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All sources NASA NTRS DOE OSTI

DOE OSTI2026

Feedback and Oscillations: Constructing Feedback Systems for Root Cause Analysis of Oscillations in Power Grids

Dynamic phenomena linked to inverter-based resources (IBRs) have gained global attention. Several IBR-induced dynamics have caused bulk power system-connected wind or solar power plants to trip, and some have even led to widespread outages. In addition, many oscillations have been observed involving IBR power plants. In 2023, the IEEE Power & Energy Society (PES) IBR Subsynchronous Oscillations (SSO) task force published a journal article, “Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources,” in which 19 IBR oscillation events were examined for their causation. Earlier in 2020, another PES task force article, “Definition and Classification of Power System Stability-Revisited & Extended,” authored by prominent academics, introduced converter-driven stability as a new category of stability. The international power grid industry community also took action by publishing the CIGRE Green Book, Power System Dynamic Modelling and Analysis in Evolving Networks (led by Babak Badrzadeh and Zia Emin) in 2024. In August 2024, the Energy Systems Integration Group (ESIG) released a practical guide led by Nick Miller, “Diagnosis and Mitigation of Observed Oscillations in IBR-Dominant Power System: A Practical Guide.” The goal of the guide is to assist practicing engineers in making initial judgments and conducting detailed analyses about oscillations. Finally, when addressing the classification of stability and oscillations, the guide emphasizes a causality-based taxonomy for grouping, such as voltage control-induced oscillations, synchronization-induced oscillations, and frequency or active power control-induced oscillations.

Fan, Lingling [Univ. of South Florida, Tampa, FL (↗

DOE OSTI2025

Impact of El Niño‐Southern Oscillation and Madden‐Julian Oscillation on the US Puget Sound Regional Hydroclimate

El Niño-Southern Oscillation (ENSO) and Madden-Julian Oscillation (MJO) are two major modes of climate variability with global hydroclimate impacts. However, their impacts often depend on the local climate and geography, resulting in large regional differences. In this study, we examined the connection of ENSO and MJO to the hydroclimate conditions and extremes in the Puget Sound (PS) basin located in the US Pacific Northwest coast. The results indicate that ENSO significantly modulates the cold season temperature and temperature-mediated hydrologic processes. El Niño cold seasons feature less snow accumulation and intensified surface runoff, even if the precipitation amount is similar to La Niña cold seasons. Therefore, El Niño causes more snow drought (in the form of compound dry and warm snow drought) and shifts the surface runoff seasonality by reducing runoff in the subsequent warm season. MJO phases 6–7 trigger more extreme precipitation, temperature, snowmelt, and runoff in the PS region at 0–9–day lags, and such connections are robust regardless of how the ENSO signals are removed. Meanwhile, MJO modulates large-scale extreme weather systems (e.g., atmospheric rivers) with significant enhancement during phases 6–7. ENSO impacts have intensified in the 2001–2020 period, whereas MJO impacts showed some phase shift in this period. This study reveals ENSO and MJO phases 6–7 as useful predictors of the PS hydroclimate anomalies/extremes at seasonal and daily scales, respectively. Utilizing these findings holds the potential to improve regional water resources prediction and management.

ENSO↗

DOE OSTI2025

A Twin Circuit Theory-Based Framework for Oscillation Event Analysis in Inverter-Dominated Power Systems With Case Study for Kaua‘i System

Here, this paper proposes a real-world oscillation event analysis framework for power systems that include inverter-based resources together with synchronous generators. Specifically, the proposed framework combines both measurement-and model-based techniques to readily identify potential oscillation sources, replay the oscillation event with numerical simulation, unveil the underlying oscillation mechanism, and suggest mitigation methods for a wide range of oscillation events. To strengthen the theoretical foundation of our analysis framework, this paper proposes a twin circuit theory that provides theoretical support for one key utilized but not well-proven measurement-based oscillation source identification method-Dissipating Energy Flow. Our twin circuit theory also shows that adopting well-tuned grid-forming inverters can be a potential mitigation method for oscillation events. Finally, the effectiveness of our proposed oscillation event analysis framework is demonstrated by addressing a real-world 18-20 Hz oscillation event in Kaua‘i's power system on November 21, 2021.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Injection locking and coupling dynamics in superconducting nanowire-based cryogenic oscillators

