Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on the examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma-models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a "memory" of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.Comment: 16 pages RevTeX, 14 figures; v2: Algorithm for the Weingarten model corrected; v3: published versio

Estimation of the symbol period: the frequency offset case

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 200

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change

Quantum Monte Carlo simulation in the canonical ensemble at finite temperature

A quantum Monte Carlo method with non-local update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Green's function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.Comment: 11 pages, 8 figure

Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices

We discuss the finite-temperature phase diagram in the three-dimensional Bose-Hubbard (BH) model in the strong correlation regime, relevant for Bose-Einstein condensates in optical lattices, by employing a quantum rotor approach. In systems with strong on site repulsive interactions, the rotor U(1) phase variable dual to the local boson density emerges as an important collective field. After establishing the connection between the rotor construction and the the on--site interaction in the BH model the robust effective action formalism is developed which allows us to study the superfluid phase transition in various temperature--interaction regimes

Statistical Modeling of Lower Limb Kinetics During Deep Squat and Forward Lunge.

PURPOSE: Modern statistics and higher computational power have opened novel possibilities to complex data analysis. While gait has been the utmost described motion in quantitative human motion analysis, descriptions of more challenging movements like the squat or lunge are currently lacking in the literature. The hip and knee joints are exposed to high forces and cause high morbidity and costs. Pre-surgical kinetic data acquisition on a patient-specific anatomy is also scarce in the literature. Studying the normal inter-patient kinetic variability may lead to other comparable studies to initiate more personalized therapies within the orthopedics. METHODS: Trials are performed by 50 healthy young males who were not overweight and approximately of the same age and activity level. Spatial marker trajectories and ground reaction force registrations are imported into the Anybody Modeling System based on subject-specific geometry and the state-of-the-art TLEM 2.0 dataset. Hip and knee joint reaction forces were obtained by a simulation with an inverse dynamics approach. With these forces, a statistical model that accounts for inter-subject variability was created. For this, we applied a principal component analysis in order to enable variance decomposition. This way, noise can be rejected and we still contemplate all waveform data, instead of using deduced spatiotemporal parameters like peak flexion or stride length as done in many gait analyses. In addition, this current paper is, to the authors' knowledge, the first to investigate the generalization of a kinetic model data toward the population. RESULTS: Average knee reaction forces range up to 7.16 times body weight for the forwarded leg during lunge. Conversely, during squat, the load is evenly distributed. For both motions, a reliable and compact statistical model was created. In the lunge model, the first 12 modes accounts for 95.26% of inter-individual population variance. For the maximal-depth squat, this was 95.69% for the first 14 modes. Model accuracies will increase when including more principal components. CONCLUSION: Our model design was proved to be compact, accurate, and reliable. For models aimed at populations covering descriptive studies, the sample size must be at least 50