Publications

In recent years, dedicated extreme precision radial velocity (RV) spectrographs have produced vast quantities of high-resolution, high-signal-to-noise (S/N) time-series spectra for bright stars. These data contain valuable information for the dual purposes of planet detection via the measured RVs and stellar characterization via the coadded spectra. However, considerable data analysis challenges exist in extracting these data products from the observed spectra at the highest possible precision, including the issue of poorly characterized telluric absorption features and the common use of an assumed stellar spectral template. In both of these examples, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package that uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival High Accuracy Radial Velocity Planet Searcher (HARPS) spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter–McLaughlin effect for the hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.

A saddle point plus fluctuation analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically nonthermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a nonequilibrium drive.

The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient parallel library for type 1 (nonuiform to uniform), type 2 (uniform to nonuniform), or type 3 (nonuniform to nonuniform) transforms, in dimensions 1, 2, or 3. It uses minimal RAM, requires no precomputation or plan steps, and has a simple interface to several languages. We perform the expensive spreading/interpolation between nonuniform points and the fine grid via a simple new kernel---the `exponential of semicircle' $e^{\beta \sqrt{1-x^2}}$ in $x\in[-1,1]$---in a cache-aware load-balanced multithreaded implementation. The deconvolution step requires the Fourier transform of the kernel, for which we propose efficient numerical quadrature. For types 1 and 2, rigorous error bounds asymptotic in the kernel width approach the fastest known exponential rate, namely that of the Kaiser--Bessel kernel. We benchmark against several popular CPU-based libraries, showing favorable speed and memory footprint, especially in three dimensions when high accuracy and/or clustered point distributions are desired.

Resistance in superconductors arises from the motion of vortices driven by flowing supercurrents or external electromagnetic fields and may be strongly affected by thermal or quantum fluctuations. The common expectation borne out in previous experiments is that as the temperature is lowered, vortex motion is suppressed, leading to a decreased resistance. A new generation of materials provides access to the previously inaccessible regime of clean-limit superconductivity in atomically thin superconducting layers. We show experimentally that for few-layer 2H-NbSe2 the resistance below the superconducting transition temperature may be non-monotonic, passing through a minimum and then increasing again as temperature is decreased further. The effects exists over a wide range of current and magnetic fields, but is most pronounced in monolayer devices at intermediate currents. Analytical and numerical calculations confirm that the findings can be understood in a two-fluid vortex model, in which a fraction of vortices flow in channels while the rest are pinned but thermally fluctuating in position. We show theoretically that the pinned, fluctuating vortices effectively control the mobility of the free vortices. The findings provide a new perspective on fundamental questions of vortex mobility and dissipation in superconductors.

Lecture notes of the Autumn School on Correlated Electrons 2019
1 Xavier Blase: Introduction to Density Functional Theory
2 Xinguo Ren: The Random Phase Approximation and its Application to Real Materials
3 Cyrus Umrigar: Introduction to Variational and Projector Monte Carlo
4 Arne Lüchow: Optimized Quantum Monte Carlo Wave Functions
5 Federico Becca: Variational Wave Functions for Strongly Correlated Fermionic Systems
6 Shiwei Zhang: Auxiliary-Field Quantum Monte Carlo at Zero- and Finite-Temperature
7 Erik Koch: Exact Diagonalization and Lanczos Method
8 Miles Stoudenmire: Quantum Chemistry DMRG in a Local Basis
9 Karen Hallberg: Density Matrix Renormalization
10 Marcelo Rozenberg: Dynamical Mean-Field Theory and Mott Transition
11 Eva Pavarini: Dynamical Mean-Field Theory for Materials
12 Robert Eder: Analytic Properties of Self-Energy and Luttinger-Ward Functional
13 James Freericks: Introduction to Many-Body Green Functions In and Out Of Equilibrium
14 Andrea Donarini: Electronic Transport in Correlated Single Molecule Junctions
15 Nikolay Prokof'ev: Diagrammatic Monte Carlo
16 Anders Sandvik: Stochastic Series Expansion Methods
17 Gerardo Ortiz: Algebraic Methods in Many-Body Physics