Oscillators designed to function at cryogenic temperatures play a critical role in superconducting electronics and quantum computing by providing stable, low-noise signals with minimal energy loss. Here, in this work, we present a comprehensive numerical study of injection locking and mutual coupling dynamics in superconducting nanowire (ScNW)-based cryogenic oscillators. Using the design space of a standalone ScNW-based oscillator, we investigate two critical mechanisms that govern frequency synchronization and signal coordination in cryogenic computing architectures: (1) injection locking induced by an external AC signal with a frequency near the oscillator's natural frequency, and (2) the mutual coupling dynamics between two ScNW oscillators under varying coupling strengths. We identify key design parameters—such as shunt resistance, nanowire inductance, and coupling strength—that govern the locking range. Additionally, we examine how the amplitude of the injected signal affects the amplitude of the locked oscillation, offering valuable insights for power-aware oscillator synchronization. Furthermore, we analyze mutual synchronization between coupled ScNW oscillators using capacitive and resistive coupling elements. Our results reveal that the phase difference between oscillators can be controlled by tuning the coupling strength, enabling programmable phase-encoded information processing. These findings could enable building ScNW-based oscillatory neural networks, synchronized cryogenic logic blocks, and on-chip cryogenic resonator arrays.

Artificial neural networks↗

DOE OSTI2024

Latest Three-Flavor Neutrino Oscillation Results from NOvA

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It aims to constrain neutrino oscillation parameters by analyzing $\nu_\mu (\bar{\nu}_\mu)$ disappearance and $\nu_e (\bar{\nu}_e)$ appearance data. The experiment uses the Neutrinos at Main Injector (NuMI) beamline at Fermilab, which delivers a high-purity 900 KW beam of neutrinos and anti-neutrinos. The detectors are functionally identical finely granulated liquid tracking calorimeters, both situated 14.6 mrad off-axis to the beam direction. The NOvA Near Detector (ND), situated 100 meters underground and 1 kilometer from the beam source, detects the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and beam $\nu_e (\bar{\nu}_e)$ events. The Far Detector (FD), located in Ash River, MN, USA, 809 kilometers from the ND, records the oscillated $\nu_e (\bar{\nu}_e)$ and the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ events. NOvA employs an extrapolation technique to predict the expected events at the Far Detector based on the Near Detector data, thereby providing a significant constraint on systematic uncertainties in the oscillation analyses. As NOvA accumulates more data, controlling these systematic uncertainties becomes increasingly important. This talk will detail the NOvA neutrino oscillation analysis framework and its approach to minimizing dominant systematic uncertainties using Near Detector data. The latest three flavor neutrino oscillation results based on a neutrino-beam exposure of $26.60 \times 10^{20}$ POT and an anti-neutrino beam exposure of $12.50\times 10^{20}$ POT and a novel low energy $\nu_e$ sample, will also be presented.

Choudhary, Brajesh↗

DOE OSTI2025

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗

DOE OSTI2026

Observation of Synchronization between Two Quantum van der Pol Oscillators in Trapped Ions

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

Liu, Jiarui↗

DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗

DOE OSTI2026

Measurement Adequacy for Monitoring Data Center Oscillations

Artificial intelligence (AI) training data centers with periodic load profiles can induce sustained grid oscillations across a wide frequency range, making accurate monitoring essential for reliable power system operation. This report evaluates the adequacy of existing measurement systems for monitoring such oscillations, focusing on phasor measurement units (PMUs) and point-on-wave (POW) measurement systems. The analysis shows that while PMUs are highly effective for monitoring low-frequency electromechanical oscillations, they have inherent limitations in accurately representing higher-frequency oscillations due to constraints imposed by reporting rates and the bandwidth of phasor estimation filters. Even when configured with higher reporting rates, the filtering inherent in the phasor estimation process can significantly attenuate oscillation magnitudes, potentially leading to underestimation of oscillatory behavior. This has important implications for compliance and performance monitoring of large loads. To address the limitations associated with PMU-based monitoring, the report examines the use of high-resolution POW measurements, which can capture oscillations across a broader frequency range. However, continuous POW monitoring introduces practical challenges related to large data volumes, communication bandwidth, and real-time data processing. For this reason, the report also discusses emerging approaches that use POW measurements as a complementary capability alongside PMUs to improve observability of oscillations from large data center loads.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Unconventional quantum oscillations and evidence of nonparabolic electronic states in quasi-two-dimensional electron system at complex oxide interfaces

