Publications

Using a nonequilibrium implementation of the extended dynamical mean field theory (EDMFT) we simulate the relaxation after photo excitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the t-J model and focus on the interplay between the charge- and spin-dynamics in different excitation and doping regimes. The appearance of string states after a weak photo excitation manifests itself in a nontrivial scaling of the relaxation time with the exchange coupling and leads to a correlated oscillatory evolution of the kinetic energy and spin-spin correlation function. A strong excitation of the system, on the other hand, suppresses the spin correlations and results in a relaxation that is controlled by hole scattering. We discuss the possibility of detecting string states in optical and cold atom experiments.

It is well-known that by placing judiciously chosen image point forces and doublets to the Stokeslet above a flat wall, the no-slip boundary condition can be conveniently imposed on the wall [Blake, J. R. Math. Proc. Camb. Philos. Soc. 70(2), 1971: 303.]. However, to further impose periodic boundary conditions on directions parallel to the wall usually involves tedious derivations because single or double periodicity in Stokes flow may require the periodic unit to have no net force, which is not satisfied by the well-known image system. In this work we present a force-neutral image system. This neutrality allows us to represent the Stokes image system in a universal formulation for non-periodic, singly periodic and doubly periodic geometries. This formulation enables the black-box style usage of fast kernel summation methods. We demonstrate the efficiency and accuracy of this new image method with the periodic kernel independent fast multipole method in both non-periodic and doubly periodic geometries. We then extend this new image system to other widely used Stokes fundamental solutions, including the Laplacian of the Stokeslet and the Rotne-Prager-Yamakawa tensor.

Temporally precise movement patterns underlie many motor skills and innate actions, yet the flexibility with which the timing of such stereotyped behaviors can be modified is poorly understood. To probe this, we induce adaptive changes to the temporal structure of birdsong. We find that the duration of specific song segments can be modified without affecting the timing in other parts of the song. We derive formal prescriptions for how neural networks can implement such flexible motor timing. We find that randomly connected recurrent networks, a common approximation for how neocortex is wired, do not generally conform to these, though certain implementations can approximate them. We show that feedforward networks, by virtue of their one-to-one mapping between network activity and time, are better suited. Our study provides general prescriptions for pattern generator networks that implement flexible motor timing, an important aspect of many motor skills, including birdsong and human speech.

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is non-linear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods to validate and fully exploit quantum resources. Quantum state tomography (QST) aims to reconstruct the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. However, exact brute-force approaches to QST place a high demand on computational resources, making them unfeasible for anything except small systems. Here we show how machine learning techniques can be used to perform QST of highly entangled states with more than a hundred qubits, to a high degree of accuracy. We demonstrate that machine learning allows one to reconstruct traditionally challenging many-body quantities—such as the entanglement entropy—from simple, experimentally accessible measurements. This approach can benefit existing and future generations of devices ranging from quantum computers to ultracold-atom quantum simulators.

We develop a constructive approach to generate artificial neural networks representing the exact ground states of a large class of many-body lattice Hamiltonians. It is based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations among physical degrees of freedom in the visible layer. The approach reproduces the exact imaginary-time Hamiltonian evolution, and is completely deterministic. In turn, compact and exact network representations for the ground states are obtained without stochastic optimization of the network parameters. The number of neurons grows linearly with the system size and total imaginary time, respectively. Physical quantities can be measured by sampling configurations of both physical and neuron degrees of freedom. We provide specific examples for the transverse-field Ising and Heisenberg models by implementing efficient sampling. As a compact, classical representation for many-body quantum systems, our approach is an alternative to the standard path integral, and it is potentially useful also to systematically improve on numerical approaches based on the restricted Boltzmann machine architecture.

Laser control of solids has so far mainly been discussed in the context of strong classical nonlinear light-matter coupling in a pump-probe framework. Here we propose a quantum-electrodynamical setting to address the coupling of a low-dimensional quantum material to quantized electromagnetic fields in nanocavities. Using a protoypical model system describing FeSe/SrTiO3, we study how the formation of phonon polaritons at the 2D interface of the material modifies its superconducting properties in a Migdal-Eliashberg simulation. We find that through highly polarizable dipolar phonons, cavity-induced superconductivity is possible at temperatures above the bare critical temperature of the system. Our results demonstrate that quantum cavities enable the engineering of fundamental couplings in solids paving the way to unprecedented control of material properties.

We show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydro-elastic forces. The viscous stress field produces an elastic disturbance leading to particle-wave coupling. We derive an analytic expression for the particle trajectory in the lubrication limit, bypassing the construction of the detailed velocity and pressure fields. The normal force is quadratic in the parallel speed, and is a function of the tension and bending resistance of the membrane. Experimentally, we measure the normal displacement of spheres sedimenting along an elastic membrane and find quantitative agreement with the theoretical predictions with no fitting parameters. We experimentally demonstrate the effect to be strong enough for particle separation and sorting. We discuss the significance of these results for bio-membranes and propose our model for membrane elasticity measurements.

We develop a first-principles simulation method for attosecond time-resolved photoelectron spectroscopy. This method enables us to directly simulate the whole experimental processes, including excitation, emission and detection on equal footing. To examine the performance of the method, we use it to compute the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) experiments of gas-phase Argon. The computed RABBITT photoionization delay is in very good agreement with recent experimental results from [Kl\"under et al, Phys. Rev. Lett. 106 143002 (2011)] and [Gu\'enot et al, Phys. Rev. A 85 053424 (2012)]. This indicates the significance of a fully-consistent theoretical treatment of the whole measurement process to properly describe experimental observables in attosecond photoelectron spectroscopy. The present framework opens the path to unravel the microscopic processes underlying RABBITT spectra in more complex materials and nanostructures.

Cilia and flagella are essential building blocks for biological fluid transport and locomotion at the micrometre scale. They often beat in synchrony and may transition between different synchronization modes in the same cell type. Here, we investigate the behaviour of elastic microfilaments, protruding from a surface and driven at their base by a configuration-dependent torque. We consider full hydrodynamic interactions among and within filaments and no slip at the surface. Isolated filaments exhibit periodic deformations, with increasing waviness and frequency as the magnitude of the driving torque increases. Two nearby but independently driven filaments synchronize their beating in-phase or anti-phase. This synchrony arises autonomously via the interplay between hydrodynamic coupling and filament elasticity. Importantly, in-phase and anti-phase synchronization modes are bistable and coexist for a range of driving torques and separation distances. These findings are consistent with experimental observations of in-phase and anti-phase synchronization in pairs of cilia and flagella and could have important implications on understanding the biophysical mechanisms underlying transitions between multiple synchronization modes.