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

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673 records · Page 13

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID

Nonlinear nanoelectrodynamics of a Weyl metal

Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe 4 . As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their “symmetry fingerprints” in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe 4 single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Here, nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

On-chip terahertz emission from Floquet-Bloch states [Invited]

Floquet engineering uses time-periodic electromagnetic fields to modify the electronic properties of quantum materials via the creation of Floquet-Bloch states. These photon-dressed states inherit features from both the material and the driving field, enabling the exploration and control of quantum phenomena in light-matter hybrid systems. In non-centrosymmetric materials, shift currents can arise from the quantum geometric properties of electronic wavefunctions. However, shift currents from Floquet-Bloch states remain experimentally unexplored. Here, we employ an on-chip optoelectronic circuit to detect intrinsic terahertz emission from Floquet-Bloch states in T d -WTe 2 under intense optical driving. We observe strong edge-localized terahertz emission that scales linearly with the driving field, consistent with the theoretical prediction for shift currents generated by Floquet-Bloch states. The results advance our understanding of strongly driven quantum materials and provide insights for developing efficient, bias-free terahertz sources for future optoelectronic technologies.

Li, Xinyu [Max Planck Institute for the Structure

Building Operation Model (Morpheus) for Dallas Fort Worth Airport (CRADA CRD-19-16301 Final Report)

The primary objective of this project was to leverage digital twin technology to enhance the design and operation of DFW Airport terminals and their associated energy systems. To achieve this, Morpheus, a building digital twin, was developed to guide improvements in airport operations, specifically targeting reductions in peak power demand and overall energy consumption.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Reconfigurable Cascaded Thermal Neuristors for Neuromorphic Computing

While the complementary metal-oxide semiconductor (CMOS) technology is the mainstream for the hardware implementation of neural networks, an alternative route is explored based on a new class of spiking oscillators called “thermal neuristors”, which operate and interact solely via thermal processes. Utilizing the insulator-to-metal transition (IMT) in vanadium dioxide, a wide variety of reconfigurable electrical dynamics mirroring biological neurons is demonstrated. Notably, inhibitory functionality is achieved just in a single oxide device, and cascaded information flow is realized exclusively through thermal interactions. To elucidate the underlying mechanisms of the neuristors, a detailed theoretical model is developed, which accurately reflects the experimental results. In conclusion, this study establishes the foundation for scalable and energy-efficient thermal neural networks, fostering progress in brain-inspired computing.

36 MATERIALS SCIENCE

A Laboratory Breadboard System for Dual-Arm Teleoperation

The computing architecture of a novel dual-arm teleoperation system is described. The novelty of this system is that: (1) the master arm is not a replica of the slave arm; it is unspecific to any manipulator and can be used for the control of various robot arms with software modifications; and (2) the force feedback to the general purpose master arm is derived from force-torque sensor data originating from the slave hand. The computing architecture of this breadboard system is a fully synchronized pipeline with unique methods for data handling, communication and mathematical transformations. The computing system is modular, thus inherently extendable. The local control loops at both sites operate at 100 Hz rate, and the end-to-end bilateral (force-reflecting) control loop operates at 200 Hz rate, each loop without interpolation. This provides high-fidelity control. This end-to-end system elevates teleoperation to a new level of capabilities via the use of sensors, microprocessors, novel electronics, and real-time graphics displays. A description is given of a graphic simulation system connected to the dual-arm teleoperation breadboard system. High-fidelity graphic simulation of a telerobot (called Phantom Robot) is used for preview and predictive displays for planning and for real-time control under several seconds communication time delay conditions. High fidelity graphic simulation is obtained by using appropriate calibration techniques.

A K Bejczy

Large Language Model for Validation, Optical Calibration, and Learning (VOCAL) Distributed Temperature Sensing Interface

