SEARCH · Search NASA

Results for “value factor”

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.

SourceResearch connectionFrom yearThrough year

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

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Enhanced Tritium Retention in LiAlO2 Pellets via Engineered Glazes: Tritium Science Project

This project investigated the impact of adding a thin (10 – 50 µm) layer of amorphous glaze to the surface of a TPBAR pellet on its retention of helium, hydrogen (as a surrogate for tritium), and water (as a surrogate for tritiated water). The hypothesis was that the glaze would significantly reduce permeation of hydrogen species with a lesser impact on hindering helium permeation. A non-crystallizing soda-lime-silicate glass, known as SCN-1, was selected for this proof-of-concept study. It was found that continuous glaze layers of the desired thickness could be applied to the pellets with two or more dip coats, depending on the targeted thickness. At 330°C, the glaze was found to have a permeability that was lower than that of the pellet by a factor of ~10 6 , implying that a thin 10 – 50 µm layer can significantly increase pellet retention of hydrogen. Meanwhile, the permeation rate of helium through the glaze was found to be ~20 times higher than that of hydrogen or water. An unanticipated outcome of the study was that unglazed pellets were measured to have hydrogen diffusivities that are a factor of ~105 greater than the diffusivity value used in the TPBAR COMSOL model to achieve observed tritium retention rates. When the higher measured diffusivity was substituted into the model and the model was run with all tritium species in the pellet in the form of T 2 O at a partial pressure of 20 Pa in equilibrium with LiOT, the resulting retention was 50% after 500 days.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A Regional Phase Amplitude Model of 2-D Attenuation for North America

We analyzed seismic attenuation patterns across the North America using over 70,000,000 Lg wave amplitudes recorded by the various networks at frequencies of 0.1-32 Hz. Our inversion solved for laterally varying attenuation, site terms, moments, and apparent stress following Phillips et al., (2016). The inversion was anchored by independently constrained: corner frequencies (via coda spectral ratios) to control the attenuation-stress tradeoff and moment measurements of teleseismic (GCMT, USGS) and regional (St. Louis University and UC Berkeley) earthquakes to provided absolute scaling. The quality factor (Q) shows clear regional patterns: low values in coastal, volcanic, and tectonically active regions, and high values in stable areas like the Great Plains and major plateaus throughout North America. These 2-D Q models enable improved regional source characterization, magnitude estimation, and yield determination.

58 GEOSCIENCES↗

DOE OSTI2024

Plan Position Indicator Hydrometeor Field Statistics (PPIHYD) Evaluation Data Product Version 1.0

The PPIHYD evaluation data product provides distinct hydrometeor field statistics calculated from U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility scanning radar plan position indicator (PPI) scans. These statistics include the equivalent reflectivity factor and Doppler spectral width percentiles, min/max values, and first four moments (mean, standard deviation, skewness, and kurtosis) of distinct hydrometeor features (clustered hydrometeor fields). Statistics also include morphological properties, water content and precipitation rate parameterization-based estimates, and thermodynamic properties interpolated using the Interpolated Sonde value-added product (INTERPSONDE VAP). The data set is organized in tabular form and is accompanied by mask arrays with corresponding indices. This straightforward file structure simplifies scanning radar data processing and renders this data set useful for process understanding and model evaluation studies. This report describes the data set and its processing algorithm and provides some examples.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Radionuclide Transport Simulations Supporting Proposed Borehole Waste Disposal in Israel

A scientific collaboration between the U.S. and Israel is underway to assess the suitability of a potential site for subsurface radioactive waste disposal in the Negev Desert, Israel. The Negev Desert has several favorable attributes for geologic disposal, including an arid climate, a deep vadose zone, interlayered low-permeability lithologies, and carbonate rocks with high uranium-sorption potential. These features may provide a robust natural barrier to radionuclide migration. Geologic and laboratory characterization data from the Negev Desert are incorporated into multiphase flow and transport models, solved using PFLOTRAN, to aid in site characterization and risk analysis that will support decision-making for waste disposal in an intermediate-depth borehole design. The lithology with the greatest uranium sorption potential at the site is phosphorite. We use modeling to evaluate the ability of this layer to impact uranium transport around a proposed disposal borehole. The current objective of the simulations is focused on characterizing hypothetical leakage from waste canisters and subsequent uranium migration under three infiltration scenarios. Here, we describe a hydrogeologic model based on data from a local exploratory borehole and present results for uranium flow and transport simulations under varying infiltration scenarios. We find that under the current climate conditions, it is likely that uranium will remain in the near-field of the borehole for thousands of years. However, under a hypothesized extreme climate scenario representing an increase in infiltration by a factor of 300x above present-day values, uranium may break through the phosphorite layer and exit the base of the model domain (~200 m above the water table) within 1000 years. Simulation results have direct implications for the planning of nuclear waste disposal in the Negev Desert, and specifically in intermediate-depth boreholes.

