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Molecular gases enable extreme compression of industrial-grade lasers, providing a more accessible platform for attosecond science.
The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process ows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.
Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.
Multi-objective transmission switching (MO-TS) problems involve the strategic reconfiguration of network topology to simultaneously optimize multiple objectives. As the system scale increases, finding feasible solutions becomes increasingly challenging due to the problem's nonlinearity and high computational complexity. To address these challenges, this paper proposes a two-stage quantum reinforcement learning method that leverages potential quantum advantages for MO-TS. In the first stage, candidate switching lines are identified using a graph-theoretical approach to reduce the problem's dimensionality. The second stage introduces a quantum-classical reinforcement learning framework, where a learnable measurement-based CNN-ResVQC architecture is developed to effectively reduce the input dimension for quantum processing, mitigate vanishing gradients, and enhance trainability while improving the quantum circuit's flexibility in modeling complex decision policies for MO-TS. Numerical studies on IEEE 14-bus, 57-bus, and 118-bus systems demonstrate that the proposed algorithm achieves superior training stability and faster convergence with approximately 1% of the network parameters required by classical algorithms, highlighting its effectiveness, efficiency, and scalability. Furthermore, the practicality is validated through its stable convergence under three common quantum noise channels.
This project advances the trapped-ion quantum simulator as a versatile platform for studying open quantum system phenomena. We aim to contribute to the emerging quantum simulation toolkits and enable simulation of nanoscale energy processes. Trapped-ion platforms offer unique capabilities: their vibrational motion can be precisely manipulated, measured, and coherently coupled to auxiliary qubits. The vibrational mode can function both as a highly sensitive quantum sensor and a programmable environment bath. Using this platform, we achieved three major outcomes. First, we demonstrated using the vibrational mode as an ultrasensitive probe for testing fundamental physics, including possible nonlinear quantum mechanics effects. Second, we established that these modes can act as controllable baths in which tunable noise and loss can enhance or modify energy-transfer dynamics, providing the experimental preparation toward studying mechanisms relevant to chemical reactions and light-harvesting systems. Third, by introducing controllable nonlinear gain and loss, we showed theoretically how simulations using trapped ions can model vibrationally-assisted energy transport in a non‐Hermitian quantum system comprising a chromophore dimer weakly coupled to a vibrational mode. Exploring the non‐Hermitian dynamics of the whole system including vibrations, we found that energy transfer accompanied by absorption of phonons from a vibrational mode can be significantly enhanced near an exceptional point. This theoretical work on simulation of energy transfer processes in driven non‐Hermitian quantum systems revealed an interesting novel path to study open quantum systems dynamics under conditions of gain and loss. We then further explored the benefits of controllable gain and loss with an experimental realization of quantum analogs of nonlinear oscillators, namely, the van der Pol oscillator. Here we observed mutual synchronization mediated by collective dissipation between two oscillators. In parallel, we explored related quantum networking protocols using the same trapped-ion platform, developing fast, high-fidelity schemes for distributing entanglement. Together, these achievements show that trapped-ion vibrational modes provide a highly programmable and high-fidelity platform for investigating complex dissipative quantum behavior, while enabling new approaches to remote quantum sensing, energy science, and nonlinear quantum dynamics.
The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter, we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain’s (ℓ,m)=(4,4) angular harmonic, here we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic (4,4) mode’s amplitude exhibits quadratic scaling with the fundamental (2,2) mode—its parent mode. The nonlinear mode’s amplitude is comparable to or even larger than that of the linear (4,4) mode. Therefore, correctly modeling the ringdown of higher harmonics—improving mode mismatches by up to 2 orders of magnitude—requires the inclusion of nonlinear effects.
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. Furthermore, the physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, Z 2 symmetry breaking, PT symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.
Nonlinear interferometers include a nonlinear optical medium that is situated to produce a conjugate optical beam in response to a pump beam and a probe beam. The pump, probe, and conjugate beams propagate displaced from each other along a common optical path. One of the beams is selectively phase shifted, and the beams are then returned to the nonlinear medium, with the selectively phase shift beam phase shifted again. The nonlinear medium provides phase sensitive gain to at least one of the probe or conjugate beams, and the amplified beam is detected to provide an estimate of the phase shift.
Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.
Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent Hamiltonian for the cavities while minimizing the operation errors. Here, the engineered Hamiltonian admits various applications including canceling unwanted cavity self-Kerr interactions, creating higher-order nonlinearities for quantum simulations, and designing quantum gates resilient to noise. Our scheme can be implemented with coupled microwave cavities and transmon qubits in superconducting circuit systems.
In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.
Here, we present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broken time-reversal symmetry in one spatial dimension. Our framework can be applied to the hydrodynamics around stationary states of open systems, broadening the applicability of previously developed ideas and methods to a wide range of systems in driven and active matter.
Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem
In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.