gate noise. We further demonstrate that our approach is compatible with noisy intermediate-scale quantum (NISQ) computing NISQ-friendly variational techniques, introducing and leveraging a technique for variational time evolution.
Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.