Related papers: Statistical Transmutation and Phases of Two-Dimens…
Statistics transmutations to composite fermions in fractional-quantum-Hall-effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground-state energy shows that the transmutations are not…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
This paper discusses why the usual notion that quantum phase transitions can be mapped onto classical phase transitions in a higher dimension, and that this makes the former uninteresting from a fundamental theoretical point of view, is in…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
Observing quantum phase transitions in mesoscopic systems is a daunting task, thwarted by the difficulty of experimentally varying the magnetic interactions, the typical driving force behind these phase transitions. Here we demonstrate that…
We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…
In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
We study the dynamics of a quantum system in which an intermediate property $m$ is measured in between initial and final measurements of two different non-commuting properties $a$ and $b$. Since this intermediate measurement must involve an…
We give a detailed discussion of our general determination of (i) the number of unremovable, physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings of fermion fields.…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical…
We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…
We discuss the effect of dissipation on quantum phase transitions. In particular we concentrate on the Superconductor to Insulator and Quantum-Hall to Insulator transitions. By invoking a phenomenological parameter $\alpha$ to describe the…