The simultaneous occurrence of electric-field controlled superconductivity and spin-orbit interaction makes two-dimensional electron systems (2DES) constructed from perovskite transition metal oxides promising candidates for the next generation of spintronics and quantum computing. It is, however, essential to understand the electronic bands thoroughly and verify the predicted electronic states experimentally in these 2DES to advance technological applications. Here, we present insights into the electronic states of the 2DES at oxide interfaces through comprehensive investigations of Shubnikov–de Haas oscillations in three different systems: EuO/KTaO 3 , LaAlO 3 /SrTiO 3 , and amorphous-LaAlO 3 /KTaO 3 . To accurately resolve these oscillations, we conducted transport measurements in high magnetic fields up to 60 T and low temperatures down to 100 mK. For 2D confined electrons at these interfaces, we observed a progressive increase of oscillations frequency and cyclotron mass with the magnetic field. We interpret these universal and intriguing findings by considering the existence of nontrivial electronic bands, for which the 𝐸−𝑘 dispersion incorporates both linear and parabolic relations. In addition to providing experimental evidence for nonparabolic electronic states in KTaO 3 and SrTiO 3 2DES, the unconventional oscillations presented in this study establish a paradigm for quantum oscillations in 2DES based on perovskite transition metal oxides, where the oscillation frequencies in 1/𝐵 exhibit quadratic dependence on the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Dynamic Oscillation and Motion of Oil‐in‐Water Emulsion Droplets

The interplay of interfacial tensions on droplets results in a range of self‐powered motions that mimic those of living systems and serve as a tunable model to understand their complex non‐equilibrium behavior. Spontaneous shape deformations and oscillations are crucial features observed in nature but difficult to incorporate in synthetic artificial systems. Here, we report sessile oil‐in‐water emulsions that exhibit rapid oscillating behavior. The oscillations depend on the nature and concentration of the surfactant, the chemical composition of the oil, and the wettability of the solid substrate. The rapid changes in the contact angle per oscillation are observed using side‐view optical microscopy. We propose that the changes in the interfacial tension of the oil droplets is due to the partitioning of the surfactant into the oil phase and the movement of self‐emulsified oil out of the parent droplets giving rise to the rhythmic variation in droplet contact‐line. The ability to control and understand droplet oscillation can help model similar oscillations in out‐of‐equilibrium systems in nature and reproduce biomimetic behavior in artificial systems for various applications, such as microfluidic lab‐on‐a‐chip and adaptive materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Self-oscillating synchronematic colloids

Self-oscillators that sustain periodic dynamics under constant input are ubiquitous in natural and engineered systems, where their interactions enable spatiotemporal coordination among many individual units. New forms of organization can emerge when these self-oscillating units are free to move and rotate, coupling their spatial arrangement and alignment with their oscillation frequencies and phases. Here, we report experiments and simulations on populations of Quincke colloids that behave as self-oscillating units with position, orientation, frequency, and phase. Depending on the initial distribution, these active oscillators spontaneously organize into distinct collective states characterized by temporal synchronization and directional alignment, which we term synchronematic order. In fluid-like clusters, this order is short-ranged and decays over a length scale set by the competition between hydrodynamic interactions and athermal noise. In crystalline clusters, these interactions drive flobal synchronization and circular alignment-synchronematic crystals-whose collective frequency increases with cluster size due to non-reciprocal interactions. Our results establish self-oscillating colloids as a model system for active oscillatory matter and reveal fundamental principles by which synchronization, alignment, and structure co-emerge, offering new pathways for designing adaptive, frequency-tunable materials.

colloids↗

DOE OSTI2024

Latest Constraints on Three-Flavor Neutrino Oscillation Parameters from the NOvA Experiment.