Distributed temperature sensing (DTS) using fiber optic sensors (FOS) offers a promising method for temperature measurements in advanced reactors, such as sodium fast reactors and molten salt cooled reactors. To support the calibration and validation of DTS measurements, Argonne National Laboratory developed the Validation, Optical Calibration, and Learning (VOCAL) software package. This report describes the integration of a local large language model (LLM) with a retrieval-augmented generation (RAG) system into the VOCAL interface to serve as an interactive user assistant. The LLM framework enhances the VOCAL platform’s accessibility to users by explaining interface components, clarifying inputs and outputs, and answering user queries dynamically in real-time. The accuracy of the LLM assistant performance was evaluated with 20 queries regarding the interface and its parameters using experimental data from the Thermal Hydraulic Experimental Test Article (THETA) facility. Results demonstrate that the LLM achieved a 95% accuracy rate, with a BERTScore of 0.8816 and SBERT value of 0.7417. Furthermore, validation of the RAG system within the LLM framework showed optimal accuracy with k-values between 1 and 2 using the k-refinement convergence test. The prompt perturbation analysis demonstrated good initial consistency for the RAG system, exhibiting the highest accuracy under punctuation variations and the greatest sensitivity under query reordering. Notably, the model’s errors were limited to data retrieval failures rather than factual hallucinations, reinforcing its baseline reliability. The integration of LLM provides a highly accurate, userfriendly enhancement to the VOCAL platform without disrupting its core computational capabilities for FOS calibration and validation.

Hong, Evan

Single‐photon emitters in PECVD‐grown silicon nitride films: from material growth to photophysical properties

Abstract Silicon nitride (SiN) is a key material for quantum photonics due to its wide transparency window, high refractive index, low optical losses, and semiconductor foundry compatibility. We study the formation of single‐photon emitters in SiN films grown by plasma‐enhanced chemical vapor deposition (PECVD), exploring their photophysical properties and dependence on growth conditions. Emitters were observed across the entire range of nitrogen‐to‐silicon precursor ratios, from silicon‐rich to nitrogen‐rich conditions, enabled by the low background fluorescence. We demonstrate single‐photon emitters in SiN films with a higher refractive index (1.8–1.9) compared to our previous reports (∼1.7). Notably, nitrogen‐rich, thinner films yield particularly bright emitters with shorter emission lifetimes, likely due to more efficient annealing. Silicon‐rich SiN films exhibit red‐shifted emission, suggesting that composition may provide a mechanism for wavelength tuning. These findings establish the feasibility of emitters formation in foundry standard PECVD tools, advancing the scalability and lab‐to‐fab transition of SiN‐based quantum photonic technologies.

Materials Science

Dynamic Diketoenamine Crosslinking Unlocks Vinyl Polymer Vitrimers From β ‐Triketone Chemistry

Covalent adaptable networks (CANs) offer a compelling strategy to unite the mechanical robustness of thermosets with the reprocessability of thermoplastics, yet achieving simultaneous durability, processability, and true recyclability remains challenging. We introduce diketoenamine (DKE) vitrimers derived from β-triketone methacrylate monomers and demonstrate how rational monomer design dictates network processability, viscoelasticity, and recyclability. By systematically varying the spacer length between the β-triketone (TK) moiety and the polymer backbone, we identify a key structure–property relationship that dictates vitrimer behavior. Networks bearing TK pendants minimally displaced from the backbone suppress creep but exhibit limited stress relaxation, whereas extended spacers yield lower glass transition temperatures, higher effective crosslink densities, and efficient stress dissipation, enabling optical transparency and reprocessability. Extending this platform to ultra-high molecular-weight prepolymers introduces physical entanglements as secondary crosslinks, further enhancing dimensional stability without compromising processability. Both mechanical and chemical recycling validate the closed-loop circularity of these materials. Furthermore, these results establish TK methacrylates as a versatile platform for designing high-performance vitrimers that integrate durability, reprocessability, and true closed-loop recyclability.

closed-loop recyclability

Block copolymer self-assembly derived mesoporous magnetic materials with three-dimensionally (3D) co-continuous gyroid nanostructure

Magnetic nanomaterials are gaining interest for their many applications in technological areas from information science and computing to next-generation quantum energy materials. While magnetic materials have historically been nanostructured through techniques such as lithography and molecular beam epitaxy, there has recently been growing interest in using soft matter self-assembly. In this work, a triblock terpolymer, poly(isoprene-block-styrene-block-ethylene oxide) (ISO), is used as a structure directing agent for aluminosilicate sol nanoparticles and magnetic material precursors to generate organic–inorganic bulk hybrid films with co-continuous morphology. After thermal processing into mesoporous materials, results from a combination of small angle X-ray scattering (SAXS) and scanning electron microscopy (SEM) are consistent with the double gyroid morphology. Nitrogen sorption measurements reveal a type IV isotherm with H1 hysteresis, and yield a specific surface area of around 200 m 2 g −1 and an average pore size of 23 nm. The magnetization of the mesostructured material as a function of applied field shows magnetic hysteresis and coercivity at 300 K and 10 K. Comparison of magnetic measurements between the mesoporous gyroid and an unstructured bulk magnetic material, derived from the identical inorganic precursors, reveals the structured material exhibits a coercivity of 250 Oe, opposed to 148 Oe for the unstructured at 10 K, and presence of remnant magnetic moment not conventionally found in bulk hematite; both of these properties are attributed to the mesostructure. This scalable route to mesoporous magnetic materials with co-continuous morphologies from block copolymer self-assembly may provide a pathway to advanced magnetic nanomaterials with a range of potential applications.