58 GEOSCIENCES↗

DOE OSTI2020

Revised and New Proper Motions for Confirmed and Candidate Milky Way Dwarf Galaxies

A new derivation of systemic proper motions of Milky Way satellites is presented and applied to 59 confirmed or candidate dwarf galaxy satellites using Gaia Data Release 2. This constitutes all known Milky Way dwarf galaxies (and likely candidates) as of 2020 May, except for the Magellanic Clouds, the Canis Major and Hydra 1 stellar overdensities, and the tidally disrupting Bootes III and Sagittarius dwarf galaxies. We derive systemic proper motions for the first time for Indus 1, DES J0225+0304, Cetus 2, Pictor 2, and Leo T, but note that the latter three rely on photometry that is of poorer quality than that of the rest of the sample. We cannot resolve a signal for Bootes 4, Cetus 3, Indus 2, Pegasus 3, or Virgo 1. Our method is inspired by the maximum likelihood approach of Pace & Li and examines simultaneously the spatial, color–magnitude, and proper motion distribution of sources. Systemic proper motions are derived without the need to identify confirmed radial velocity members, although the proper motions of these stars, where available, are incorporated into the analysis through a prior on the model. The associated uncertainties on the systemic proper motions are on average a factor of ∼1.4 smaller than existing literature values. Analysis of the implied membership distribution of the satellites suggests that we accurately identify member stars with a contamination rate lower than 1 in 20.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Contributions to Dielectric Constant Enhancement in Thin Film Metal Insulator Metal Capacitors

Thin film metal-insulator-metal capacitors were fabricated with varying dielectric and electrode thicknesses and areas. Measurement of the dielectric properties of the capacitors consistently yielded higher than predicted capacitance values, which prompted the exploration of three factors that could enhance the capacitance. Modeling of the fringing capacitance and field enhancement due to the capacitor geometry, both yield capacitance gains, albeit insufficient to fully explain the observed behavior. The possible role of changes in polarizability of the dielectric film constituents, due to the amorphous nature of the films was also evaluated, but the results of the investigation of this contribution were inconclusive. Herein, the role of accumulation/depletion layers on capacitance enhancement was also analyzed. For capacitors fabricated with thinner dielectrics, the presence of these layers can effectively reduce the dielectric thickness, resulting in contributions to capacitance that are significant. The calculations completed suggest these contributions may be more important than fringing field contributions. Additional studies of these mechanisms are in progress.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Effects of the U.S. inflation reduction act on SMR economics

The U.S. Inflation Reduction Act (IRA) of 2022 provides a wide array of tax credits and other incentives for low-carbon energy. The technology-neutral clean generation production tax credit (PTC) (Section 45Y of the U.S. Internal Revenue Code) and the technology-neutral investment tax credit (ITC) (Section 48E) lower the net cost of new electricity generation projects with zero or negative greenhouse gas emission rates. We evaluate the impact of the IRA legislation—specifically the PTC and ITC—on the cost-competitiveness of small modular reactors (SMRs). We use the Argonne Low-carbon Energy Analysis Framework (A-LEAF) model to calculate the capacity factor of an SMR with a range of hypothetical variable operating and maintenance (O&M) costs in the Electric Reliability Council of Texas (ERCOT) electricity market. We selected ERCOT for market modeling because of its competitive structure, available data, and extensive use in prior literature. We use a discounted cash flow model to calculate the SMR’s net present value based on the market prices and capacity factors from A-LEAF, hypothetical ranges of capital and variable O&M costs, and other input parameters, with or without the IRA tax credits. We determine the SMR owner’s optimal choice of PTC or ITC for the hypothetical ranges of capital and variable O&M costs. We also evaluate potential shifts in the SMR owner’s optimal choice of PTC or ITC based on historical patterns of nuclear capital cost overruns in the United States. We also assess the sensitivity of our results to longer PTC period and electricity prices from the New England market, which tend to be higher than electricity prices in ERCOT. We find that even with the IRA tax credits, only SMRs with low capital and variable O&M costs would be economically feasible in the low-price ERCOT market scenario modeled. A longer PTC period and higher-price market such as New England, however, would significantly expand the economic feasibility of SMRs in the United States.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Renewable-battery hybrid power plants in congested electricity markets: Implications for plant configuration

