We generalize the linked cluster expansion of Matsubara Green functions into nonequilibrium situations. This allows us to compute nonequilibrium correlation functions and, consequently, physical observables for interacting quantum systems with intermediate interaction strengths. As a specific example, we study nonlinear dc transport in a resonant tunneling system with electron-phonon interactio...

High-harmonic generation is shown to be capable of providing time-resolved information about the particle density of a complex system. As an example, we study numerically high-harmonic generation from expanding xenon clusters in a pump-probe laser scheme, where the pump laser pulse induces the cluster explosion and the probe pulse generates harmonics in the expanding cluster. We show that the h...

The Lovász Local Lemma (LLL) is a powerful tool that can be used to prove that an object having none of a set of bad properties exists, using the probabilistic method. In many applications of the LLL it is also desirable to explicitly construct the combinatorial object. Recently it was shown that this is possible using a randomized algorithm in the full asymmetric LLL setting [R. Moser and G. T...

The problem of phase stability calculation (and crystal structure prediction) is a fundamental problem in materials research and development, and it is typically addressed with highly accurate quantum mechanical computations on a large set of candidate structures, but has limited predictive power. To allow fast prediction of crystal structures, two concepts, usual suspect structure database and...

MOTIVATION Graphical models are often employed to interpret patterns of correlations observed in data through a network of interactions between the variables. Recently, Ising/Potts models, also known as Markov random fields, have been productively applied to diverse problems in biology, including the prediction of structural contacts from protein sequence data and the description of neural acti...

CLUSTER EXPANSION WITH APPLICATIONS 3 In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so that the left side is roughly proportional to l(x). This suggests to try a(x) = cl(x), and one can then optimize on the v...

We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared φ 4...

An old result by Shearer relates the Lovász Local Lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard core lattice gas on graphs. We use this connection and a recent result on the analyticity of the logarithm of the partition function of the abstract polymer gas to get an improved version of the Lovász Lo...

Using the maximum entropy method, we derive the"adaptive cluster expansion"(ACE), which can be trained to estimate probability density functions in high dimensional spaces. The main advantage of ACE over other Bayesian networks is its ability to capture high order statistics after short training times, which it achieves by making use of a hierarchical vector quantisation of the input data. We d...

To predict the ground-state structures and finite-temperature properties of an alloy, the total energies of many different atomic configurations s;hsi ; i=1, . . . ,Nj, with N sites i occupied by atom A ssi=−1d, or B ssi = +1d, must be calculated accurately and rapidly. Direct local-density approximation (LDA) calculations provide the required accuracy, but are not practical because they are li...