Publications

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules in both the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents. To illustrate the generality of our approach, we apply it to a novel formulation of dimensionality reduction combined with whitening. We confirm numerically that the networks with learning rules derived from principled objectives perform better than those with heuristic learning rules.

Insights from spectroscopic experiments led to the development of quantum mechanics as the common theoretical framework for describing the physical and chemical properties of atoms, molecules and materials. Later, a full quantum description of charged particles, electromagnetic radiation and special relativity was developed, leading to quantum electrodynamics (QED). This is, to our current understanding, the most complete theory describing photon–matter interactions in correlated many–body systems. In the low-energy regime, simplified models of QED have been developed to describe and analyse spectra over a wide spatiotemporal range as well as physical systems. In this Review, we highlight the interrelations and limitations of such theoretical models, thereby showing that they arise from low-energy simplifications of the full QED formalism, in which antiparticles and the internal structure of the nuclei are neglected. Taking molecular systems as an example, we discuss how the breakdown of some simplifications of low-energy QED challenges our conventional understanding of light–matter interactions. In addition to high-precision atomic measurements and simulations of particle physics problems in solid-state systems, new theoretical features that account for collective QED effects in complex interacting many-particle systems could become a material-based route to further advance our current understanding of light–matter interactions.

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems.

The Auger decay is a relevant recombination channel during the first few femtoseconds of molecular targets impinged by attosecond XUV or soft X-ray pulses. Including this mechanism in time--dependent simulations of charge--migration processes is a difficult task, and Auger scatterings are often ignored altogether. In this work we present an advance of the current state-of-the-art by putting forward a real--time approach based on nonequilibrium Green's functions suitable for first-principles calculations of molecules with tens of active electrons. To demonstrate the accuracy of the method we report comparisons against accurate grid simulations of one-dimensional systems. We also predict a highly asymmetric profile of the Auger wavepacket, with a long tail exhibiting ripples temporally spaced by the inverse of the Auger energy.

We have recently proposed a nonequilibrium Green’s function (NEGF) approach to include Auger decay processes in the ultrafast charge dynamics of photoionized molecules. Within the so-called generalized Kadanoff–Baym ansatz the fundamental unknowns of the NEGF equations are the reduced one-particle density matrix of bound electrons and the occupations of the continuum states. Both unknowns are one-time functions like the density in time-dependent functional theory (TDDFT). In this work, we assess the accuracy of the approach against configuration interaction (CI) calculations in one-dimensional model systems. Our results show that NEGF correctly captures qualitative and quantitative features of the relaxation dynamics provided that the energy of the Auger electron is much larger than the Coulomb repulsion between two holes in the valence shells. For the accuracy of the results dynamical electron-electron correlations or, equivalently, memory effects play a pivotal role. The combination of our NEGF approach with the Sham–Schlüter equation may provide useful insights for the development of TDDFT exchange-correlation potentials with a history dependence.

We present high-precision timing data over timespans of up to 11 years for 45 millisecond pulsars observed as part of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project, aimed at detecting and characterizing low-frequency gravitational waves. The pulsars were observed with the Arecibo Observatory and/or the Green Bank Telescope at frequencies ranging from 327 MHz to 2.3 GHz. Most pulsars were observed with approximately monthly cadence, with six high--timing-precision pulsars observed weekly, and all were observed at widely separated frequencies at each observing epoch in order to fit for time-variable dispersion delays. We describe our methods for data processing, time-of-arrival (TOA) calculation, and the implementation of a new, automated method for removing outlier TOAs. We fit a timing model for each pulsar which includes spin, astrometric, and, if necessary, binary parameters, in addition to time-variable dispersion delays and parameters that quantify pulse-profile evolution with frequency. The new timing solutions provide three new parallax measurements, two new Shapiro-delay measurements, and two new measurements of large orbital-period variations. We fit models that characterize sources of noise for each pulsar. We find that 11 pulsars show significant red noise, with generally smaller spectral indices than typically measured for non-recycled pulsars, possibly suggesting a different origin. Future papers will use these data to constrain or detect the signatures of gravitational-wave signals.

I describe the design, implementation, and usage of galpy, a python package for galactic-dynamics calculations. At its core, galpy consists of a general framework for representing galactic potentials both in python and in C (for accelerated computations); galpy functions, objects, and methods can generally take arbitrary combinations of these as arguments. Numerical orbit integration is supported with a variety of Runge-Kutta-type and symplectic integrators. For planar orbits, integration of the phase-space volume is also possible. galpy supports the calculation of action-angle coordinates and orbital frequencies for a given phase-space point for general spherical potentials, using state-of-the-art numerical approximations for axisymmetric potentials, and making use of a recent general approximation for any static potential. A number of different distribution functions (DFs) are also included in the current release; currently, these consist of two-dimensional axisymmetric and non-axisymmetric disk DFs, a three-dimensional disk DF, and a DF framework for tidal streams. I provide several examples to illustrate the use of the code. I present a simple model for the Milky Way's gravitational potential consistent with the latest observations. I also numerically calculate the Oort functions for different tracer populations of stars and compare them to a new analytical approximation. Additionally, I characterize the response of a kinematically warm disk to an elliptical m = 2 perturbation in detail. Overall, galpy consists of about 54,000 lines, including 23,000 lines of code in the module, 11,000 lines of test code, and about 20,000 lines of documentation. The test suite covers 99.6% of the code. galpy is available at http://github.com/jobovy/galpy with extensive documentation available at http://galpy.readthedocs.org/en/latest.

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles
of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid
multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296
(2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can
efficiently generate deterministic and random displacements for many particles using preconditioned
Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-
Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions.
These kernel operations can be computed with near linear scaling for periodic domains using the
positively split Ewald method. Here we study particles partially confined by gravity above a no-
slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector
product, combined with a preconditioned Lanczos iteration for generating Brownian displacements.
We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that
arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint
scheme, our methods utilize random finite differences and do not require the solution of resistance
problems or the computation of the action of the inverse square root of the RPY mobility matrix. We
construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama
traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to
be solved per time step while capturing the required stochastic drift terms. We validate and compare
these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near
a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense
suspensions of confined microrollers, whose height above the wall is set by a combination of thermal
noise and active flows. We find the existence of two populations of active particles, slower ones closer
to the bottom and faster ones above them, and demonstrate that our method provides quantitative
accuracy even with relatively coarse resolutions of the particle geometry.

We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of illustrative results. These include numerically exact calculations on the ground-state properties of the spin-balanced, attractive two-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonian with repulsive interaction. These systems are formally connected via the Hubbard Hamiltonian plus SOC, but cover different physics ranging from superfluidity and triplet pairing to SOC in real materials in the presence of strong interactions in localized orbitals. We carry out detailed benchmark studies of the method in the latter case when an approximation is needed to control the sign problem for repulsive Coulomb interactions. The methods presented here provide an approach for predictive computations in materials to study the interplay of SOC and strong correlation.

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr2RuO4 using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates the Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC found to change significantly the electronic structure at k-points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an "energy-dependent quasiparticle spin-orbit coupling". This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.