Publications

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.

Sensation of light is essential for all organisms. The eye-less nematode Caenorhabditis elegans detects UV and blue light to evoke escape behavior. The photosensor LITE-1 absorbs UV photons with an unusually high extinction coefficient, involving essential tryptophans. Here, we modeled the structure and dynamics of LITE-1 using AlphaFold2-multimer and molecular dynamics (MD) simulations and performed mutational and behavioral assays in C. elegans to characterize its function. LITE-1 resembles olfactory and gustatory receptors from insects, recently shown to be tetrameric ion channels. We identified residues required for channel gating, light absorption, and mechanisms of photo-oxidation, involving a likely binding site for the peroxiredoxin PRDX-2. Furthermore, we identified the binding pocket for a putative chromophore. Several residues lining this pocket have previously been established as essential for LITE-1 function. A newly identified critical cysteine pointing into the pocket represents a likely chromophore attachment site. We derived a model for how photon absorption, via a network of tryptophans and other aromatic amino acids, induces an excited state that is transferred to the chromophore. This evokes conformational changes in the protein, possibly leading to a state receptive to oxidation of cysteines and, jointly, to channel gating. Electrophysiological data support the idea that LITE-1 is a photon and H2O2-coincidence detector. Other proteins with similarity to LITE-1, specifically C. elegans GUR-3, likely use a similar mechanism for photon detection. Thus, a common protein fold and assembly, used for chemoreception in insects, possibly by binding of a particular compound, may have evolved into a light-activated ion channel.

Stellar obliquity, the angle between a planet's orbital axis and its host star's spin axis, traces the formation and evolution of a planetary system. In transiting-exoplanet observations, only the sky-projected stellar obliquity can be measured, but this can be deprojected using an estimate of the stellar obliquity. In this paper, we introduce a flexible, hierarchical Bayesian framework that can be used to infer the stellar obliquity distribution solely from sky-projected stellar obliquities, including stellar inclination measurements when available. We demonstrate that while a constraint on the stellar inclination is crucial for measuring the obliquity of an individual system, it is not required for robust determination of the population-level stellar obliquity distribution. In practice, the constraints on the stellar obliquity distribution are mainly driven by the sky-projected stellar obliquities. When applying the framework to all systems with measured sky-projected stellar obliquity, which are mostly hot Jupiter systems, we find that the inferred population-level obliquity distribution is unimodal and peaked at zero degrees. Misaligned systems have nearly isotropic stellar obliquities with no strong clustering near 90°. The diverse range of stellar obliquities prefers dynamic mechanisms, such as planet-planet scattering after a convergent disk migration, which could produce both prograde and retrograde orbits of close-in planets with no strong inclination concentrations other than that at 0°.