We study localized plasma configurations in 3 + 1 dimensional massive field theories obtained by Scherk-Schwarz compactification of 4 + 1 dimensional CFT to predict the thermodynamic properties of localized blackholes and blackrings in Scherk-Schwarz compactified AdS 6 using the AdS/CFT correspondence. We present an exact solution to the relativistic Navier-Stokes equation in the thin ring limit of the fluid configuration. We also perform a thorough numerical analysis to obtain the thermodynamic properties of the most general solution. Finally we compare our results with the recent proposal for the phase diagram of blackholes in six flat dimensions and find some similarities but other differences.

We propose that the entanglement of mixed states is characterised properly in terms of a probability density function Pρ(E ). There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two qubit systems are rough benchmarks, and not monotones of each other. Focussing on the two qubit states, we provide an explicit construction of Pρ(E ) and show that it is characterised by a set of parameters, of which concurrence is but one particular combination. Pρ(E ) is manifestly invariant under SU (2) × SU (2) transformations. It can, in fact, reconstruct the state up to local operations -with the specification of at most four additional parameters. Finally the new measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.

We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing them with numerical simulations of the network model. PACS numbers: 72.15.Rn, 73.20.Fz, INTRODUCTIONAnderson localization of a quantum particle [1] or a classical wave in a random environment is a vibrant research field [2]. One of its central research directions is the physics of Anderson transitions [3], quantum critical points tuned by disorder. These include metal-insulator transitions and transitions of quantum Hall type separating distinct phases of topological insulators. While such transitions are conventionally observed in electronic (metallic and semiconductor) structures, there is also a considerable number of other experimental realizations actively studied in recent and current works. These include localization of light [4] and microwaves [5], cold atoms [6] (see a recent review [7]), ultrasound [8], and optically driven atomic systems [9].From the theoretical point of view, symmetries play a central role in determination of universality classes of critical phenomena. This idea was applied to Anderson localization by Altland and Zirnbaueer (AZ) [10] who identified ten distinct symmetry classes. In three of these classes, classes A, C, and D in AZ classification, the timereversal invariance is broken, and there is a possibility for a quantum Hall transition in two dimensions.The transition in class A is the usual integer quantum Hall (IQH) transition in a two-dimensional (2D) electronic system in a strong perpendicular magnetic field (see Ref.[11] for a review). Class A also includes the model of electrons in a random magnetic field, where all states are believed to be localized [12].Class C is one of the four Bogolyubov-de Gennes classes which describe transport of quasiparticles in disordered superconductors at a mean field level, and possess the particle-hole symmetry. In this class the spinrotation invariance is preserved, the quasiparticles have conserved spin, and one can study spin transport. The corresponding Hall transition is known as the spin quantum Hall (SQH) transition [13,14], at which the system exhibits a jump in the spin Hall conductance from 0 to 2 in appropriate units.In spite of tremendous efforts, most models of Anderson transitions have resisted analytical treatment. The IQH transition is one prominent example where only recently some analytical progress has been achieved [15]. On the other hand, the SQH transition enjoys a special status, since a network model of this transition was mapped exactly to classical percolation on a square lattice [16]. The original mapping used the supersymme...

We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the superspin ladder and the corresponding supersymmetric nonlinear sigma model allows us to establish the phase diagram of the network model, and the form of the critical line of the weak-field IQH transition. Our results confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. We apply the suspersymmetry method to several related network models that were introduced in the literature to describe the quantum Hall effect in graphene, the spin-degenerate Landau levels, and localization of electrons in a random magnetic field.