Chemistry

The Earth Observing System (EOS) nickel-hydrogen battery

Information is given in viewgraph form on the Earth Observing System (EOS) nickel hydrogen battery. Information is given on the life evaluation test, cell characteristics, acceptance and characterization tests, and the battery system description.

Bennett, Charles W.

Water Observations of Flow/No-Flow for the East-Taylor Watershed, Colorado (June-July 2025 and 2026)

This dataset provides multi-year, ground-truth visual observations of surface water flow/no-flow conditions within the East-Taylor Watershed, Colorado, collected during June and July of 2025 and 2026. In June and July 2025, on-the-ground visual observations of flow/no-flow were collected as part of the Watershed Function Scientific Focus Area (SFA) and Rocky Mountain Biological Laboratory (RMBL) Colorado Headwaters Ecological Spectroscopy Study (CHESS) campaign (further details are provided within the CHESS Project Description). We obtained 377 water observations of flow/no-flow within the East-Taylor Watershed, Colorado. These ground-truth observations were collected to validate classification maps from remote sensing data and model results within the East-Taylor Watershed. In 2025, flow/no-flow measurements were collected using a field-based app for the CHESS Campaign (Zerion iForm). Within the field app, a water observation form was created to collect coordinates and metadata about the observation. Information collected for the water observation points included information about visually-assessed streamflow presence/absence (standard question obtained from Colorado State University’s StreamTracker project), flow estimate, stream or ponded area width, canopy cover, manganese films, iron seeps, and beaver activity. For 2025 water observations, this dataset contains: (1) a data file with the water observations and coordinates (2025_Water_Observations.csv); (2) a Keyhole Markup Language Zipped (KMZ) with the water observation locations and metadata (2025_Water_Observations_Locations.kmz); (3) photos (.jpg and .jpeg) of the water observation points, organized by location, contained within 2025_Water_Observations_FieldPhotographs.zip file; and (4) water observation protocols and figures (2025_Water_Observation_Protocols.pdf). In June and July 2026, on-the-ground visual observations of flow/no-flow were collected as part of the Watershed Function SFA project. We obtained 365 water observations of flow/no-flow within the East-Taylor Watershed, Colorado. The 2026 observations focused on collecting repeat measurements at the 2025 flow/no-flow observation locations conducted as part of the CHESS campaign. These ground-truth observations were collected to understand differences in flow/no-flow in 2026, given the unprecedented 2026 drought in Colorado. In 2026, flow/no-flow measurements were collected using ArcGIS (Geographic Information System) Survey123. Within the field app, a water observation form was created to collect coordinates and metadata about the observation. Information collected for the water observation points included repeat information from the 2025 water observation effort, including visually-assessed streamflow presence/absence (standard question obtained from Colorado State University’s StreamTracker project), flow estimate, stream or ponded area width, canopy cover, manganese films, iron seeps, beaver activity, and a new metadata component of estimated stream depth (for select locations). For 2026 water observations, this dataset contains: (1) a data file with the water observations and coordinates (2026_Water_Observations.csv); (2) a Keyhole Markup Language Zipped (KMZ) with the water observation locations and metadata (2026_Water_Observations_Locations.kmz); (3) photos (.jpg) of the water observation points, organized by location, contained within 2026_Water_Observations_FieldPhotographs.zip file; and (4) water observation protocols and figures (2026_Water_Observation_Protocols.pdf). For 2025 and 2026 water observations, this dataset contains: (1) a location metadata file (locations.csv); (6) a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and (7) a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type. CHESS Project Description: The Colorado Headwaters Ecological Spectroscopy Study (CHESS) comprised a multi-week airborne remote sensing and field observation campaign in the Upper Gunnison Basin, Colorado, conducted in June and July of 2025. Airborne remote sensing was conducted by the National Ecological Observatory Network Airborne Observation Platform (NEON AOP), concurrent with a field campaign run by the Rocky Mountain Biological Laboratory (RMBL), the Lawrence Berkeley National Laboratory (LBNL) and SLAC National Accelerator Laboratory Watershed Function Science Focus Area (SFA), and NASA-JPL (Jet Propulsion Laboratory) Earth Surface Mineral Dust Source Investigation (EMIT) program. Between June 10 and July 18, 2025, the NEON AOP flight team collected high-resolution aerial imaging spectroscopy and Light Detection and Ranging (LiDAR) data over three domains: the Upper East River (CRBU), Almont Triangle (ALMO), and the Upper Taylor Basin (UPTA). In coordination with the flights, a field campaign acquired ground-truth observations, including observations of vegetation composition, foliar traits, forest demography, and subsurface properties in 18 core sampling areas within the domains. Additional surface water observations were taken at over 380 point locations. All CHESS campaign datasets can be found within the CHESS ESS-DIVE data portal: https://data.ess-dive.lbl.gov/portals/chess. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231. 2026-09-02: This dataset was updated to include 2026 water observation measurements. The 2025 observation files were also updated to ensure a consistent file naming convention across water observation years.