Examining coupled renewable-battery power plants (“hybrids”) in congested areas provides insights into a future of increased wind and solar penetration. Our study focuses on two types of congested regions, Variable Renewable Energy (VRE)-rich Areas and Load Centers, and explores likely plant configuration choices for developers and transmission network planners. Here, this paper examines how hybrid value, comprising energy and capacity value, varies by plant configuration and congested region type considering factors such as storage duration, battery degradation, and ability to charge from the grid. We select plant locations from across the seven main U.S. independent system operators (ISOs). Hybrid value for each configuration is computed based on profit-maximizing plant operation given perfect foresight, according to observed wholesale power market real time prices from 2018 to 2021. In VRE-rich Areas, the median increase in energy value from extending storage duration from one to 4h is 29.4% for solar and 26.8% for wind, assuming low battery degradation costs and storage sized to 100% of the plant's nameplate generation capacity. Increasing storage duration beyond 4h does not substantially increase its value from energy markets, even in VRE-rich Areas. We find that solar hybrids reach a 90% capacity credit with 4h of storage, while wind hybrids require 8h of storage, based on the capacity factor of each hybrid during the top 100 net load hours.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Valuing EV Managed Charging for Bulk Power Systems

When and where electric vehicle (EV) charging occurs has significant implications for power systems supporting widespread EV adoption, especially with high shares of wind and solar generation. This study extends previous works by leveraging detailed simulation models for EV adoption, EV use, EV charging, and bulk power system operations, and by linking them with methods for describing charging flexibility at both the individual vehicle and aggregate levels. This technical potential study focuses on how the value of EV managed charging (EVMC) changes depending on charging flexibility type (within-charging session or within-week scheduling), dispatch mechanism (direct load control or one of several price-based mechanisms), and managed charging participation rate. We show that naively aggregating EV charging flexibility from individual vehicles into megawatt-scale resources grossly overestimates the flexibility of the fleet, because such aggregate models can unrealistically pair, e.g., one already-fully-charged vehicle's ability to increase load with another already-charging vehicle's ability to accept more charge, effectively requesting a charging rate that is infeasible for the latter vehicle. We find per-vehicle bulk system value is highest at low participation rates for all dispatch mechanisms. Factoring in production cost savings, avoided firm capacity savings, and combustion-related power sector emissions savings, we estimate the value of EVMC at low participation rates (5%) to be $33/vehicle-year to $69/vehicle-yr for within-session charging flexibility and $40/vehicle-yr to $120/vehicle-yr for within-week charging flexibility in an envisioned 2038 New England power system and monetary value reported in 2016 U.S. dollars. At 100% participation, per-vehicle value declines to $25/vehicle-yr to $31/vehicle-yr for within-session charging flexibility and to $29/vehicle-yr to $36/vehicle-yr for within-week charging flexibility; however, 100% participation yields the highest total system savings.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

High resolution electronic spectroscopy of uranium mononitride, UN

The isoelectronic molecules UN and UO + are known to have Ω = 3.5 and Ω = 4.5 ground states, respectively (where Ω is the unsigned projection of the electronic angular momentum along the internuclear axis). A ligand field theory model has been proposed to account for the difference [Matthew and Morse, J. Chem. Phys. 138, 184303 (2013)]. The ground state of UO + arises from the U 3+ (5f 3 ( 4 I 4.5 ))O 2− configuration. Owing to the higher nominal charge of the N 3− ligand, the U 3+ ion in UN is stabilized by promoting one of the 5f electrons to the more polarizable 7s orbital, reducing the repulsive interaction with the ligand and rendering U 3+ (5f 2 7s( 4 H 3.5 ))N 3− the lowest energy configuration. In the present work, we have advanced the characterization of the UN ground state through studies of two electronic transitions, [18.35]4.5-X(1)3.5 and [18.63]4.5-X(1)3.5, using sub-Doppler laser excitation techniques with fluorescence detection. Further, spectra were recorded under field-free conditions and in the presence of static electric or magnetic fields. The ground state electric dipole moment [μ = 4.30(2) D] and magnetic g e -factor [2.160(9)] were determined from these data. These values were both consistent with the 5f 2 7s configurational assignment. Dispersed fluorescence measurements were used to determine vibrational constants for the ground and first electronically excited states. Electric dipole moments and magnetic g e -factors are also reported for the higher-energy electronically excited states.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2020

Vertical profiles of light absorption and scattering associated with black carbon particle fractions in the springtime Arctic above 79° N

Despite the potential importance of black carbon (BC) for radiative forcing of the Arctic atmosphere, vertically resolved measurements of the particle light scattering coefficient (σ sp ) and light absorption coefficient (σ ap ) in the springtime Arctic atmosphere are infrequent, especially measurements at latitudes at or above 80° N. Here, relationships among vertically distributed aerosol optical properties (σap, σsp and single scattering albedo or SSA), particle microphysics and particle chemistry are examined for a region of the Canadian archipelago between 79.9 and 83.4° N from near the surface to 50 hPa. Airborne data collected during April 2015 are combined with ground-based observations from the observatory at Alert, Nunavut and simulations from the Goddard Earth Observing System (GEOS) model, GEOS-Chem, coupled with the TwO-Moment Aerosol Sectional (TOMAS) model (collectively GEOS-Chem–TOMAS; Kodros et al., 2018) to further our knowledge of the effects of BC on light absorption in the Arctic troposphere. The results are constrained for σsp less than 15 Mm -1 , which represent 98% of the observed σsp, because the single scattering albedo (SSA) has a tendency to be lower at lower σsp, resulting in a larger relative contribution to Arctic warming. At 18.4 m 2 g -1 , the average BC mass absorption coefficient (MAC) from the combined airborne and Alert observations is substantially higher than the two averaged modelled MAC values (13.6 and 9.1 m2 g -1 ) for two different internal mixing assumptions, the latter of which is based on previous observations. The higher observed MAC value may be explained by an underestimation of BC, the presence of small amounts of dust and/or possible differences in BC microphysics and morphologies between the observations and model. In comparing the observations and simulations, we present σap and SSA, as measured, and σ ap 2 and the corresponding SSA to encompass the lower modelled MAC that is more consistent with accepted MAC values. Median values of the measured σap, rBC and the organic component of particles all increase by a factor of 1.8±0.1, going from near-surface to 750 hPa, and values higher than the surface persist to 600 hPa. Modelled BC, organics and σap agree with the near-surface measurements but do not reproduce the higher values observed between 900 and 600 hPa. The differences between modelled and observed optical properties follow the same trend as the differences between the modelled and observed concentrations of the carbonaceous components (black and organic). Model-observation discrepancies may be mostly due to the modelled ejection of biomass burning particles only into the boundary layer at the sources. For the assumption of the observed MAC value, the SSA range between 0.88 and 0.94, which is significantly lower than other recent estimates for the Arctic, in part reflecting the constraint of σsp<15 Mm -1 . The large uncertainties in measuring optical properties and BC, and the large differences between measured and modelled values here and in the literature, argue for improved measurements of BC and light absorption by BC and more vertical profiles of aerosol chemistry, microphysics and other optical properties in the Arctic.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Supporting Bioproducts Industry Growth with a System Dynamics Decision-Support Tool

A bio-based economy requires chemical products as well as fuels to be produced from biomass. Although a variety of universities, government agencies, start-ups and established firms have engaged in bioproduct development, many projects have failed to reach the point of commercialization and commercialized bioproducts struggle to capture and maintain market share. To date, there has been no general research into the factors that contribute to bioproduct failure or success. This work presents the Bioproduct Transition Dynamics (BTD) system dynamics model, a decision-support tool that simulates the bioproduct development process from pre-piloting research through construction of the first commercial-scale plant, as well as the processes of obtaining funding from investors and government agencies. The core of the BTD is a feedback loop between bioproduct developers and funders, which relates development progress measured with indicators such as net present value to funders’ decisions to continue investing. External factors such as feedstock prices, market size and growth, and the existence of bioproduct consumers also influence a development project’s chances of receiving follow-on funding. Virtually any bioproduct can be represented with the BTD: direct replacements, performance-advantaged products, niche and commodity markets can all be modeled. The goal of the BTD project is to inform decisions made by developers in both established firms and start-ups, investors, government agencies, and other stakeholders interested in growing the nascent U.S. bioproducts industry. This talk will cover the general structure and functionality of the BTD, and present results from an analysis performed with the BTD to demonstrate its use as a decision-support tool and the insights it can provide. The goal of the analysis is to identify the most critical factors that lead to direct replacement and performance-advantaged bioproduct projects emerging successfully from the “Valley of Death”, and to determine if these factors differ between the two bioproduct types.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2026

How to Minimize Faradaic Efficiency Error in Electrochemical CO 2 Reduction for Gas Products

