QCD-like theories at nonzero temperature and density

We investigate the properties of hot and/or dense matter in QCD-like theories with quarks in a (pseudo)real representation of the gauge group using the Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice spin model with nearest-neighbor interactions. We first keep our discussion as general as possible, and only later focus on theories with adjoint quarks of two or three colors. Calculating the phase diagram in the plane of temperature and quark chemical potential, it is qualitatively confirmed that the critical temperature of the chiral phase transition is much higher than the deconfinement transition temperature. At a chemical potential equal to half of the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC) phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is used to study the tetracritical behavior around the intersection point of the deconfinement and BEC transition lines, which are both of second order. We obtain a compact expression for the expectation value of the Polyakov loop in an arbitrary representation of the gauge group (for any number of colors), which allows us to study Casimir scaling at both nonzero temperature and chemical potential.Comment: JHEP class, 31 pages, 7 eps figures; v2: error in Eq. (3.11) fixed, two references added; matches published versio

Chiral Lagrangian at finite temperature from the Polyakov-Chiral Quark Model

We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result and also the correct large $N_c$ counting for the thermal corrections. We find that new coefficients are introduced at ${\cal O}(p^4)$ to account for the Lorentz breaking at finite temperature. As a byproduct, we obtain the effective Lagrangian which describes the coupling of the Polyakov loop to the Goldstone bosons.Comment: 16 pages, no figure

Composition of quantum operations and products of random matrices

Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing the composition of s random maps and demonstrate that their complex eigenvalues are asymptotically described by the law of Burda et al. obtained for a product of s independent random complex Ginibre matrices. Numerical data support the conjecture that the same results are applicable to characterize the distribution of eigenvalues of the s-th power of a random Ginibre matrix. Squared singular values of Psi are shown to be described by the Fuss-Catalan distribution of order s. Results obtained for products of random Ginibre matrices are also capable to describe the s-step evolution operator for a model deterministic dynamical system - a generalized quantum baker map subjected to strong interaction with an environment.Comment: 19 pages, 7 figure

Image segmentation and pattern classification using support vector machines

Image segmentation and pattern classification have long been important topics in computer science research. Image segmentation is one of the basic and challenging lower-level image processing tasks. Feature extraction, feature reduction, and classifier design based on selected features are the three essential issues for the pattern classification problem. In this dissertation, an automatic Seeded Region Growing (SRG) algorithm for color image segmentation is developed. In the SRG algorithm, the initial seeds are automatically determined. An adaptive morphological edge-linking algorithm to fill in the gaps between edge segments is designed. Broken edges are extended along their slope directions by using the adaptive dilation operation with suitably sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to local properties. For feature reduction, an improved feature reduction method in input and feature spaces using Support Vector Machines (SVMs) is developed. In the input space, a subset of input features is selected by the ranking of their contributions to the decision function. In the feature space, features are ranked according to the weighted support vectors in each dimension. For object detection, a fast face detection system using SVMs is designed. Twoeye patterns are first detected using a linear SVM, so that most of the background can be eliminated quickly. Two-layer 2nd-degree polynomial SVMs are trained for further face verification. The detection process is implemented directly in feature space, which leads to a faster SVM. By training a two-layer SVM, higher classification rates can be achieved. For active learning, an improved incremental training algorithm for SVMs is developed. Instead of selecting training samples randomly, the k-mean clustering algorithm is applied to collect the initial set of training samples. In active query, a weight is assigned to each sample according to its distance to the current separating hyperplane and the confidence factor. The confidence factor, calculated from the upper bounds of SVM errors, is used to indicate the degree of closeness of the current separating hyperplane to the optimal solution

Variable illumination and invariant features for detecting and classifying varnish defects

This work presents a method to detect and classify varnish defects on wood surfaces. Since these defects are only partially visible under certain illumination directions, one image doesn\u27t provide enough information for a recognition task. A classification requires inspecting the surface under different illumination directions, which results in image series. The information is distributed along this series and can be extracted by merging the knowledge about the defect shape and light direction

Formulating Light Cone QCD on the Lattice

We present the near light cone Hamiltonian $H$ in lattice QCD depending on the parameter $\eta$, which gives the distance to the light cone. Since the vacuum has zero momentum we can derive an effective Hamiltonian $H_{eff}$ from $H$ which is only quadratic in the momenta and therefore solvable by standard methods. An approximate ground state wave functional is determined variationally in the limit $\eta \to 0$.Comment: 48 pages, 8 figure

Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional

We study a gauge-invariant variational framework for the Yang-Mills vacuum wave functional. Our approach is built on gauge-averaged Gaussian trial functionals which substantially extend previously used trial bases in the infrared by implementing a general low-momentum expansion for the vacuum-field dispersion (which is taken to be analytic at zero momentum). When completed by the perturbative Yang-Mills dispersion at high momenta, this results in a significantly enlarged trial functional space which incorporates both dynamical mass generation and asymptotic freedom. After casting the dynamics associated with these wave functionals into an effective action for collections of soft vacuum-field orbits, the leading infrared improvements manifest themselves as four-gradient interactions. Those turn out to significantly lower the minimal vacuum energy density, thus indicating a clear overall improvement of the vacuum description. The dimensional transmutation mechanism and the dynamically generated mass scale remain almost quantitatively robust, however, which ensures that our prediction for the gluon condensate is consistent with standard values. Further results include a finite group velocity for the soft gluonic modes due to the higher-gradient corrections and indications for a negative differential color resistance of the Yang-Mills vacuum.Comment: 47 pages, 5 figures (vs2 contains a few minor stylistic adjustments to match the published version