2018 NEON and 2025 CHESS Campaigns

Expanding the Horizons of Polymer Aerogels

As the Space Community endeavors to reach new heights of human exploration, materials for extreme environments are at the forefront of research. One class of materials of particular focus are polymer aerogels; lightweight solids with nanoscale pore size, high internal surface area, and extremely high porosities. These interesting properties allow aerogels to act as superior thermal insulators, IR scattering filters, sensor platforms, and vibro-acoustic mitigating materials. Polymer aerogels also have the potential to combat issues found in lunar environments such as dust and radiation mitigation. Herein, past and present research, synthesis, and applications of polymer aerogels will be discussed.

Stephanie L Vivod

Fast Growth of Ga2O3 on Highly Offcut (100)-Oriented Substrates

Beta-Ga2O3 has emerged as a leading candidate for next-generation power electronics, radio frequency (RF) switches, and extreme environment electronics due to a wide band gap (4.6 - 4.9 eV), high dopability (approximately 40 meV activation energy for an isolated silicon donor), and melt growth characteristics resulting in commercially available 4-inch substrates and commercial demonstrations of 6-inch substrates by multiple techniques. The (100) surface of Ga2O3 is highly desirable from a device and epitaxy standpoint - bulk growth of (100) material is more scalable than (010), the surface is nearly lattice-matched to p-type partner NiO, and Al2O3 incorporates at higher concentrations without phase separation. More importantly, the impact ionization coefficients along the [100] direction are low, leading to the highest possible critical fields. This is advantageous compared to the current state of the art, (001), due to reduced surface defects and increased possible breakdown voltage. However, the epitaxial growth rate on (100) surfaces is less than 10% of other faces due to weak bonding and favorable desorption, and on-axis (100) growth easily forms twin domains. Recent demonstrations have shown growth rate improvements from 0.4 nm/min to 1.5 nm/min by growing on (100) wafers that are offcut 6 degrees in the -c direction. These films show step-flow growth from (20-1) step-edges and high electron mobility due to suppressed twins. Despite these exciting results, offcuts greater than 6 degrees have not been explored due to the waste associated with grinding and polishing large offcuts. In this talk we will discuss the molecular beam epitaxy (MBE) growth and properties of Beta-Ga2O3 grown on (100) substrates offcut in the -c direction up to 13.4 degrees. These large offcuts are enabled by edge-fed film-defined growth (EFG) where the offcut is grown into the surface by pulling the crystal through the EFG die with the seed crystal rotated by the desired offcut angle. We will demonstrate that 13.4 degrees offcut substrates still exhibit a terraced (100) surface, and that a >10x increase (>5 nm/min) in growth rate is achieved. As previously reported on lower offcuts, we observe reversal of substrate twin domains around the (001) direction at the substrate-epilayer interface. We will discuss electrical properties including record-low (by MBE) unintentional doping densities of < 5E15 cm-3 and critical breakdown field in Schottky barrier diodes comparable with state-of-the-art (001) Ga2O3 without edge termination.

