Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy

We present a generalization of the classical Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.Comment: Added a plot showing the efficiency at first order phase transition

MCMC based Generative Adversarial Networks for Handwritten Numeral Augmentation

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.In this paper, we propose a novel data augmentation framework for handwritten numerals by incorporating the probabilistic learning and the generative adversarial learning. First, we simply transform numeral images from spatial space into vector space. The Gaussian based Markov probabilistic model is then developed for simulating synthetic numeral vectors given limited handwritten samples. Next, the simulated data are used to pre-train the generative adversarial networks (GANs), which initializes their parameters to fit the general distribution of numeral features. Finally, we adopt the real handwritten numerals to fine-tune the GANs, which increases the authenticity of generated numeral samples. In this case, the outputs of the GANs can be employed to augment original numeral datasets for training the follow-up inference models. Considering that all simulation and augmentation are operated in 1-D vector space, the proposed augmentation framework is more computationally efficient than those based on 2-D images. Extensive experimental results demonstrate that our proposed augmentation framework achieves improved recognition accuracy.This work was supported by grants from the Chinese Scholarship Council (CSC) program

Transition matrix Monte Carlo method for quantum systems

We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.Comment: 6 pages, 4 figure

Anisotropy in the helicity modulus of a 3D XY-model: application to YBCO

We present a Monte Carlo study of the helicity moduli of an anisotropic classical three-dimensional (3D) XY-model of YBCO in superconducting state. It is found that both the ab-plane and the c-axis helicity moduli, which are proportional to the inverse square of the corresponding magnetic field penetration depth, vary linearly with temperature at low temperatures. The result for the c-axis helicity modulus is in disagreement with the experiments on high quality samples of YBCO. Thus we conclude that purely classical phase fluctuations of the superconducting order parameter cannot account for the observed c-axis electrodynamics of YBCO.Comment: 7 pages, 1 figur

Volumetric real-time particle-based representation of large unstructured tetrahedral polygon meshes

In this paper we propose a particle-based volume rendering approach for unstructured, three-dimensional, tetrahedral polygon meshes. We stochastically generate millions of particles per second and project them on the screen in real-time. In contrast to previous rendering techniques of tetrahedral volume meshes, our method does not need a prior depth sorting of geometry. Instead, the rendered image is generated by choosing particles closest to the camera. Furthermore, we use spatial superimposing. Each pixel is constructed from multiple subpixels. This approach not only increases projection accuracy, but allows also a combination of subpixels into one superpixel that creates the well-known translucency effect of volume rendering. We show that our method is fast enough for the visualization of unstructured three-dimensional grids with hard real-time constraints and that it scales well for a high number of particles

Assessing the effects of foregrounds and sky removal in WMAP

Many recent analyses have indicated that large scale WMAP data display anomalies that appear inconsistent with the standard cosmological paradigm. However, the effects of foreground contamination, which require elimination of some fraction of the data, have not been carefully investigated due to the complexity in the analysis. Here we develop a general formalism of how to incorporate these effects in any analysis of this type. Our approach is to compute the full multi-dimensional probability distribution function of all possible sky realizations that are consistent with the data and with the allowed level of contamination. As an example we apply this method to compute the joint probability distribution function for the possible realizations of quadrupole and octopole using the WMAP data. This 12 dimensional distribution function is explored using the Markov Chain Monte Carlo technique. The resulting chains are used to asses the statistical significance of the low quadrupole using frequentist methods, the quadrupole-octopole alignment using several methods (angular momentum dispersion, multipole vectors and a new method based of feature matching) and the quadrupole-octopole aligment with ecliptic.Comment: 12 pages, 11 figures, 3 tables; replaced with the version accepted by PRD. Added a few statistical tests and expanded discussion. Results unchanged. Added acknowledgement in v3, clarified discussion of other work in v

Projected single-spin flip dynamics in the Ising Model

We study transition matrices for projected dynamics in the energy-magnetization space, magnetization space and energy space. Several single spin flip dynamics are considered such as the Glauber and Metropolis canonical ensemble dynamics and the Metropolis dynamics for three multicanonical ensembles: the flat energy-magnetization histogram, the flat energy histogram and the flat magnetization histogram. From the numerical diagonalization of the matrices for the projected dynamics we obtain the sub-dominant eigenvalue and the largest relaxation times for systems of varying size. Although, the projected dynamics is an approximation to the full state space dynamics comparison with some available results, obtained by other authors, shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size. The transition matrices for arbitrary single-spin flip dynamics are obtained from a single Monte-Carlo estimate of the infinite temperature transition-matrix, for each system size, which makes the method an efficient tool to evaluate the relative performance of any arbitrary local spin-flip dynamics. We also present new results for appropriately defined average tunnelling times of magnetization and compute their finite-size scaling exponents that we compare with results of energy tunnelling exponents available for the flat energy histogram multicanonical ensemble.Comment: 23 pages and 6 figure

Monte Carlo simulation method for Laughlin-like states in a disk geometry

We discuss an alternative accurate Monte Carlo method to calculate the ground-state energy and related quantities for Laughlin states of the fractional quantum Hall effect in a disk geometry. This alternative approach allows us to obtain accurate bulk regime (thermodynamic limit) values for various quantities from Monte Carlo simulations with a small number of particles (much smaller than that needed with standard Monte Carlo approaches).Comment: 13 pages, 6 figures, 2 table

Final State Interactions Effects in Neutrino-Nucleus Interactions

Final State Interactions effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of Formation Time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current $\pi^0$ production data in $\sim 1$ GeV neutrino flux experiments is demonstrated.Comment: 13 pages, 16 figure