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1. Realizing tight-binding Hamiltonians using site-controlled coupled cavity arrays

   https://doi.org/10.1038/s41467-023-41034-x  

   Saxena, Abhi; Manna, Arnab; Trivedi, Rahul; Majumdar, Arka (December 2023, Nature Communications)

   Abstract Analog quantum simulators rely on programmable and scalable quantum devices to emulate Hamiltonians describing various physical phenomenon. Photonic coupled cavity arrays are a promising alternative platform for realizing such simulators, due to their potential for scalability, small size, and high-temperature operability. However, programmability and nonlinearity in photonic cavities remain outstanding challenges. Here, using a silicon photonic coupled cavity array made up of$$8$$ $8$high quality factor ($$Q$$ $Q$up to$$\, \sim 7.1\times {10}^{4}$$ $~7.1\times {10}^4$) resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable photonic cavity array in the telecom regime, implementing tight-binding Hamiltonians with access to the full eigenenergy spectrum. We report a$$\sim 50\%$$ $~50\%$reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight-binding Hamiltonian. The ability to independently program high-Q photonic cavities, along with the compatibility of silicon photonics to high volume manufacturing opens new opportunities for scalable quantum simulation using telecom regime infrared photons. 

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2. The power particle-in-cell method

   https://doi.org/10.1145/3528223.3530066  

   Qu, Ziyin; Li, Minchen; De Goes, Fernando; Jiang, Chenfanfu (July 2022, ACM Transactions on Graphics)

   This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al. 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al. 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations. 

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3. Anomalous Crystalline-Electromagnetic Responses in Semimetals

   https://doi.org/10.1103/PhysRevX.14.041060  

   Hirsbrunner, Mark R; Dubinkin, Oleg; Burnell, F J; Hughes, Taylor L (December 2024, Physical Review X)

   We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to $D=3$through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models. Published by the American Physical Society2024 

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4. The nanocaterpillar's random walk: diffusion with ligand–receptor contacts

   https://doi.org/10.1039/D1SM01544C  

   Marbach, Sophie; Zheng, Jeana Aojie; Holmes-Cerfon, Miranda (April 2022, Soft Matter)

   Particles with ligand–receptor contacts bind and unbind fluctuating “legs” to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such “nanoscale caterpillars” is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli , and DNA-coated colloids) and present guidelines to control the mode of motion for materials design. 

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5. Detailed balance for particle models of reversible reactions in bounded domains

   https://doi.org/10.1063/5.0085296  

   Zhang, Ying; Isaacson, Samuel A. (May 2022, The Journal of Chemical Physics)

   In particle-based stochastic reaction–diffusion models, reaction rates and placement kernels are used to decide the probability per time a reaction can occur between reactant particles and to decide where product particles should be placed. When choosing kernels to use in reversible reactions, a key constraint is to ensure that detailed balance of spatial reaction fluxes holds at all points at equilibrium. In this work, we formulate a general partial-integral differential equation model that encompasses several of the commonly used contact reactivity (e.g., Smoluchowski-Collins-Kimball) and volume reactivity (e.g., Doi) particle models. From these equations, we derive a detailed balance condition for the reversible A + B ⇆ C reaction. In bounded domains with no-flux boundary conditions, when choosing unbinding kernels consistent with several commonly used binding kernels, we show that preserving detailed balance of spatial reaction fluxes at all points requires spatially varying unbinding rate functions near the domain boundary. Brownian dynamics simulation algorithms can realize such varying rates through ignoring domain boundaries during unbinding and rejecting unbinding events that result in product particles being placed outside the domain. 

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