36 MATERIALS SCIENCE

From Rules to Reasoning: A Survey of Large Language Model-Based Approaches to Scientific Hypothesis and Idea Generation

Scientific hypothesis generation represents a fundamental challenge in contemporary research due to exponentially expanding literature volumes and increasing disciplinary specialization. Large language models (LLMs) have emerged as transformative tools for automated scientific discovery, moving beyond traditional rule-based and literature-mining approaches. Four paradigmatic approaches define current LLM-driven hypothesis generation: direct prompting and fine-tuning methods, knowledge-enhanced frameworks integrating retrieval-augmented generation (RAG), multi-agent collaborative systems simulating research teams, and reasoning-focused approaches implementing cognitive architectures. Domain-specific applications demonstrate statistical equivalence to human expert performance in social psychology, experimental validation in biomedical research, and near-expert quality in astronomy. Evaluation methodologies encompass human expert assessment, LLM-as-judge frameworks, and comprehensive benchmarking systems. Technical challenges include hallucination management, knowledge integration limitations, and balancing novelty with feasibility. Future directions emphasize hybrid neural-symbolic architectures and sophisticated human-AI collaboration models for responsible scientific discovery acceleration.

AI-driven discovery

Ferrimagnetism of ultracold fermions in a multiband Hubbard system

Strongly correlated materials feature multiple electronic orbitals, which are crucial to accurately understanding their many-body properties. In such multiband models, quantum interference can lead to flat energy bands with large degeneracy that gives rise to itinerant magnetic phases. Here, we report on signatures of a ferrimagnetic state realized in a Lieb lattice with ultracold fermions, characterized by antialigned magnetic moments with antiferromagnetic correlations, and concomitant with a finite spin polarization. The signatures remain robust when increasing repulsive interactions from the weakly interacting to the Heisenberg regime and emerge when continuously tuning the lattice unit cell from a square to a Lieb geometry. Our flexible approach paves the way toward exploring exotic phases, such as quantum spin liquids in kagome lattices and heavy fermion behavior in Kondo models.

Lebrat, Martin [Harvard Univ., Cambridge, MA (Unit

Exposure of Highly Reflective Far-Ultraviolet Coatings to LEO Environment for TRL Advancement for the Habitable Worlds Observatory

Over the past several years, our team at the NASA Goddard Space Flight Center (GSFC), in collaboration with the Jet Propulsion Laboratory (JPL) and the Naval Research Laboratory (NRL), have developed several new protected Al coating technologies with improved Far-Ultraviolet (FUV) reflectance performance and more robust environmental stability. These include Al protected with lithium-based fluoride (LiF) coatings such as hot deposited LiF (eLiF), XeF 2 -passivated LiF coatings (XeLiF), Li 3 AlF 6 overcoats, AlF 3 (plasma passivated), and XeF 2 passivated MgF 2 coatings (XeMgF 2 ). However, despite these developments, relatively little experimental information exists regarding the long-term stability of these coatings after simultaneous exposure to the Low Earth Orbit (LEO) environment. To evaluate their environmental durability and advance their Technology Readiness Level (TRL), representative samples of these coating technologies, Al+XeLiF, Al+eLiF, Al+Li 3 AlF 6 , Al+AlF 3 , Al+XeMgF 2 , and bare Al as reference samples, were flown onboard the International Space Station (ISS) as part of the Materials International Space Station Experiment 20 (MISSE-20). The MISSE platform is operated by Aegis Aerospace for relatively long-duration (e.g. 6 months) external exposure experiments in a space environment. The coatings were deposited on ULE and Zerodur substrates, and witness samples deposited on the same coatings runs, but on glass slides were left on Earth as control. A subset of the flight samples were fitted with MgF 2 windows to reduce direct exposure to atomic oxygen (AO) and charged particles, and still let through UV and other types of radiation on these samples. After approximately 6 months of exposure in the forward-facing (RAM) direction, the samples were returned to Earth and characterized by performing FUV/NUV/VIS/NIR reflectance measurements to quantify degradation, spectroscopic ellipsometry to evaluate coating thickness and optical constants, atomic force microscopy (AFM) to quantify surface roughness evolution during the flight in the ISS. The MgF 2 protective windows were also analyzed through FUV transmission measurements. Comparison with the witness samples left on the ground and with the flown bare Al samples (with just the naturally occurring Al 2 O 3 layer) provided a quantitative assessment of coating thickness variations, optical performance degradation, and morphological changes induced by prolonged exposure to the LEO environment.

Far Ultraviolet (FUV)

Thermal Bekenstein-Hawking entropy from the worldsheet

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS 3 reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,ℂ) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS