Publications

Ultrafast laser pulses can redistribute charges in Mott insulators on extremely short time scales, leading to the fast generation of photocarriers. It has recently been demonstrated that these photocarriers can form a novel η--paired condensate at low temperatures, featuring a staggered superconducting pairing field. In this conference paper, we discuss the origin of the η--paired hidden phase and its optical response which may be detected in a pump-probe experiment. The hidden phase may be relevant for possible light-induced superconductivity in Mott insulators.

The well-developed separate universe technique enables accurate calibration of the response of any observable to an isotropic long-wavelength density fluctuation. The large-scale environment also hosts tidal modes that perturb all observables anisotropically. As in the separate universe, both the long tidal and density modes can be absorbed by an effective anisotropic background, on which the interaction and evolution of the short modes change accordingly. We further develop the tidal simulation method, including proper corrections to the second order Lagrangian perturbation theory (2LPT) to generate initial conditions of the simulations. We measure the linear tidal responses of the matter power spectrum, at high redshift from our modified 2LPT, and at low redshift from the tidal simulations. Our results agree qualitatively with previous works, but exhibit quantitative differences in both cases. We also measure the linear tidal response of the halo shapes, or the shape bias, and find its universal relation with the linear halo bias, for which we provide a fitting formula. Furthermore, analogous to the assembly bias, we study the secondary dependence of the shape bias, and discover for the first time dependence on halo concentration and axis ratio. Our results provide useful insights for studies of the intrinsic alignment as source of either contamination or information. These effects need to be correctly taken into account when one uses intrinsic alignments of galaxy shapes as a precision cosmological tool.

We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective, except for a collection of small absorbing patches. The narrow escape problem is the dual problem: it models the behavior of a Brownian particle confined to the interior of a sphere whose surface is reflective, except for a collection of small patches through which it can escape. Mathematically, these give rise to mixed Dirichlet/Neumann boundary value problems of the Poisson equation. They are numerically challenging for two main reasons: (1) the solutions are non-smooth at Dirichlet-Neumann interfaces, and (2) they involve adaptive mesh refinement and the solution of large, ill-conditioned linear systems when the number of small patches is large. By using the Neumann Green's functions for the sphere, we recast each boundary value problem as a system of first-kind integral equations on the collection of patches. A block-diagonal preconditioner together with a multiple scattering formalism leads to a well-conditioned system of second-kind integral equations and a very efficient approach to discretization. This system is solved iteratively using GMRES. We develop a hierarchical, fast multipole method-like algorithm to accelerate each matrix-vector product. Our method is insensitive to the patch size, and the total cost scales with the number N of patches as O(N log N), after a precomputation whose cost depends only on the patch size and not on the number or arrangement of patches. We demonstrate the method with several numerical examples, and are able to achieve highly accurate solutions with 100,000 patches in one hour on a 60-core workstation.

The wavelet scattering transform is an invariant and stable signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks, including PyTorch and TensorFlow/Keras. The transforms are implemented on both CPUs and GPUs, the latter offering a significant speedup over the former. The package also has a small memory footprint. Source code, documentation, and examples are available under a BSD license at https://www.kymat.iohttps://www.kymat.io.

In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and multiscale features, and our algorithm has computational complexity which is linear in the number of input triangles. We use a smoothing kernel to define a function $\phi$ whose level set defines the surface of interest. Charts are subsequently generated as maps from the original user-specified triangles to $\mathbb {R}^3$. The degree of smoothness is controlled locally by the kernel to be commensurate with the fineness of the input triangulation. The expression for~$\Phi$ can be transformed into a boundary integral, whose evaluation can be accelerated using a fast multipole method. We demonstrate the effectiveness and cost of the algorithm with polyhedral and quadratic skeleton surfaces obtained from CAD and meshing software.

It is difficult to quantify structure–property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it difficult to define structural metrics. In this work, we apply deep learning algorithms to accurately classify amorphous materials and characterize their structural features. Specifically, we show that convolutional neural networks and message passing neural networks can classify two-dimensional liquids and liquid-cooled glasses from molecular dynamics simulations with greater than 0.98 AUC, with no a priori assumptions about local particle relationships, even when the liquids and glasses are prepared at the same inherent structure energy. Furthermore, we demonstrate that message passing neural networks surpass convolutional neural networks in this context in both accuracy and interpretability. We extract a clear interpretation of how message passing neural networks evaluate liquid and glass structures by using a self-attention mechanism. Using this interpretation, we derive three novel structural metrics that accurately characterize glass formation. The methods presented here provide a procedure to identify important structural features in materials that could be missed by standard techniques and give unique insight into how these neural networks process data."

The role of planetary-scale zonally-asymmetric thermal forcing on large-scale atmospheric dynamics is crucial for understanding low-frequency phenomena in the atmosphere. Despite its paramount importance, good theoretical foundation for the understanding is still lacking. Here, we address this issue by providing a general framework for including planetary-scale thermal forcing in large-scale atmospheric dynamics studies. This is accomplished by identifying two distinct geostrophic motions of horizontal length scale Lin terms of the external Rossby deformation length scale LD: i) L ∼ ϵ0 LD and ii) L ∼ ϵ1/2 LD, whereϵ is the Rossby number. In addition, via multi-scale analysis, we show that the large-scale atmospheric dynamics can be described by mutual interaction between the two scales. The analysis results in planetary geostrophic equations with large-scale thermal forcing that provide the basic balanced states for processes such as the growth of synoptic waves. In the long-time limit, the continuous growth and decay of synoptic waves provide the convergence of horizontal heat and vorticity fluxes, which contributes to the energy flux balance in the planetary geostrophic scale with planetary-scale advection and thermal forcing.

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo (DQMC) algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers, and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and inter-layer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave (CDW) state. We extract the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature from superfluid density and a finite size scaling analysis of the correlation functions, and explain our results in terms of an effective biexcitonic hardcore boson model.

The brain takes uncertainty intrinsic to our world into account. For example, associating spatial locations with rewards requires to predict not only expected reward at new spatial locations but also its uncertainty to avoid catastrophic events and forage safely. A powerful and flexible framework for nonlinear regression that takes uncertainty into account in a principled Bayesian manner is Gaussian process (GP) regression. Here I propose that the brain implements GP regression and present neural networks (NNs) for it. First layer neurons, e.g. hippocampal place cells, have tuning curves that correspond to evaluations of the GP kernel. Output neurons explicitly and distinctively encode predictive mean and variance, as observed in orbitofrontal cortex (OFC) for the case of reward prediction. Because the weights of a NN implementing exact GP regression do not arise with biological plasticity rules, I present approximations to obtain local (anti-)Hebbian synaptic learning rules. The resulting neuronal network approximates the full GP well compared to popular sparse GP approximations and achieves comparable predictive performance.