Publications

Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to construct constitutive models based on various calibration data. In this work, we propose a neural operator to develop nonlocal constitutive models for tensorial quantities through a vector-cloud neural network with equivariance (VCNN-e). The VCNN-e respects all the invariance properties desired by constitutive models, faithfully reflects the region of influence in physics, and is applicable to different spatial resolutions. By design, the model guarantees that the predicted tensor is invariant to the frame translation and ordering (permutation) of the neighboring points. Furthermore, it is equivariant to the frame rotation, i.e., the output tensor co-rotates with the coordinate frame. We evaluate the VCNN-e by using it to emulate the Reynolds stress transport model for turbulent flows, which directly computes the Reynolds stress tensor to close the Reynolds-averaged Navier--Stokes (RANS) equations. The evaluation is performed in two situations: (1) emulating the Reynolds stress model through synthetic data generated from the Reynolds stress transport equations with closure models, and (2) predicting the Reynolds stress by learning from data generated from direct numerical simulations. Such a priori evaluations of the proposed network pave the way for developing and calibrating robust and nonlocal, non-equilibrium closure models for the RANS equations.

Electron-electron (e-e) and electron-phonon (e-ph) interactions are challenging to describe in correlated materials, where their joint effects govern unconventional transport, phase transitions, and superconductivity. Here we combine first-principles e-ph calculations with dynamical mean field theory (DMFT) as a step toward a unified description of e-e and e-ph interactions in correlated materials. We compute the e-ph self-energy using the DMFT electron Green's function, and combine it with the e-e self-energy from DMFT to obtain a Green's function including both interactions. This approach captures the renormalization of quasiparticle dispersion and spectral weight on equal footing. Using our method, we study the e-ph and e-e contributions to the resistivity and spectral functions in the correlated metal Sr

We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a non-uniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may posses interesting phases beyond Landau level physics.

Strong light-matter interactions as realized in an optical cavity provide a tantalizing opportunity to control the properties of condensed matter systems. Inspired by experimental advances in cavity quantum electrodynamics and the fabrication and control of two-dimensional magnets, we investigate the fate of a quantum critical antiferromagnet coupled to an optical cavity field. Using unbiased quantum Monte Carlo simulations, we compute the scaling behavior of the magnetic structure factor and other observables. While the position and universality class are not changed by a single cavity mode, the critical fluctuations themselves obtain a sizable enhancement, scaling with a fractional exponent that defies expectations based on simple perturbation theory. The scaling exponent can be understood using a generic scaling argument, based on which we predict that the effect may be even stronger in other universality classes. Our microscopic model is based on realistic parameters for two-dimensional magnetic quantum materials and the effect may be within the range of experimental detection.

We present an approach to interface branching random walks with Markov chain Monte Carlo sampling, and to switch seamlessly between the two. The approach is discussed in the context of auxiliary-field quantum Monte Carlo (AFQMC) but is applicable to other Monte Carlo calculations or simulations. In AFQMC, the formulation of branching random walks along imaginary-time is needed to realize a constraint to control the sign or phase problem. The constraint is derived from an exact gauge condition, and is in practice implemented approximately with a trial wave function or trial density matrix, which can break exactness in the algorithm. We use the generalized Metropolis algorithm to sample a selected portion of the imaginary-time path after it has been produced by the branching random walk. This interfacing allows a constraint release to follow seamlessly from the constrained-path sampling, which can reduce the systematic error from the latter. It also provides a way to improve the computation of correlation functions and observables that do not commute with the Hamiltonian. We illustrate the method in atoms and molecules, where improvements in accuracy can be clearly quantified and near-exact results are obtained. We also discuss the computation of the variance of the Hamiltonian and propose a convenient way to evaluate it stochastically without changing the scaling of AFQMC.

