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ItemRigidity percolation in a random tensegrity via analytic graph theory( 2022-04-19) Rocklin, D. ZebTensegrities are mechanical structures that include cable-like elements that are strong and lightweight relative to rigid rods yet support only extensile stress. From suspension bridges to the musculoskeletal system to individual biological cells, humanity makes excellent use of tensegrities, yet the sharply nonlinear response of cables presents serious challenges to analytical theory. Here we consider large tensegrity structures with randomly placed cables (and struts) overlaid on a regular rigid backbone whose corresponding system of inequalities is reduced via analytic theory to an exact graph theory. We identify a novel coordination number that controls two rigidity percolation transitions: one in which global interactions between cables first support external loads and one in which the structure becomes fully rigid. We show that even the addition of a few cables strongly modifies conventional rigidity percolation, both by modifying the sharpness of the transition and by introducing avalanche effects in which a single constraint can eliminate multiple floppy modes.
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ItemFeynman rules for wave turbulence( 2022-04-12) Rosenhaus, VladimirIt has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state (the Kolmogorov-Zakharov state) with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. As a check, we reproduce the next-to-leading order term in the kinetic equation. The correlation functions and corrections to the KZ state that we compute should, in principle, be experimentally measurable quantities.
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ItemCompact Penning Traps for Quantum Science with Cold Atomic Ions(Georgia Institute of Technology, 2022-04-11) Sawyer, Brian C.Penning ion traps are useful experimental platforms for quantum simulation, mass spectrometry, precision metrology, and molecular ion spectroscopy. The GTRI Quantum Systems Division (QSD) has developed a compact, permanent-magnet-based Penning trap that is compatible with cold ion experiments, and we have recently updated our compact trap design with printed-circuit-board electrodes and improved trap magnetic field stability. We describe some near-term applications of this system including compact atomic clocks with dual-species, three-dimensional (3D) ion crystals and demonstration of the quantum approximate optimization algorithm (QAOA) with 2D ion arrays. We also highlight other notable results from the QSD in the field of ion trap quantum information.
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ItemOpportunities Created by Spin-Orbit Interactions(Georgia Institute of Technology, 2022-04-04) Cao, GangEffects of spin-orbit interactions in condensed matter are an important and rapidly evolving topic. A sea change occurred with the discovery of spin-orbit interactions in graphene by Mele and Kane, which has led to the exciting new field of physics addressing a rare interplay between spin-orbit and Coulomb interactions in condensed matter. I will describe an entirely new hierarchy of energy scales inherent in 4d- and 5d-electron based oxides and its unique consequences, highlighting discrepancies between experimental confirmation and theoretical proposals that address superconducting, topological and quantum spin liquid phases in iridates. I will then present our recent discoveries of novel quantum phenomena in iridates and ruthenates and conclude by venturing a perspective for research on spin-orbit-coupled oxides [1,2]. References: 1. Physics of Spin-Orbit-Coupled Oxides, Gang Cao and Lance E. De Long, Oxford University Press; Oxford, 2021 2. The Challenge of Spin-Orbit-Tuned Ground States in Iridates: A Key Issues Review, Gang Cao and Pedro Schlottmann, Reports on Progress in Physics, 81 042502 (2018)
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ItemOptical Lattice Clocks: From Timekeepers to Spies of the Quantum Realm(Georgia Institute of Technology, 2022-03-28) Rey, Ana MariaHarnessing the behavior of complex systems is at the heart of quantum technologies. Precisely engineered ultracold gases are emerging as a powerful tool for this task. In this talk I will explain how ultracold strontium atoms trapped by light can be used to create optical lattice clocks – the most precise timekeepers ever imagined. I am going to explain why these clocks are not only fascinating, but of crucial importance since they can help us to answer cutting-edge questions about complex many-body phenomena and magnetism, to unravel big mysteries of our universe and to build the next generation of quantum technologies.
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ItemProtecting the Space Environment: Sustainability and Security(Georgia Institute of Technology, 2022-03-07) Borowitz, MarielIn recent years, the number of objects in space has grown rapidly, and this growth is projected to continue to accelerate over the next decade. There has also been increased military activity in space, including rendezvous and proximity operations and debris-creating anti-satellite tests. These trends pose risks to the sustainability and security of the space environment – risks that have the potential to negatively affect all space users, including those in the astronomy and astrophysics communities. In many cases, addressing these issues requires international coordination and cooperation. This talk reviews some of the current challenges and risks to the space environment and discusses ongoing efforts to develop international policy solutions.
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ItemJust Enough Entanglement: Simulating Quantum Systems without a Quantum Computer(Georgia Institute of Technology, 2021-12-06) White, Steven R.The general solution of many-particle quantum systems is exponentially complex, requiring a quantum computer to solve. But for many of the most important properties of realistic experimental systems, the exponential complexity is avoidable, because while the entanglement of the system is high enough to make the system interesting, it is much lower than quantum mechanics allows. Tensor network methods exploit this low entanglement to enable simulations of many quantum systems on an ordinary computer. In this talk, I will give an overview of these ideas and methods and then detail our recent progress in simulating high temperature superconductors, systems with exotic entangled states which we are increasingly able to understand through simulation.
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ItemCharting dynamics from data( 2021-11-10) Floryan, DanielWe often find ourselves working with systems for which governing equations are unknown, or if they are known, they may be high-dimensional to the point of being difficult to analyze and prohibitively expensive to make predictions with. These difficulties, together with the ever-increasing availability of data, have led to the new paradigm of data-driven model discovery. I will present recent work that fruitfully combines a classical idea from applied mathematics with modern methods of machine learning to learn minimal dynamical models directly from time series data. In full analogy with cartography, we learn a representation of a system as an atlas of charts. This approach allows us to obtain dynamical models of the lowest possible dimension, leads to computational benefits, and can separate state space into regions of distinct behaviors. https://arxiv.org/abs/2108.05928
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ItemPhysics of Morphogenetic Matter(Georgia Institute of Technology, 2021-11-08) Gardel, MargaretMy lab studies how the movement and shape of living cells is controlled by living materials constructed by protein assemblies within the cell interior. In this talk, I will describe my lab’s recent efforts to understand the design principles of the active, soft materials that drive morphogenesis of epithelial tissue. In particular, we are interested in the design principles by which protein-based materials generate, relax, sense and adapt to mechanical force. Here I will describe our current experimental efforts to study the regulation of the shape and size of epithelial cells. If time allows, I will discuss how physical constraints govern cell size regulation in epithelial tissue.
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ItemData-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold( 2021-11-03) Pérez De Jesús, CarlosModel reduction techniques have previously been applied to evolve the Navier-Stokes equations in time, however finding the minimal dimension needed to correctly capture the key dynamics is not a trivial task. To estimate this dimension we trained an undercomplete autoencoder on weakly chaotic vorticity data (32x32 grid) from Kolmogorov flow simulations, tracking the reconstruction error as a function of dimension. We also trained a discrete time stepper that evolves the reduced order model with a nonlinear dense neural network. The trajectory travels in the vicinity of relative periodic orbits (RPOs) followed by sporadic bursting events. At a dimension of five (as opposed to the full state dimension of 1024), power input-dissipation probability density function is well-approximated; Fourier coefficient evolution shows that the trajectory correctly captures the heteroclinic connections (bursts) between the different RPOs, and the prediction and true data track each other for approximately a Lyapunov time.