arXiv subjects

Nicholas Cox

Publications and source records attributed to Nicholas Cox.

11 recordsLinked to original sources

arXiv2026

Symbolic Regression for Interpretable Emulation of Proton Collective Flow in Intermediate-Energy Heavy-Ion Collisions

Symbolic regression provides an interpretable machine-learning approach for constructing explicit analytic relations between physical inputs and observables. In this work, we develop symbolic-regression emulators for the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model and compare their performance with deep neural network (DNN) emulators. Using the same transport-model data employed in our previous emulator studies, we show that symbolic regression can reproduce the proton mid-rapidity slope $F_1$ of transverse flow $v_1$ and elliptic flow $v_2$ with accuracy comparable to that of DNNs, while providing explicit analytic expressions and substantially faster prediction once trained. We further demonstrate the use of symbolic regression in the reverse direction by constructing analytic relations that predict the in-medium nucleon-nucleon cross-section modification factor $X$ from the flow observables. Although the symbolic-regression models require substantially longer training times and exhibit greater run-to-run variation than DNNs, their analytic form and rapid evaluation make them promising tools for future transport-model sensitivity and uncertainty analyses.

nucl-th↗

arXiv2026

Nonlinear pluggable optics: Digital signal processing-free Intensity Modulated Direct Detection links using analog photonic Next Generation Reservoir Computing

In this work, we propose a Nonlinear Pluggable Optic (NLPO) transceiver that combines the low latency and low power consumption of Linear Pluggable Optics (LPO) with the range and robustness of digital signal processing (DSP)-based transceivers. The proposed NLPO uses an analog photonic Next-Generation Reservoir Computing (NGRC) architecture, constructed on a photonic integrated circuit (PIC), to compensate for electrical-domain distortions as well as optical-channel impairments from chromatic dispersion and Kerr nonlinearity. Focusing on a simulated 50 GBd PAM-4 link, we find that the NGRC-based NLPO not only extends the range of LPO, but actually outperforms DSP-based solutions as well. Our simulations reveal two key advantages compared to DSP-based Intensity Modulation/Direct Detection (IM/DD) links: (1) the NGRC can take advantage of the optical phase information without requiring a local oscillator and (2) the NGRC can optically sample the transmitted data well above the symbol rate without requiring high-bandwidth electronics. This work showcases the potential for photonic NGRCs to outperform state-of-the-art digital solutions in real-world applications and opens a path to low-latency, lower-power IM/DD links at ranges of 10s of km.

physics.optics↗

arXiv2025

A broadband silicon photonic-integrated-circuit based RF spectrum analyzer with 10 MHz spectral resolution

Designing miniaturized optical spectrometers is an increasingly active area of research as spectrometers are crucial components for a wide range of applications including chemical and material analysis, medical diagnostics, classical and quantum sensing, characterization of light sources, and radio frequency (RF) spectrum analysis. Among these applications, designing on-chip spectrometers for RF spectrum analysis is particularly challenging since it requires combining high resolution and large bandwidth with a fast update rate. Existing chip-scale spectrometers cannot achieve the resolution required for RF analysis, setting aside challenges in maintaining a fast update rate and broad bandwidth. In this work, we address these challenges by introducing a silicon photonic integrated circuit (PIC)-based RF spectrum analyzer that combines an ultra-high-resolution speckle spectrometer with an interferometric RF-to-optical encoding scheme. The PIC-based speckle spectrometer uses a path-mismatched multimode interferometer with inverse designed splitters to compensate for waveguide loss, enabling a record-high resolution of 100 MHz (0.8 pm at a wavelength of 1550 nm). To further improve the resolution of the overall RF spectrum analyzer, we modify the RF-to-optical encoding scheme by directing the RF signal through a path mismatched interferometer and encoding the outputs of the RF interferometer on separate optical carriers. This further reduces the RF spectral correlation width of the combined system, enabling the RF spectrum analyzer to resolve RF tones separated by 10 MHz across a bandwidth of 10 GHz. Since this approach operates as a single-shot spectrometer, it can support fast update rates, providing a path to compact, persistent wideband RF spectrum analysis.

physics.optics↗

arXiv2024

Photonic frequency multiplexed next-generation reservoir computer

In this work, we introduce and experimentally demonstrate a photonic frequency-multiplexed next generation reservoir computer (FM-NGRC) capable of performing real-time inference at GHz speed. NGRCs apply a feed-forward architecture to produce a feature vector directly from the input data over a fixed number of time steps. This feature vector, analogous to the reservoir state in a conventional RC, is used to perform inference by applying a decision layer trained by linear regression. Photonic NGRC provides a flexible platform for real-time inference by forgoing the need for explicit feedback loops inherent to a physical reservoir. The FM-NGRC introduced here defines the memory structure using an optical frequency comb and dispersive fiber while the sinusoidal response of electro-optic Mach-Zehnder interferometers controls the nonlinear transform applied to elements of the feature vector. A programmable waveshaper modulates each comb tooth independently to apply the trained decision layer weights in the analog domain. We apply the FM-NGRC to solve the benchmark nonlinear channel equalization task; after theoretically determining feature vectors that enable high-accuracy distortion compensation, we construct an FM-NGRC that generates these vectors to experimentally demonstrate real-time channel equalization at 5 GS/s with a symbol error rate of $\sim 2\times 10^{-3}$.

