Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “random”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Statistical properties of sites visited by independent random walks

The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. Here, we consider two independent random walks on hyper-cubic lattices and study ordering probabilities associated with these characteristics. The first is the probability that during the time interval (0, t), the number of sites visited by a walker never exceeds that of another walker. The second is the probability that the sites visited by a walker remain a subset of the sites visited by another walker. Using numerical simulations, we investigate the leading asymptotic behaviors of the ordering probabilities in spatial dimensions d = 1, 2, 3, 4. We also study the time evolution of the number of ties between the number of visited sites. We show analytically that the average number of ties increases as a 1 ln t with a 1 = 0.970 508 in one dimension and as (ln t) 2 in two dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Critical points of the random cluster model with Newman–Ziff sampling

Here, we present a method for computing transition points of the random cluster model using a generalization of the Newman–Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is straightforward to implement and works for real cluster weight q > 0. Furthermore, results for an arbitrary number of values of q can be found at once within a single simulation. Because the algorithm used to sweep through bond configurations is identical to that of Newman and Ziff, which was conceived for percolation, the method loses accuracy for large lattices when q > 1. However, by sampling the critical polynomial, accurate estimates of critical points in two dimensions can be found using relatively small lattice sizes, which we demonstrate here by computing critical points for non-integer values of q on the square lattice, to compare with the exact solution, and on the unsolved non-planar square matching lattice. The latter results would be much more difficult to obtain using other techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}\left({2}^{n/2}\right)$, the optimal oracle complexity of quantum unstructured search.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Effectiveness of supervised exercise, home-based exercise, or walk advice strategies on walking performance and muscle endurance in patients with intermittent claudication (SUNFIT trial): a randomized clinical trial

Abstract Aims Supervised exercise is a guideline-recommended treatment in intermittent claudication (IC). Hospital-based supervised exercise programmes (SEPs) are underutilized, while home-based structured exercise programmes (HSEPs) have attracted interest. The results from HSEP in IC are inconsistent and may confer no benefit over walk advice (WA) and be less effective than SEP. The aim of the study was to compare the effectiveness of best medical treatment, including Nordic pole WA alone, or WA + SEP or WA + HSEP for patients with IC. Methods and results This three-armed, multicentre randomized clinical trial enrolled patients with IC; all patients received best medical treatment including walking poles and the advice of regular Nordic pole walking (WA). For HSEP and SEP, additional exercise programmes were provided. The primarily investigated hypothesis was a non-inferiority analysis of SEP vs. HSEP regarding the 6-min walk test (6MWT) maximum distance, with a pre-defined non-inferiority margin of 50 m. Supporting outcomes included muscle endurance tests and the walking impairment questionnaire. Outcomes were assessed at baseline, 3, 6, and 12 months by a blinded evaluator. Altogether 166 patients (mean age 72 years; 59% males) were randomized. In HSEP and SEP, 24 and 26% patients, respectively, were fully exercise adherent. All three groups improved pain-free walking distance over time, but there were no significant intergroup differences. The intergroup 6MWT difference between SEP and HSEP from 0 to 12 months was –11.6 m, 95% confidence interval: –36.4 to 13.0 m (i.e. within the pre-specified non-inferiority margin). Conclusion The HSEP was non-inferior to SEP in patients with IC. There were no significant differences observed between the three groups at 1 year. Registration ClinicialTrials.gov: NCT02341716.

Sandberg, Anna (ORCID:0000000258432784)↗
DOE OSTI2026

Solovay-Kitaev algorithm and randomized compilation

This paper discusses a technique for randomizing over synthesized one-qubit gate sequences in order to mitigate coherent errors in fault-tolerant circuits. We present simulated and experimental data showing that randomization can reduce the trace distance to the target state.