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. The NOvA experiment was designed primarily to constrain neutrino oscillation parameters by analyzing $\nu_\mu (\bar{\nu}_\mu)$ disappearance and $\nu_e (\bar{\nu}_e)$ appearance data observed at the far detector. The Neutrinos at Main Injector (NuMI) beamline at Fermilab provides a high purity beam of neutrinos and anti-neutrinos to the experiment. The NOvA experiment consists of two functionally identical, finely granulated liquid tracking calorimeters, both situated 14.6 mrad off-axis to the beam direction. The NOvA near detector, situated 100 meters underground and 1 kilometer from the beam source, detects the non-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and beam $\nu_e (\bar{\nu}_e)$ events. The far detector, located in Ash River, MN, USA, 810 kilometers from the beam source, records the non-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and the oscillated $\nu_\mu (\bar{\nu}_\mu) \to \nu_e (\bar{\nu}_e)$ events. The most recent measurements of three flavor neutrino oscillation parameters based on an analysis of the data collected from neutrino-beam exposure of $26.60 \times 10^{20}$ POT and anti-neutrino beam exposure of $12.50\times 10^{20}$ POT including an additional low energy $\nu_e$ sample, will be presented in this talk.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

A Methodology to Evaluate the Grid Reliability Impact of Oscillations Induced by Large Loads

The rapid growth of hyperscale AI data centers is bringing renewed attention to the reliability risk that sustained forced oscillations pose to bulk power systems, with cyclic computational workloads emerging as a new forcing source. Unlike the broadband, stochastic disturbances from traditional industrial loads such as arc furnaces, AI training and inference facilities can inject large active power swings concentrated at specific frequencies over extended durations - characteristics that existing grid planning practices do not account for. While the North American Electric Reliability Corporation (NERC) has recognized this gap and called for system-level studies of large load interconnections, no standardized methodology exists to screen, simulate, and quantify these risks at the planning stage. This report presents the Risk Assessment Tool for Large Load-induced Events (RATLLE), a Python-based, publicly available script suite developed at the Pacific Northwest National Laboratory to evaluate bulk power system reliability risks from data center-induced oscillations. RATLLE implements a three-module workflow: a screening module that identifies vulnerable interconnection locations and excitable system modes; a simulation module that models cyclic data center load behavior using a commercial positive sequence simulation platform; and an analysis module that computes risk metrics and generates interactive visualization dashboards. The risk metrics, formulated around simulation observables, map oscillation impacts to a three-stage severity scale spanning latent equipment fatigue through imminent cascading failure. The methodology is demonstrated on two Western Electricity Coordinating Council (WECC) system models: a publicly available 240-bus reduced representation and a detailed 2031 Heavy Winter planning case. Case studies illustrate that even modest 50 MW forced oscillations at resonant frequencies can produce wide-area power swings, N-1 security constraint violations, and cascading generator trips through protection actions - outcomes that would not occur under normal operating conditions without oscillations present. The results underscore the need for standardized oscillation impact assessment in large load interconnection studies and provide a reproducible, extensible framework for utilities to adopt or customize within their existing planning workflows.

Biswas, Shuchismita↗

DOE OSTI2024

Latest Three-Flavor Neutrino Oscillation Results from NOvA

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. NOvA was designed primarily to constrain neutrino oscillation parameters by analyzing $\nu_\mu (\bar{\nu}_\mu)$ disappearance and $\nu_e (\bar{\nu}_e)$ appearance data at the far detector. The Neutrinos at Main Injector (NuMI) beamline at Fermilab provides a high purity beam of neutrinos and anti-neutrinos to the experiment. The NOvA experiments consists of two functionally identical, finely granulated liquid tracking calorimeters, both situated 14.6 mrad off-axis to the beam direction. The NOvA near detector, situated 100 meters underground and 1 kilometer from the beam source, detects the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and beam $\nu_e (\bar{\nu}_e)$ events. The far detector, located in Ash River, MN, USA, 810 kilometers from the beam source, records the un-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and the oscillated $\nu_e (\bar{\nu}_e)$ events. The most recent measurements of three flavor neutrino oscillation parameters based on an analysis of the data collected from a neutrino-beam exposure of $26.60 \times 10^{20}$ POT and an anti-neutrino beam exposure of $12.50\times 10^{20}$ POT with an additional low energy $\nu_e$ sample, will be presented in this talk.