physics.optics↗

arXiv2024

Neural Network Emulation of Flow in Heavy-Ion Collisions at Intermediate Energies

Applications of new techniques in machine learning are speeding up progress in research in various fields. In this work, we construct and evaluate a deep neural network (DNN) to be used within a Bayesian statistical framework as a faster and more reliable alternative to the Gaussian Process (GP) emulator of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions at intermediate beam energies. We found strong evidence of DNN being able to emulate the IBUU simulator's prediction on the strengths of protons' directed and elliptical flow very efficiently even with small training datasets and with accuracy about ten times higher than the GP. Limitations of our present work and future improvements are also discussed.

nucl-th↗

arXiv2024

Photonic next-generation reservoir computer based on distributed feedback in optical fiber

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the R\"ossler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, this scheme is easily scalable to high-dimensional systems while maintaining low latency and low power consumption.

physics.optics↗

arXiv2023

Identification of the Chromophores in Prussian blue

Prussian blue was the world's first synthetic dye. Its structural, optical and magnetic properties have led to many applications in technology and medicine, and provide paradigms for understanding coordination polymers, framework materials and mixed-valence compounds. The intense red absorption of Prussian blue that characterises chemical and physical properties critical to many of these applications is now shown to arise from localised intervalence charge transfer transitions within two chromophoric variants (ligand isomers) of an idealised "dimer" fragment {(NC)5FeII}(mu-CN){FeIII(NC)3(H2O)2}. This fragment is only available in modern interpretations of the material's crystal structure, with the traditional motif {(NC)5FeII}(mu-CN){FeIII(NC)5} shown not to facilitate visible absorption. Essential to the analysis is the demonstration, obtained independently using absorption and magnetic circular dichroism spectroscopies, that spectra of Prussian blues are strongly influenced by particle size and (subsequent) light scattering. These interpretations are guided and supported by density functional theory calculations (CAM-B3LYP), supplemented by coupled cluster and Bethe-Salpeter spectral simulations, as well as electron paramagnetic resonance spectroscopy of Prussian blue and a model molecular dimeric ion [Fe2(CN)11]6-.

cond-mat.mtrl-sci↗

arXiv2021

Exact solutions to the quantum many-body problem using the geminal density matrix

It is virtually impossible to directly solve the Schr\"odinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM) formalism reduces this coordinate dependence to that of four particles irrespective of the wave function's dimensionality, providing a promising path to solve the many-body problem. Unfortunately, errors arise in this approach because the 2-RDM cannot practically be constrained to guarantee that it corresponds to a valid wave function. Here we approach this so-called $N$-representability problem by expanding the 2-RDM in a complete basis of two-electron wave functions and studying the matrix formed by the expansion coefficients. This quantity, which we call the geminal density matrix (GDM), is found to evolve in time by a unitary transformation that preserves $N$-representability. This evolution law enables us to calculate eigenstates of strongly correlated systems by a fictitious adiabatic evolution in which the electron-electron interaction is slowly switched on. We show how this technique is used to diagonalize atomic Hamiltonians, finding that the problem reduces to the solution of $\sim N(N-1)/2$ two-electron eigenstates of the Helium atom on a grid of electron-electron interaction scaling factors.

quant-ph↗

arXiv2021

Properties and $N$-representability conditions of the two-body density matrix

A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave function and these so-called two-body density matrices enables the derivation of necessary $N$-representability conditions that ensure a given matrix obeys the postulates of many-body quantum mechanics.

quant-ph↗

arXiv2020

Three-Photon Absorption Spectra and Bandgap Scaling in Direct-Gap Semiconductors

This paper presents three-photon absorption (3PA) measurement results for nine direct-gap semiconductors, including full 3PA spectra for ZnSe, ZnS, and GaAs. These results, along with our theory of 3PA using an 8-band Kane model (4 bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the 8-band model exhibits quantum interference between the various possible pathways that is not observed in previous 2-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, Eg, scaling using 2-band tunneling and perturbation theories that show agreement with the predicted Eg^-7 dependence; however, For those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both 2-band theories. On the other hand, our 8-band model shows excellent agreement with the spectral data. We then use our 8-band theory to predict the 3PA spectra for 15 different semiconductors in their zincblende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors.

physics.optics↗

arXiv2019

Nondegenerate Two-Photon Absorption in GaAs/AlGaAs Multiple Quantum Well Waveguides

We present femtosecond pump-probe measurements of the nondegenerate (1960$\,$nm excitation and 1176--1326$\,$nm probe) two-photon absorption spectra of 8 $\,$nm GaAs/12$\,$nm Al$_{0.32}$Ga$_{0.68}$As quantum well waveguides. Experiments were performed with light pulses co-polarized normal and tangential to the quantum well plane. The results are compared to perturbative calculations of transition rates between states determined by the $\mathbf{k}\cdot\mathbf{p}$ method with an 8 or 14 band basis. We find excellent agreement between theory and experiment for normal polarization, then use the model to support predictions of orders-of-magnitude enhancement of nondegenerate two-photon absorption as one constituent photon energy nears an intersubband resonance.

physics.optics↗