Quantum Hall Physics - hierarchies and CFT techniques

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure

Quadratic cavity soliton optical frequency combs

We theoretically investigate the formation of frequency combs in a dispersive second-harmonic generation cavity system, and predict the existence of quadratic cavity solitons in the absence of a temporal walk-off

Belief Revision in Structured Probabilistic Argumentation

In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data with varying degrees of uncertainty attached. Likewise, an important aspect of the effort associated with maintaining knowledge bases is deciding what information is no longer useful; pieces of information (such as intelligence reports) may be outdated, may come from sources that have recently been discovered to be of low quality, or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing the basic issues of handling contradictory and uncertain data. Then, to address the last issue, we focus on the study of non-prioritized belief revision operations over probabilistic PreDeLP programs. We propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how such operations should behave, and study a class of operators along with theoretical relationships with the proposed postulates, including a representation theorem stating the equivalence between this class and the class of operators characterized by the postulates

Solitons and Quasielectrons in the Quantum Hall Matrix Model

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons.Comment: 15 pages, 9 figure

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte

Locking of domain walls and quadratic frequency combs in doubly resonant optical parametric oscillators

The formation of frequency combs (FCs) in high-Q microresonators with Kerr type of nonlinearity has attracted a lot of attention in the past decade [1]. Recently it has been shown that FCs can be also generated in dissipative dispersive cavities with quadratic nonlinearities [2,3], opening a new possibility of generating combs in previously unattainable spectral regions. Previous work has shown that modulational instability (MI) induces pattern and FC formation in degenerate optical parametric oscillators (OPOs) [4]. However, the existence of dissipative solitons or localized structures (LSs) is still unclear

Computing Quantiles in Markov Reward Models

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with non-negative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in time polynomial in the size of the chain and the maximum reward.Comment: 17 pages, 1 figure; typo in example correcte

Skyrmion ↔\leftrightarrow pseudoSkyrmion Transition in Bilayer Quantum Hall States at ν=1\nu =1

Bilayer quantum Hall states at $\nu =1$ have been demonstrated to possess a distinguished state with interlayer phase coherence. The state has both excitations of Skyrmion with spin and pseudoSkyrmion with pseudospin. We show that Skyrmion $\leftrightarrow$ pseudoSkyrmion transition arises in the state by changing imbalance between electron densities in both layers; PseudoSkyrmion is realized at balance point, while Skyrmion is realized at large imbalance. The transition can be seen by observing the dependence of activation energies on magnetic field parallel to the layers.Comment: 12 pages, no figure

Two-vibron bound states in alpha-helix proteins : the interplay between the intramolecular anharmonicity and the strong vibron-phonon coupling

The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an $\alpha$-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then, a mean field procedure is realized to obtain the dressed anharmonic vibron Hamiltonian. It is shown that the anharmonicity modifies the vibron-phonon interaction which results in an enhancement of the dressing effect. In addition, both the anharmonicity and the dressing favor the occurrence of two different bound states which the properties strongly depend on the interplay between the anharmonicity and the dressing. Such a dependence was summarized in a phase diagram which characterizes the number and the nature of the bound states as a function of the relevant parameters of the problem. For a significant anharmonicity, the low frequency bound states describe two vibrons trapped onto the same amide-I vibration whereas the high frequency bound states refer to the trapping of the two vibrons onto nearest neighbor amide-I vibrations.Comment: may 2003 submitted to Phys. Rev.