Widzowski Maupin, Oliver Gabriel [Sandia National ↗
DOE OSTI2026

Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics

We report a phase transition in the projected ensemble—the collection of postmeasurement wave functions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar random), from a phase where it is minimally entropic (“classical bit-string ensemble”). Crucially, this deep thermalization transition is invisible to the subsystem’s density matrix, which always exhibits thermalization to infinite temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Impacts of random filling on spin squeezing via Rydberg dressing in optical clocks

Here, we analyze spin squeezing via Rydberg dressing in optical lattice clocks with random fractional filling. We compare the achievable clock stability in different lattice geometries, including unity-filled tweezer clock arrays and fractionally filled lattice clocks with varying dimensionality. We provide practical considerations and useful tools in the form of approximate analytical expressions and fitting functions to aid in the experimental implementation of Rydberg-dressed spin squeezing. We demonstrate that spin squeezing via Rydberg dressing in one-, two-, and three-dimensional optical lattices can provide significant improvements in stability in the presence of random fractional filling.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Sensitivity Enhancement and Random Telegraph Noise in Magnetic Tunnel Junctions with Compensated Anisotropy

We demonstrate the manipulation of perpendicular magnetic anisotropy (PMA) in magnetic tunnel junctions (MTJs) by varying the layer stacks and temperature. PMA is tuned to compensate the shape anisotropy, giving a nonhysteretic magnetic response, a noteworthy sensitivity enhancement, and a field detectability of 1.8 nT/$\sqrt{Hz}$ at 100 kHz. Such a method is further exemplified in multiple MTJs, providing a solution to obtain desired sensitivities and operating temperatures. Additionally, the electronic noise of this MTJ is revealed as a random telegraph noise (RTN) due to a generation-recombination process. In conclusion, the observed voltage-dependent RTN could potentially be applied to true random number generators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Theory of the phase transition in random unitary circuits with measurements

Here, we present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von Neumann entanglement entropy $\textit{S}$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities $\tilde{S}^{(n)}$ and $\mathcal{F}^{(n)}$ that depend on the $\textit{n}$th moments of density matrices and reduce to $\textit{S}$ and $\mathcal{F}$ in the limit $\textit{n}$ → 1. These quantities with $\textit{n}$ ≥ 2 are mapped to free energies of a classical spin model with $\textit{n}$! internal states in two dimensions with specific boundary conditions. In particular, $\tilde{S}^{(n)}$ is the excess free energy of a domain wall terminating on the top boundary, and $\mathcal{F}^{(n)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $\textit{q}$ followed by the replica limit $\textit{n}$ → 1, we obtain the critical measurement probability $p_c$ = 1/2 and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Measurement-induced criticality in random quantum circuits

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the n th Rényi entropies for n ≥ 1 in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. Here, we also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Slow scrambling and hidden integrability in a random rotor model

In this work, we analyze the out-of-time-order correlation functions of a solvable model of a large number $\textit{N}$ of $\textit{M}$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature $\textit{T}$ above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large $\textit{N, M}$ limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticlelike excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and points out interesting connections to random-matrix theory. At leading order in 1/$\textit{M}$, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving $\textit{p}$-pair rotor interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Magnetic order and disorder in a quasi-two-dimensional quantum Heisenberg antiferromagnet with randomized exchange

In this work, we present an investigation of the effect of randomizing exchange coupling strengths in the S = 1 / 2 square lattice quasi-two-dimensional quantum Heisenberg antiferromagnet (QHAF) ( QuinH ) 2 Cu ( Cl x Br 1 - x ) 4 · 2 H 2 O (QuinH = Quinolinium, C 9 H 8 N + ), with 0 ≤ x ≤ 1 . Pulsed-field magnetization measurements allow us to estimate an effective in-plane exchange strength J in a regime where exchange fosters short-range order, while the temperature T N at which long-range order (LRO) occurs is found using muon-spin relaxation, allowing us to construct a phase diagram for the series. We evaluate the effectiveness of disorder in suppressing T N and the ordered moment size, and we find an extended disordered phase in the region 0.4 ≲ x ≲ 0.8 where no magnetic order occurs. The observed critical substitution levels are accounted for by an energetics-based competition between different local magnetic orders. Furthermore, we demonstrate experimentally that the ground-state disorder is driven by quantum effects of the exchange randomness, which is a feature that has been predicted theoretically and has implications for other disordered quasi-two-dimensional QHAFs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Excitation spectra of quantum matter without quasiparticles. II. Random t - J models

