Publications

We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent Galilean invariance. The theory also becomes qualitatively inaccurate very near half filling if nesting is important.

We studied the low-energy electronic response of the prototypical correlated metal SrVO

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel K

Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high computational costs, especially when multiple evaluations must be made for different parameters or conditions. After training, neural operators can provide PDEs solutions significantly faster than traditional PDE solvers. In this work, invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity. Neural operator based on graph kernel network (GKN) operates on graph-structured data to incorporate nonlocal dependencies. Here we propose a modified formulation of GKN to achieve frame invariance. Vector cloud neural network (VCNN) is an alternate neural operator with embedded frame invariance which operates on point cloud data. GKN-based neural operator demonstrates slightly better predictive performance compared to VCNN. However, GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.

We introduce a numerical method for the solution of the time-dependent Schrödinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary conditions, and for free space problems with compactly supported initial data and potential. A spatially uniform electric field may be included, making the solver applicable to simulations of light-matter interaction. The primary computational challenge in using the Volterra formulation is the application of a spacetime history dependent integral operator. This may be accomplished by projecting the solution onto a set of Fourier modes, and updating their coefficients from one time step to the next by a simple recurrence. In the periodic case, the modes are those of the usual Fourier series, and the fast Fourier transform (FFT) is used to alternate between physical and frequency domain grids. In the free space case, the oscillatory behavior of the spectral Green's function leads us to use a set of complex-frequency Fourier modes obtained by discretizing a contour deformation of the inverse Fourier transform, and we develop a corresponding fast transform based on the FFT. Our approach is related to pseudospectral methods, but applied to an integral rather than the usual differential formulation. This has several advantages: it avoids the need for artificial boundary conditions, admits simple, inexpensive, high-order implicit time marching schemes, and naturally includes time-dependent potentials. We present examples in one and two dimensions showing spectral accuracy in space and eighth-order accuracy in time for both periodic and free space problems.

In the Gaia era it is increasingly apparent that traditional static, parameterized models are insufficient to describe the mass distribution of our complex, dynamically evolving Milky Way (MW). In this work, we compare different time-evolving and time-independent representations of the gravitational potentials of simulated MW-mass galaxies from the FIRE-2 suite of cosmological baryonic simulations. Using these potentials, we calculate actions for star particles in tidal streams around three galaxies with varying merger histories at each snapshot from 7 Gyr ago to the present day. We determine the action-space coherence preserved by each model using the Kullback-Leibler Divergence to gauge the degree of clustering in actions and the relative stability of the clusters over time. We find that all models produce a clustered action space for simulations with no significant mergers. However, a massive (mass ratio prior to infall more similar than 1:8) interacting galaxy not present in the model will result in mischaracterized orbits for stars most affected by the interaction. The locations of the action space clusters (i.e. the orbits of the stream stars) are only preserved by the time-evolving model, while the time-independent models can lose significant amounts of information as soon as 0.5--1 Gyr ago, even if the system does not undergo a significant merger. Our results imply that reverse-integration of stream orbits in the MW using a fixed potential is likely to give incorrect results if integrated longer than 0.5 Gyr into the past.

Ca2RuO4 is a transition-metal oxide that exhibits a Mott insulator-metal transition (IMT) concurrent with a symmetry-preserving Jahn-Teller distortion (JT) at 350 K. The coincidence of these two transitions demonstrates a high level of coupling between the electronic and structural degrees of freedom in Ca2RuO4. Using spectroscopic measurements with nanoscale spatial resolution, we interrogate the interplay of the JT and IMT through the temperature-driven transition. Then, we introduce photoexcitation with subpicosecond temporal resolution to explore the coupling of the JT and IMT via electron-hole injection under ambient conditions. Through the temperature-driven IMT, we observe phase coexistence in the form of a stripe phase existing at the domain wall between macroscopic insulating and metallic domains. Through ultrafast carrier injection, we observe the formation of midgap states via enhanced optical absorption. We propose that these midgap states become trapped by lattice polarons originating from the local perturbation of the JT.

Gaia Data Release 2 revealed that the Milky Way contains significant indications of departures from equilibrium in the form of asymmetric features in the phase space density of stars in the Solar neighbourhood. One such feature is the z–vz phase spiral, interpreted as the response of the disc to the influence of a perturbation perpendicular to the disc plane, which could be external (e.g. a satellite) or internal (e.g. the bar or spiral arms). In this work, we use Gaia Data Release 3 to dissect the phase spiral by dividing the local data set into groups with similar azimuthal actions, Jϕ, and conjugate angles, θϕ, which selects stars on similar orbits and at similar orbital phases, thus having experienced similar perturbations in the past. These divisions allow us to explore areas of the Galactic disc larger than the surveyed region. The separation improves the clarity of the z–vz phase spiral and exposes changes to its morphology across the different action-angle groups. In particular, we discover a transition to two armed ‘breathing spirals’ in the inner Milky Way. We conclude that the local data contain signatures of not one, but multiple perturbations with the prospect to use their distinct properties to infer the properties of the interactions that caused them.

To demonstrate a clear link between predicted blood shear forces during valve closure and thrombogenicity that explains the thrombogenic difference between tissue and mechanical valves and provides a practical metric to develop and refine prosthetic valve designs for reduced thrombogenicity.

Cytosolic Ca2+ is a highly dynamic, tightly regulated and broadly conserved cellular signal. Ca2+ dynamics have been studied widely in cellular monocultures, yet organs in vivo comprise heterogeneous populations of stem and differentiated cells. Here, we examine Ca2+ dynamics in the adult Drosophila intestine, a self-renewing epithelial organ in which stem cells continuously produce daughters that differentiate into either enteroendocrine cells or enterocytes. Live imaging of whole organs ex vivo reveals that stem-cell daughters adopt strikingly distinct patterns of Ca2+ oscillations after differentiation: enteroendocrine cells exhibit single-cell Ca2+ oscillations, whereas enterocytes exhibit rhythmic, long-range Ca2+ waves. These multicellular waves do not propagate through immature progenitors (stem cells and enteroblasts), of which the oscillation frequency is approximately half that of enteroendocrine cells. Organ-scale inhibition of gap junctions eliminates Ca2+ oscillations in all cell types – even, intriguingly, in progenitor and enteroendocrine cells that are surrounded only by enterocytes. Our findings establish that cells adopt fate-specific modes of Ca2+ dynamics as they terminally differentiate and reveal that the oscillatory dynamics of different cell types in a single, coherent epithelium are paced independently.