Singh, Ishwar↗

DOE OSTI2026

Latest Constraints on Three-Flavor Neutrino Oscillation Parameters from the NOvA Experiment

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. The NOvA experiment was designed primarily to constrain neutrino oscillation parameters by analyzing $\nu_\mu (\bar{\nu}_\mu)$ disappearance and $\nu_e (\bar{\nu}_e)$ appearance data observed at the far detector using a high purity beam of neutrinos and anti-neutrinos from Fermilab's NuMI beamline. The NOvA experiment consists of two functionally identical, finely granulated liquid tracking calorimeters, both situated 14.6 mrad off-axis to the beam direction. The NOvA near detector, situated 100 meters underground and 1 kilometer from the beam source, detects the non-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and beam $\nu_e (\bar{\nu}_e)$ events. The far detector, located in Ash River, MN, USA, 810 kilometers from the beam source, records the non-oscillated $\nu_\mu (\bar{\nu}_\mu)$ and the oscillated $\nu_\mu (\bar{\nu}_\mu) \to \nu_e (\bar{\nu}_e)$ events. The most recent measurements of three flavor neutrino oscillation parameters based on an analysis of the data collected from neutrino-beam exposure of $26.60 \times 10^{20}$ POT and anti-neutrino beam exposure of $12.50\times 10^{20}$ POT including an additional low energy $\nu_e$ sample, will be discussed here.

Choudhary, Brajesh [Delhi U.] (ORCID:0000000150291↗

DOE OSTI2026

Measurements of three-flavor neutrino oscillations from a PISCES two-detector fit to the NOvA Experiment data

NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA s primary physics goals are to measure the neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ with high precision, determine the neutrino mass hierarchy, and constrain the value of $\delta_{CP}$, primarily via the study of muon neutrino to electron neutrino oscillation. Extracting values for oscillation parameters from fits to data usually relies on treating systematic uncertainties as nuisance parameters, a strategy that suffers from poor scalability as the number of uncertainties becomes larger. This work introduces PISCES (Parameter Inference with Systematic Covariance and Exact Statistics), a novel method that circumvents this scalability problem by encoding systematic uncertainties into a covariance matrix. PISCES utilizes a nested minimization in which optimal systematic pulls are first computed using the covariance matrix in an inner minimization step, then the oscillation parameters are profiled over in the outer minimization. PISCES also uses a Poisson Likelihood term, making it ideal for the inclusion of low-statistic samples in the fits. PISCES is a flexible framework that also supports complex fits, such as a joint Near and Far detector fit. In the standard NOvA analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data indirectly constrain the FD prediction via a ratio method. PISCES, on the other hand, enables a simultaneous ND+FD fit, allowing the high-statistics ND data to directly constrain systematic uncertainties across all samples. This thesis presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, details its implementation, and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method using the full NOvA 10-year data set. The results demonstrate that PISCES can successfully fit NOvA data while incorporating the constraints from the ND detectors consistently, using physically motivated systematic uncertainties to account for data/MC discrepancies.

Rajaoalisoa, Miriama [Cincinnati U.]↗

DOE OSTI2024

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) from the Hamiltonian for two, coupled QHOs and provide a physical picture for the Kravchuk function eigenstates of the oscillator. The familiar $\mathfrak{su}(2)$ structure of the coupled QHO Hamiltonian divides its spectrum into sets corresponding to the DQHO at different resolutions. In addition to energy ladder operators, the formulation allows for the introduction of resolution ladder operators connecting all DQHOs with different resolutions, thus enabling the dynamic scaling of the resolution of finite degree-of-freedom quantum simulations. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator. The DQHO coherent state recovers that of the quantum harmonic oscillator at large resolution.

97 MATHEMATICS AND COMPUTING↗