Here, we present numerical solutions of the spectral functions of large dimension t -J models with random nearest neighbor exchange and global SU(M) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large dimension limit, followed by the large M limit. The same saddle point equations also apply to the model with all-to-all and random hopping and exchange. Such a t -J model realizes a deconfined critical state proposed as a model for the optimally doped cuprates. The large M theory involves Green’s functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions with good agreement. We also compute the low frequency and temperature behavior of experimentally observable gauge-invariant observables: the electron Green’s function, the local spin susceptibility and the optical conductivity, along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables and provides a linear-in-temperature contribution to the d.c. resistivity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Energy transfer in random-matrix ensembles of Floquet Hamiltonians

Here, we explore the statistical properties of energy transfer in ensembles of doubly driven random-matrix Floquet Hamiltonians based on universal symmetry arguments. The energy-pumping efficiency distribution P⁡($\overline{E}$) is associated with the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet operator. For specific Hamiltonian ensembles, P⁡($\overline{E}$) undergoes a transition which cannot be associated with a symmetry breaking of the instantaneous Hamiltonian. The Floquet eigenvalue spacing distribution indicates the considered ensembles constitute generic nonintegrable Hamiltonian families. As a step towards Hamiltonian engineering, we develop a machine-learning classifier to understand the relative parameter importance in resulting high-conversion efficiency. We propose random Floquet Hamiltonians as a general framework to investigate frequency conversion effects in a class of generic dynamical processes beyond adiabatic pumps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Oscillations and random walk of the soliton core in a fuzzy dark matter halo

We report that a fuzzy dark matter halo consists of a soliton core close to the center and a Navarro-Frenk-White–like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference - a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the evolution of a satellite halo undergoing tidal disruption. As the outer halo is stripped away, reducing the amplitudes of the excited states, the ground state evolves adiabatically. This suggests diminished soliton oscillations and random walk excursions, an effect to consider in deducing constraints from stellar heating.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Spectral form factors of clean and random quantum Ising chains

We compute the spectral form factor of two integrable quantum-critical many-body systems in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in time in the scaling limit described by a conformal field theory; we also compute corrections from lattice effects and deviation from criticality. Iin this work, criticality in the random Ising chain is described by rare regions associated with a strong randomness fixed point, and these control the long-time limit of the spectral form factor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Shock interacting with a random array of stationary particles underwater

Accurately predicting the force experienced by particles within a random bed during shock traversal is a challenging problem. In this paper, particle-resolved inviscid simulations of shock propagation over randomly distributed beds are performed, with the goal of quantifying the force on individual particles. Water was considered the continuum material, and then results were compared with previous research completed in air and the differences resulting from these different mediums were examined. Simulations were conducted for four different combinations of incident Mach number and bed volume fraction with the particles remaining stationary. Additionally, time-resolved streamwise and transverse force coefficients were calculated for each particle in the bed. It was observed that while the average force coefficient was similar to that of an isolated particle, the force on individual particles was substantially different. An important observation was that the inviscid drag force on some particles remained consistently positive, but others consistently negative even long after the passage of the shock. This persistent force on the particle was attributed to the potential flow fields that result from neighbors' specific locations upstream and downstream. Similar behavior was observed in the transverse force, with particles experiencing sustained force in the same lateral direction. These persistent forces are inviscid quasisteady contributions which with the viscous counterpart will play an essential role in the particle's long-term dispersion if allowed to move in response to the force.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Finite-Time Teleportation Phase Transition in Random Quantum Circuits

How long does it take to entangle two distant qubits in a quantum circuit evolved by generic unitary dynamics? Here, we show that if the time evolution is followed by measurements of all but two infinitely separated test qubits, then the entanglement between them can undergo a phase transition and become nonzero at a finite critical time t c . The fidelity of teleporting a quantum state from an input qubit to an infinitely distant output qubit shows the same critical onset. Specifically, these finite-time transitions occur in short-range interacting two-dimensional random unitary circuits and in sufficiently long-range interacting one-dimensional circuits. The phase transition is understood by mapping the random continuous-time evolution to a finite-temperature thermal state of an effective spin Hamiltonian, where the inverse temperature equals the evolution time in the circuit. In this framework, the entanglement between two distant qubits at times t > t c corresponds to the emergence of long-range ferromagnetic spin correlations below the critical temperature. We verify these predictions using numerical simulation of Clifford circuits and propose potential realizations in existing platforms for quantum simulation.

36 MATERIALS SCIENCE↗