Faradaic efficiency (FE) is an important metric for evaluating electrochemical processes, such as carbon dioxide reduction, that is often used for performance comparisons. Although the equation to calculate FE is well-known, details needed to yield accurate values are often overlooked, potentially leading to errors exceeding 100%. Avoiding any errors is crucial for drawing correct conclusions, especially during a catalysis optimization process. Factors with high potential for FE errors include incorrect mass flow rates and temperature values, imprecise gas chromatography calibrations, and uncorrected gas viscosities, while factors with less potential are also identified. In conclusion, this manuscript presents FE calculation guidelines intended for both newcomers and experts in the field of electrochemical fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Tucker-1 Boolean Tensor Factorization with Quantum Annealers

Quantum annealers are an emerging computational architecture that have the potential to address some challenging computational issues that will be left unresolved as we approach the end of the Moore's Law era of computing. D-Wave quantum annealers are designed to solve a challenging set of problems - quadratic unconstrained binary optimization problems. This makes them a natural fit for solving problems with binary or Boolean variables. Here, we explore the use of a quantum annealer to solve Boolean tensor factorization. The goal of Boolean tensor factorization is to represent a high-dimensional tensor filled with Boolean values as a product of Boolean matrices and a Boolean core tensor. We show that a particular Boolean tensor factorization problem (called Tucker-1 factorization) can be decomposed into a sequence of quadratic unconstrained binary optimization problems that can be solved with a D-Wave 2000Q quantum annealer. While quantum annealers specifically and quantum computers in general are at a fairly early stage in their development, they are currently capable of solving these Boolean tensor factorization problems. Importantly, our results show that for fairly small tensors, we are frequently able to obtain an accurate (sometimes exact) factorization using quantum annealing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Implementing an electronic sideband offset lock for isotope shift spectroscopy in radium

We demonstrate laser frequency stabilization with at least 6 GHz of offset tunability using an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) on a titanium sapphire laser at 714 nm and we apply this technique to perform isotope shift spectroscopy of 226 Ra and 225 Ra. By locking the laser to a single resonance of a high finesse optical cavity and adjusting the lock offset, we determine the frequency difference between the magneto-optical trap (MOT) transitions in the two isotopes to be 2630.0 ± 0.3 MHz, a factor of 29 more precise than the previously available data. Using the known value of the hyperfine splitting of the 3 P 1 level, we calculate the isotope shift for the 1 S 0 to 3 P 1 transition to be 2267.0 ± 2.2 MHz, a factor of 8 more precise than the best available value. Our technique could be applied to countless other atomic systems to provide unprecedented precision in isotope shift spectroscopy and other relative frequency comparisons.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Conus-Wide Mapping of Water Availability and Cost

Background: New demands for water can be satisfied through a variety of source options. In some basins surface and/or groundwater may be available through permitting with the state water management agency (termed unappropriated water), alternatively water might be purchased and transferred out of its current use to another (termed appropriated water), or non-traditional water sources can be captured and treated (e.g., wastewater). The relative availability and cost of each source are key factors in the development decision. Unfortunately, these measures are location dependent with no consistent or comparable set of data available for evaluating competing water sources. With the help of water managers, water availability was mapped for over 2500 watersheds throughout CONUS. These values are unique in that they account for institutional factors (i.e., water rights, compacts, treaties, instream flows) that locally limit water use. Five water sources were individually examined, including unappropriated surface water, unappropriated groundwater, appropriated water, municipal wastewater and brackish groundwater. Associated costs to acquire, convey and treat the water, as necessary, for each of the five sources were estimated. These metrics were developed to support regional water planning and policy analysis with initial application to electric transmission planning in the western US. Problem: These data were originally developed in 20141 and updated in 20182. New datasets on which these data depend have been published. As such, there is need to update the water availability and cost data. There is also need to map this same data to a county resolution and to publish the data in a more accessible place. Organization of the dataset: Data are organized according to five primary water sources: • Unappropriated fresh surface water • Unappropriated fresh groundwater • Appropriated water • Recycled wastewater, and • Brackish water

Tidwell, Vincent [Pacific Northwest National Labor↗

DOE OSTI2020

Time Evolution of Correlation Functions in Quantum Many-Body Systems

We give rigorous analytical results on the temporal behavior of two-point correlation functions—also known as dynamical response functions or Green’s functions—in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times $\langle$A ( t ) B$\rangle$ β → $\langle$ A$\rangle$ β $\langle$ B$\rangle$ β , thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For autocorrelation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values and does not increase with system size. We give numerical examples that show that this bound is a good estimate in nonintegrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