High-harmonic generation (HHG) in liquids is opening new opportunities for attosecond light sources and attosecond time-resolved studies of dynamics in the liquid phase. In gas-phase HHG, few-cycle pulses are routinely used to create isolated attosecond pulses and to extend the cut-off energy. Here, we study the properties of HHG in liquids, including water and several alcohols, by continuously tuning the pulse duration of a mid-infrared driver from the multi- to the sub-two-cycle regime. Similar to the gas phase, we observe the transition from discrete odd-order harmonics to continuous extreme-ultraviolet emission. However, the cut-off energy is shown to be entirely independent of the pulse duration. This observation is confirmed by ab-initio simulations of HHG in large clusters. Our results support the notion that the cut-off energy is a fundamental property of the liquid, independent of the driving-pulse properties. Combined with the recently reported wavelength-independence of the cutoff, these results confirm the direct sensitivity of HHG to the mean-free paths of slow electrons in liquids. Our results additionally imply that few-cycle mid-infrared laser pulses are suitable drivers for generating isolated attosecond pulses from liquids.

High-harmonic spectroscopy (HHS) is a nonlinear all-optical technique with inherent attosecond temporal resolution, which has been applied successfully to a broad variety of systems in the gas phase and solid state. Here, we extend HHS to the liquid phase, and uncover the mechanism of high-harmonic generation (HHG) for this phase of matter. Studying HHG over a broad range of wavelengths and intensities, we show that the cut-off (E

https://arxiv.org/abs/2211.04241

This dissertation investigates two fundamental aspects of neural population coding: adaptive coding efficiency and stochastic representational geometry. We introduce a theory for adaptive statistical whitening revolving around a gain control mechanism, based on a novel overcomplete matrix factorization of the whitening transform. From this theory, we derive an online whitening algorithm that maps directly onto a recurrent neural network with primary neurons and an over-complete, auxiliary set of gain-modulating interneurons. Further elaborating on this framework, we integrate adaptive gain control with existing theories of adaptive whitening into a single unified adaptation objective using synaptic plasticity in a multi-timescale mechanistic model. This model adapts to changing sensory statistics by modifying gains and synapses at varying rates, resulting in improved adaptive whitening responses that is robust to non-stationary environments. Leveraging V1 population adaptation data, we demonstrate that propagation of single neuron gain changes through recurrent network structures is sufficient to explain the entire set of observed adaptation effects. Finally, we shift our focus to stochastic representational geometry, and introduce a family of distance metrics for comparing geometry between stochastic neural networks. These metrics are based on concepts from optimal transport theory and provide unique insights into the representations of noisy artificial and biological neural networks. Taken together, this thesis advances our understanding of neural population coding by examining the adaptive coding efficiency and the stochastic geometry of neural representations, with possible implications to the fields of neuroscience and machine learning.

The circumgalactic medium (CGM) plays a pivotal role in regulating gas flows around galaxies and thus shapes their evolution. However, the details of how galaxies and their CGM co-evolve remain poorly understood. We present a new time-dependent two-zone model that self-consistently tracks not just mass and metal flows between galaxies and their CGM but also the evolution of the global thermal and turbulent kinetic energy of the CGM. Our model accounts for heating and turbulence driven by both supernova winds and cosmic accretion as well as radiative cooling, turbulence dissipation, and halo outflows due to CGM overpressurization. We demonstrate that, depending on parameters, the CGM can undergo a phase transition (``thermalization'') from a cool, turbulence-supported phase to a virial-temperature, thermally-supported phase. This CGM phase transition is largely determined by the ability of radiative cooling to balance heating from supernova winds and turbulence dissipation. We perform an initial calibration of our model to the FIRE-2 cosmological hydrodynamical simulations and show that it can approximately reproduce the baryon cycles of the simulated halos. In particular, we find that, for these parameters, the phase transition occurs at high-redshift in ultrafaint progenitors and at low redshift in classical Mvir∼1011M⊙ dwarfs, while Milky Way-mass halos undergo the transition at z≈0.5. We see a similar transition in the simulations though it is more gradual, likely reflecting radial dependence and multi-phase gas not captured by our model. We discuss these and other limitations of the model and possible future extensions.