Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.In solid state physics, transport properties are among the key observables, the most prominent example being the electrical conductivity, which e.g. allows to distinguish normal conductors from insulators or superconductors. Furthermore, many of today's most intriguing solid state phenomena manifest themselves in transport properties, examples including high-temperature superconductivity, giant magnetoresistance, quantum hall physics, topological insulators and disorder phenomena. Especially in strongly correlated systems, where the interactions between the conductance electrons are important, transport properties are difficult to calculate beyond the linear response regime. In general, predicting out-of-equilibrium fermionic dynamics represents an even harder problem than the prediction of static properties like the nature of the ground state. In real solids further complications arise due to the effects of e.g. impurities, lattice defects and phonons. These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1-3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].Using both bosonic and fermionic [8-10] atoms, it has become possible to simulate models of strongly interacting quantum particles, for which the Hubbard model [11] * ulrich.schneider@lmu.de is probably the most important example. A major advantage of these systems compared to real solids is the possibility to change all relevant parameters in real-time by e.g. varying laser intensities or magnetic fields. While first studies of dynamical properties of both bosonic and fermionic quantum gases [12][13][14] have already been performed, a remaining...

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

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Activity coefficients, which are a measure of the non-ideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed to calculate the activity coefficients in many relevant mixtures that have not been explored to-date. In this report, we propose a probabilistic matrix factorization model for predicting the activity coefficients in arbitrary binary mixtures. Although no physical descriptors for the considered components were used, our method outperforms the state-of-the-art method that has been refined over three decades while requiring much less training effort. This opens perspectives to novel methods for predicting physico-chemical properties of binary mixtures with the potential to revolutionize modeling and simulation in chemical engineering. Activity Coefficients at Infinite Dilution   Solutes SolventsThis document is the unedited authors' version of a submitted work that was subsequently accepted for publication in TheIn this work, we describe a novel application of Machine Learning (ML) to the field of physical chemistry and thermodynamics: the prediction of physico-chemical properties of binary liquid mixtures by matrix completion. We focus on the prediction of a single property: the so-called activity coefficient, which is a measure of the non-ideality of a liquid mixture and of enormous relevance in practice. The interesting aspect of our approach is that no expert knowledge about the components that make up the mixture was used: all we needed was an incomplete, sparse data set of binary mixtures and their measured activity coefficients that our method was able to successfully complete. We show that this simple approach outperforms an established procedure that has been the state of the art for several decades.ML approaches to chemical and engineering sciences date back more than 50 years ago, but the genuine exploitation of the potential of ML in these fields has only recently begun 1 . An overview of recent advances in chemical and material sciences has, e.g., been given by Ramprasad et al. 2 and Butler et al. 3 ML has already been used to predict physico-chemical properties of mixtures, including activity coefficients 4-10 . Most of these approaches are basically quantitative structureproperty relationships (QSPR) methods 11 that use physical descriptors of the components as input data to characterize the considered mixtures and relate them to the property of interest by an ML algorithm, e.g., a neural network. However, the scope of these approaches is in general rather small.Binary mixtures are of fundamental importance in chemical engineering. The properties of mixtures can in general not be described based on properties of the pure components alone. If, however, the respective properties of the binary constituent 'sub-mixtures' of a multi-component mixture are known, the properties of the multi...

As highly tunable interacting systems, cold atoms in optical lattices are ideal to realize and observe negative absolute temperatures, T<0. We show theoretically that, by reversing the confining potential, stable superfluid condensates at finite momentum and T<0 can be created with low entropy production for attractive bosons. They may serve as "smoking gun" signatures of equilibrated T<0. For fermions, we analyze the time scales needed to equilibrate to T<0. For moderate interactions, the equilibration time is proportional to the square of the radius of the cloud and grows with increasing interaction strengths as atoms and energy are transported by diffusive processes.

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We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves differently: It expands symmetrically such that gains of potential energy at the top are compensated by losses at the bottom. Interactions stabilize the necessary heat currents by inducing gradients of the inverse temperature 1/T , with T < 0 at the bottom of the cloud. An analytic solution of hydrodynamic equations shows that the width of the cloud increases with t 1/3 for long times consistent with results from our Boltzmann simulations. 05.60.Gg, 05.70.Ln Measuring the conductivity is probably the most fundamental experiment when investigating the properties of a metal. The influence of constant forces arising from electric or gravitational fields on quantum particles in periodic potentials is an old and well studied problem [1]. For free particles, Bragg scattering from the periodic potential induces Bloch oscillations [1][2][3] . While difficult to observe in solids due to disorder and interactions, such Bloch oscillations have been measured in semiconductor superlattices [4] and for ultracold bosonic atoms in optical lattices [2,3] created by standing waves of lasers, e.g., to determine the masses of atoms with high precision [5].Recent experimental developments make it also possible to load fermionic ultracold atoms in the lowest band of optical lattices. Using an equal population of two hyperfine levels and Feshbach resonances (e.g., of 40 K) it became possible to realize the Hubbard model (see below) with tunable interaction strength. While the temperatures in current experiments are still rather high, it was possible to see [6,7] signatures of the onset of a metal-insulator transition induced by strong interactions. Constant external forces can be realized using either gravitation or accelerated lattices [2] (after a careful elimination of other confining potentials as in Ref. [8]).The Hubbard model in an electric or gravitational field has attracted previously considerable attention [9][10][11][12][13][14][15][16], partially motivated by the question how large electric fields can lead to a breakdown of the Mott insulating state. When discussing the physics of such systems either for weak or strong interactions, it is important to take energy conservation into account. While real solids are usually probed in contact with some thermal bath, ultracold atoms provide almost ideal realizations of closed quantum systems implying severe restrictions on the dynamics. For a translationally invariant, infinite system one expects that even weak interactions lead to a damping of the Bloch oscillations (at least in the absence of superfluidity and in dimensions larger than 1). During this process, potential energy is converted into heat. As long as there is no coupling to an external bath which can transport the heat away, the system gets hotter and hotter. It finally reaches ...

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