arXiv subjects

James Walkling

Publications and source records attributed to James Walkling.

4 recordsLinked to original sources

arXiv2026

Fractal deconfinement and confinement in Sierpinski ice

We study the six-vertex model on the Sierpinski gasket, a four-coordinated hierarchical fractal with Hausdorff dimension $d_f=\log_23$. Given the importance of dimensionality for the long-wavelength behavior of such models, we specifically consider correlations and confinement as a function of the vertex weights, with the equal-weight point corresponding to the ice model. We calculate the partition function and correlators recursively to obtain a rich phase diagram hosting many different regimes. While the ice model shows entropic charge confinement, a particular four-vertex limit exhibits fractal deconfinement, with the string joining the deconfined charges itself a statistical fractal with fractal dimension $d_l=\log_2(5/2)\approx 1.3$. Finally, we propose a setup as an artificial spin ice to enable experimental study of the rich phenomenology of Sierpinski ice and its generalisations.

cond-mat.stat-mech↗

arXiv2025

Localization and topological signatures under periodic twisting

We theoretically explore a dynamical generalization of the Aubry-Andr\'e model in two dimensions formed by superimposing two square-lattice potentials. Motivated by the rich physics emerging at different twist angles between the two lattices at equilibrium, we introduce periodic twisting by continuously rotating one of the lattices with respect to the other in the plane. We demonstrate that the distinct time-dependent twisting in this system gives rise to an intricate form of periodic multi-frequency driving that changes with the distance from the rotation axis. We find that the incommensurate nature of the potential no longer plays the pivotal role as it does in the static case. Rather, the tunneling can be understood in terms of a local, spatially varying dynamical localization effect, which we show to yield ring-shaped states localized within the bulk that have interesting transport signatures. Quantifying the eigenstates with the Bott index and local Chern marker, we find that there is a zoo of states with non-trivial topological signatures, the most ubiquitous of which result in relatively uniform ring-shaped regions of the Chern marker. We investigate the origin of these effects from various angles and identify that hybridization between different delocalized ring states plays a vital role. Lastly, we discuss possible experimental realizations in quantum simulation settings. Our results open a new avenue of investigation with periodic twisting inducing a spatially varying multi-frequency drive.

cond-mat.quant-gas↗

arXiv2025

Walsh-Floquet Theory of Periodic Kick Drives

Periodic kick drives are ubiquitous in digital quantum control, computation, and simulation, and are instrumental in studies of chaos and thermalization for their efficient representation through discrete gates. However, in the commonly used Fourier basis, kick drives lead to poor convergence of physical quantities. Instead, here we use the Walsh basis of periodic square-wave functions to describe the physics of periodic kick drives. In the strongly kicked regime, we find that it recovers Floquet dynamics of single- and many-body systems more accurately than the Fourier basis, due to the shape of the system's response in time. To understand this behavior, we derive an extended Sambe space formulation and an inverse-frequency expansion in the Walsh basis. We explain the enhanced performance within the framework of single-particle localization on the frequency lattice, where localization is correlated with small truncation errors. We show that strong hybridization between states of the kicked system and Walsh modes gives rise to Walsh polaritons that can be studied on digital quantum simulators. Our work lays the foundations of Walsh-Floquet theory, which is naturally implementable on digital quantum devices and suited to Floquet state manipulation using discrete gates.

quant-ph↗

arXiv2023

A Comprehensive Model of Snow Crystal Faceting

Crystal faceting can emerge via two broad physical mechanisms: anisotropic attachment kinetics on growing crystals and anisotropic surface energies on near-equilibrium crystals. For the case of the ice/vapor system, anisotropic attachment kinetics is the dominant faceting mechanism, while the possible occurrence of equilibrium faceting has been debated for many decades. In this investigation we examine ice/vapor faceting at low supersaturations over the temperature range -15C -2C, thus suggesting that snow crystal faceting is caused by anisotropic attachment kinetics even at extremely slow growth rates.

cond-mat.mtrl-sci↗