Composite fermion wave functions as conformal field theory correlators

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure

Statistical wave scattering through classically chaotic cavities in the presence of surface absorption

We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch" to the inner wall of the cavity. In our model, the cavity is connected to the outside by a waveguide with N open modes (or channels), while an experimental patch is simulated by an "absorbing mirror" attached to the inside wall of the cavity; the mirror, consisting of a waveguide that supports Na channels, with absorption inside and a perfectly reflecting wall at its end, is described by a subunitary scattering matrix Sa. The number of channels Na, as a measure of the geometric cross section of the mirror, and the lack of unitarity of Sa as a measure of absorption, are under our control: these parameters have an important physical significance for real experiments. The absorption strength in the cavity is quantified by the trace of the lack of unitarity. The statistical distribution of the resulting S matrix for N=1 open channel and only one absorbing channel, Na =1, is solved analytically for the orthogonal and unitary universality classes, and the results are compared with those arising from numerical simulations. The relation with other models existing in the literature, in some of which absorption has a volumetric character, is also studied.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Scattering phases in quantum dots: an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.Comment: 18 pages, 9 figures. to appear in Physical Review

Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.Comment: Added two appendices and references. Corrected typo

Bosonizing one-dimensional cold atomic gases

We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as ``bosonization''), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method to compute the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.Comment: 39 pages + 14 EPS figures; typos corrected, references update

Value of tissue harmonic imaging (THI) and contrast harmonic imaging (CHI) in detection and characterisation of breast tumours

The purpose of this study was to investigate the extent to which tissue harmonic imaging (THI), speckle reduction imaging (SRI), spatial compounding (SC) and contrast can improve detection and differentiation of breast tumours. We examined 38 patients (14 benign, 24 malignant tumours) with different combinations of THI, SRI and SC. The effect on delineation, margin, tissue differentiation and posttumoral phenomena was evaluated with a three-point score. Additionally, 1oo not palpable tumours (diameters: 4–15 mm) were examined by contrast harmonic imaging (CHI) with power Doppler. After bolus injection (0.5 ml Optison), vascularisation and enhancement were observed for 20 min. The best combination for detection of margin, infiltration, echo pattern and posterior lesion boundary was the combination of SRI level 2 with SC low. THI was helpful for lesions OF more than 1 cm depth. In native Power Doppler, vessels were found in 54 of 100 lesions. Within 5 min after contrast medium (CM) injection, marginal and penetrating vessels increased in benign and malignant tumours and central vessels mostly in carcinomas (p<0.05). A diffuse CM accumulation was observed up to 20 min after injection in malignant tumours only (p<0.05). THI, SRI and SC improved delineation and tissue differentiation. Second-generation contrast agent allowed detection of tumour vascularisation with prolonged enhancement

International prospective cohort study of microvascular angina - Rationale and design.

Background: Patients with signs and symptoms of myocardial ischemia and non-obstructive coronary artery disease (CAD) frequently have coronary functional abnormalities, including coronary microvascular dysfunction. Those with the latter are grouped under the term "microvascular angina" (MVA). Although diagnostic criteria exist for MVA, as recently proposed by our COVADIS (COronary VAsomotor Disorders International Study) group and the condition has been increasingly recognized in clinical practice, the clinical characteristics and long-term prognosis of MVA patients in the current era remain to be fully elucidated. Aims: In the present study, we aimed to prospectively assess the clinical characteristics and long-term prognosis of MVA subjects in the current era in an international, multicenter, observational, and prospective registry study. Methods: A total of 15 medical centers across 7 countries (USA, UK, Germany, Spain, Italy, Australia, and Japan) enrolled subjects fulfilling the COVADIS diagnostic criteria for MVA as follows; (1) signs and/or symptoms of myocardial ischemia, (2) absence of obstructive CAD, and (3) objective evidence of myocardial ischemia and/or coronary microvascular dysfunction. The primary endpoint was the composite of major cardiovascular events (MACE), including cardiovascular death, non-fatal myocardial infarction, non-fatal stroke, hospitalization due to heart failure or unstable angina. Between July 2015 and December 2018, a total of 706 subjects with MVA (M/F 256/450, 61.1 ± 11.8 [SD] yrs.) were registered. Subjects will be followed for at least 1 year. Summary: The present study will provide important information regarding the clinical characteristics, management, and long-term prognosis of MVA patients in the current era