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David Roberts

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quant-ph astro-ph math-ph math.MP Artificial Intelligence cond-mat.mes-hall cond-mat.str-el cond-mat.supr-con gr-qc hep-ph Machine Learning math.CT math.GR Software Engineering

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preprint2026arXiv

When Your LLM Reaches End-of-Life: A Framework for Confident Model Migration in Production Systems

We present a framework for migrating production Large Language Model (LLM) based systems when the underlying model reaches end-of-life or requires replacement. The key contribution is a Bayesian statistical approach that calibrates automated evaluation metrics against human judgments, enabling confident model comparison even with limited manual evaluation data. We demonstrate this framework on a commercial question-answering system serving 5.3M monthly interactions across six global regions; evaluating correctness, refusal behavior, and stylistic adherence to successfully identify suitable replacement models. The framework is broadly applicable to any enterprise deploying LLM-based products, providing a principled, reproducible methodology for model migration that balances quality assurance with evaluation efficiency. This is a capability increasingly essential as the LLM ecosystem continues to evolve rapidly and organizations manage portfolios of AI-powered services across multiple models, regions, and use cases.

preprint2020arXiv

Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability

We present a new approach for deriving exact, closed-form solutions for the steady state of a wide class of driven-dissipative nonlinear resonators that is distinct from more common positive-$P$ function methods. Our method generalizes the coherent quantum absorber approach of Stannigel et al. to include nonlinear driving and dissipation, and relies crucially on exploiting the Segal-Bargmann representation of Fock space. Our solutions and method reveal a wealth of previously unexplored observable phenomena in these systems, including new generalized photon-blockade and anti-blockade effects, and an infinite number of new parameter choices that yield quantum-bistability.

preprint2019arXiv

Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model

To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits $N$ in the limit that $N\to \infty$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground-state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.

preprint2016arXiv

Monopole-Enriched Groundstates of Two-Dimensional BCS Models

We extract the macroscopic characteristics of the groundstate sectors of two dimensional Bose-condensed BCS models with a fixed number of magnetic flux quanta, on length scales much larger than the characteristic size of the Cooper-pair bound states. We show that this reduces to the problem of computing the moduli space of gauge-inequivalent solutions to the Gross-Pitaevskii equations on a nontrivial fibre bundle. Inspired in part by the physical arguments of Oshikawa and Senthil in Fractionalization, Topological Order, and Quasiparticle Statistics, we extract a large class of groundstates from this moduli space.

preprint2016arXiv

The Total Green's Function of a Non-Interacting System

Despite its centrality in the mathematical structure of perturbative many-body theory, the total Green's function for the many-body time-dependent Schrodinger equation has been ignored for decades, superseded by single-particle Green's functions, for which a vast portion of the literature has been devoted. In this paper, we give the first computation the total Green's function for the time-dependent Schrodinger equation for a non-interacting system of identical particles, setting the stage for a fresh interpretation of perturbative many-body physics.

preprint2008arXiv

The inner automorphism 3-group of a strict 2-group

Any group $G$ gives rise to a 2-group of inner automorphisms, $\mathrm{INN}(G)$. It is an old result by Segal that the nerve of this is the universal $G$-bundle. We discuss that, similarly, for every 2-group $G_{(2)}$ there is a 3-group $\mathrm{INN}(G_{(2)})$ and a slightly smaller 3-group $\mathrm{INN}_0(G_{(2)})$ of inner automorphisms. We describe these for $G_{(2)}$ any strict 2-group, discuss how $\mathrm{INN}_0(G_{(2)})$ can be understood as arising from the mapping cone of the identity on $G_{(2)}$ and show that its underlying 2-groupoid structure fits into a short exact sequence $G_{(2)} \to \mathrm{INN}_0(G_{(2)}) \to ΣG_{(2)}$. As a consequence, $\mathrm{INN}_0(G_{(2)})$ encodes the properties of the universal $G_{(2)}$ 2-bundle.

preprint2002arXiv

Conditions for the confirmation of three-particle non-locality

The notion of genuine three-particle non-locality introduced by Svetlichny \cite{Svetlichny} is discussed. Svetlichny's inequality which can distinguish between genuine three-particle non-locality and two-particle non-locality is analyzed by reinterpreting it as a frustrated network of correlations. Its quantum mechanical maximum violation is derived and a situation is presented that produces the maximum violation. It is shown that the measurements performed in recent experiments to demonstrate GHZ entanglement \cite{Bouwmeester}, \cite{Pan} do not allow this inequality to be violated, and hence can not be taken as confirmation of genuine three-particle non-locality. Modifications to the experiments that would make such a confirmation possible are discussed.

preprint1996arXiv

Cosmological consequences of particle creation during inflation

Particle creation during inflation is considered. It could be important for species whose interaction is of gravitational strength or weaker. A complete but economical formalism is given for spin-zero and spin-half particles, and the particle abundance is estimated on the assumption that the particle mass in the early universe is of order the Hubble parameter $H$. It is roughly the same for both spins, and it is argued that the same estimate should hold for higher spin particles in particular the gravitino. The abundance is bigger than that from the usual particle collision mechanism if the inflationary energy scale is of order $10^{16} GeV$, but not if it is much lower.

preprint1995arXiv

Open Cold Dark Matter Models

Motivated by recent developments in inflationary cosmology indicating the possibility of obtaining genuinely open universes in some models, we compare the predictions of cold dark matter (CDM) models in open universes with a variety of observational information. The spectrum of the primordial curvature perturbation is taken to be scale invariant (spectral index $n=1$), corresponding to a flat inflationary potential. We allow arbitrary variation of the density parameter $Ω_0$ and the Hubble parameter $h$, and take full account of the baryon content assuming standard nucleosynthesis. We normalize the power spectrum using the recent analysis of the two year {\it COBE} DMR data by Górski et al. We then consider a variety of observations, namely the galaxy correlation function, bulk flows, the abundance of galaxy clusters and the abundance of damped Lyman alpha systems. For the last two of these, we provide a new treatment appropriate to open universes. We find that, if one allows an arbitrary $h$, then a good fit is available for any $Ω_0$ greater than 0.35, though for $Ω_0$ close to 1 the required $h$ is alarmingly low. Models with $Ω_0 < 0.35$ seem unable to fit observations while keeping the universe over $10$ Gyr old; this limit is somewhat higher than that appearing in the literature thus far. If one assumes a value of $h > 0.6$, as favoured by recent measurements, concordance with the data is only possible for the narrow range $0.35 < Ω_0 < 0.55$. We have also investigated $n \neq 1$; the extra freedom naturally widens the allowed parameter region. Assuming a range $0.9<n<1.1$, the allowed range of $Ω_0$ assuming $h > 0.6$ is at most $0.30 < Ω_0 < 0.60$.

preprint1994arXiv

False Vacuum Inflation with a Quartic Potential

We consider a variant of Hybrid Inflation, where inflation is driven by two interacting scalar fields, one of which has a `Mexican hat' potential and the other a quartic potential. Given the appropriate initial conditions one of the fields can be trapped in a false vacuum state, supported by couplings to the other field. The energy of this vacuum can be used to drive inflation, which ends when the vacuum decays to one of its true minima. Depending on parameters, it is possible for inflation to proceed via two separate epochs, with the potential temporarily steepening sufficiently to suspend inflation. We use numerical simulations to analyse the possibilities, and emphasise the shortcomings of the slow-roll approximation for analysing this scenario. We also calculate the density perturbations produced, which can have a spectral index greater than one.