arXiv subjects

Andrew Osborne

Publications and source records attributed to Andrew Osborne.

11 recordsLinked to original sources

arXiv2026

Chiral and bond-ordered phases in a triangular-ladder superconducting-qubit quantum simulator

Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between interactions, geometric frustration, and magnetic flux gives rise to rich physics. Superconducting qubits naturally enable analog quantum simulation of Bose-Hubbard models, while offering tunable parameters, site-resolved control, and rapid experimental repetition rates. Here, we study a superconducting-qubit device that realizes the Bose-Hubbard model on a triangular-ladder lattice. By tuning the magnitude and sign of couplings, we engineer a synthetic magnetic flux to characterize the resulting half-filling ground state for various parameter regimes. We measure observables analogous to current-current correlators and bond kinetic energies, finding signatures consistent with chiral superfluids, Meissner superfluids, and bond-ordered insulators. Our results establish superconducting circuits as a platform for robustly probing quantum phases of matter in frustrated Bose-Hubbard systems, even in strongly correlated and gapless regimes.

quant-ph↗

arXiv2025

Glued tree lattices with only compact localized states

Flat band physics is a central theme in modern condensed matter physics. By constructing a tight--binding single particle system that has vanishing momentum dispersion in one or more bands, and subsequently including more particles and interactions, it is possible to study physics in strongly interacting regimes. Inspired by the glued trees that first arose in one of the few known examples of quantum supremacy, we define and analyze two infinite families of tight binding single particle Bose--Hubbard models that have only flat bands, and only compact localized states despite having any nonnegative number of translation symmetries. The first class of model that we introduce is constructed by replacing a sufficiently large fraction of the edges in a generic countable graph with glued trees modified to have complex hoppings. The second class arises from thinking of complex weighted glued trees as rhombi that can then be used to tile two dimensional space, giving rise to the familiar dice lattice and infinitely many generalizations thereof, of which some are Euclidian while others are hyperbolic.

math-ph↗

arXiv2024

Stochastic theory of nonlinear electrical circuits in thermal equilibrium

We revisit the theory of dissipative mechanics in RLC circuits, allowing for circuit elements to have nonlinear constitutive relations, and for the circuit to have arbitrary topology. We systematically generalize the dissipationless Hamiltonian mechanics of an LC circuit to account for resistors and incorporate the physical postulate that the resulting RLC circuit thermalizes with its environment at a constant positive temperature. Our theory explains stochastic fluctuations, or Johnson noise, which are mandated by the fluctuation-dissipation theorem. Assuming Gaussian Markovian noise, we obtain exact expressions for multiplicative Johnson noise through nonlinear resistors in circuits with convenient (parasitic) capacitors and/or inductors. With linear resistors, our formalism is describable using a Kubo-Martin-Schwinger-invariant Lagrangian formalism for dissipative thermal systems. Generalizing our technique to quantum circuits could lead to an alternative way to study decoherence in nonlinear superconducting circuits without the Caldeira-Leggett formalism.

cond-mat.stat-mech↗

arXiv2024

Flux-charge symmetric theory of superconducting circuits

The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to circuit quantization treat fluxes and charges, which end up as the canonically conjugate degrees of freedom on phase space, asymmetrically. By combining intuition from topological graph theory with a recent symplectic geometry approach to circuit quantization, we present a theory of circuit quantization that treats charges and fluxes on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to non-planar circuits.

quant-ph↗

arXiv2023

Locality bounds for quantum dynamics at low energy

We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of lattice-regularized $H\propto p^{2k}$), the ``butterfly velocity" of particle motion at low energies has an upper bound that must scale as $E^{(2k-1)/2k}$, as expected from dimensional analysis. We generalize these results to obtain bounds on the typical velocities of particles in many-body systems with repulsive interactions, where for certain families of Hubbard-like models we obtain similar scaling.

math-ph↗

arXiv2023

Symplectic geometry and circuit quantization

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus the standard quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of non-dissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing circuits, including those that cannot be quantized using existing methods.

quant-ph↗

arXiv2022

Depth and Singular Varieties of Exterior Edge Ideals

Edge ideals of finite simple graphs are well-studied over polynomial rings. In this paper, we initiate the study of edge ideals over exterior algebras, specifically focusing on the depth and singular varieties of such ideals. We prove an upper bound on the depth of the edge ideal associated to a general graph and a more refined bound for bipartite graphs, and we show that both are tight. We also compute the depth of several large families of graphs including cycles, complete multipartite graphs, spider graphs, and Ferrers graphs. Finally, we focus on the effect whiskering a graph has on the depth of the associated edge ideal.

math.AC↗

arXiv2021

Infinite families of fracton fluids with momentum conservation

We construct infinite families of new universality classes of fracton hydrodynamics with momentum conservation, both with multipole conservation laws and/or subsystem symmetry. We explore the effects of broken inversion and/or time-reversal symmetry at the ideal fluid level, along with momentum relaxation. In the case of one-dimensional multipole-conserving models, we write down explicit microscopic Hamiltonian systems realizing these new universality classes. All of these hydrodynamic universality classes exhibit instabilities and will flow to new non-equilibrium fixed points. Such fixed points are predicted to exist in arbitrarily large spatial dimensions.

cond-mat.stat-mech↗

arXiv2020

Simple RGC: ImageJ plugins for counting retinal ganglion cells and determining the transduction efficiency of viral vectors in retinal wholemounts

Simple RGC consists of a collection of ImageJ plugins to assist researchers investigating retinal ganglion cell (RGC) injury models in addition to helping assess the effectiveness of treatments. The first plugin named RGC Counter accurately calculates the total number of RGCs from retinal wholemount images. The second plugin named RGC Transduction measures the co-localisation between two channels making it possible to determine the transduction efficiencies of viral vectors and transgene expression levels. The third plugin named RGC Batch is a batch image processor to deliver fast analysis of large groups of microscope images. These ImageJ plugins make analysis of RGCs in retinal wholemounts easy, quick, consistent, and less prone to unconscious bias by the investigator. The plugins are freely available from the ImageJ update site https://sites.imagej.net/Sonjoonho/.

q-bio.NC↗

arXiv2020

Operator growth bounds in a cartoon matrix model

We study operator growth in a model of $N(N-1)/2$ interacting Majorana fermions, which live on the edges of a complete graph of $N$ vertices. Terms in the Hamiltonian are proportional to the product of $q$ fermions which live on the edges of cycles of length $q$. This model is a cartoon "matrix model": the interaction graph mimics that of a single-trace matrix model, which can be holographically dual to quantum gravity. We prove (non-perturbatively in $1/N$, and without averaging over any ensemble) that the scrambling time of this model is at least of order $\log N$, consistent with the fast scrambling conjecture. We comment on apparent similarities and differences between operator growth in our "matrix model" and in the melonic models.

hep-th↗

arXiv2018

Prospects of detecting the nonlinear gravitational wave memory

In GW150914, approximately $3M_{\odot}$ were radiated away as gravitational waves from the binary black hole system as it merged. The stress energy of the gravitational wave itself causes a nonlinear memory effect in the detectors here on Earth called the Christodoulou memory. We use an approximation that can be applied to numerical relativity waveforms to give an estimate of the displacement magnitude and the profile of the nonlinear memory. We give a signal to noise ratio for a single GW150914-like detection event, and by varying the total mass and distance parameters of the event, we find distances and source masses for which the memory of an optimally oriented GW150914-like event would be detectable in aLIGO and future detectors.

gr-qc↗