We study the realization of conformal symmetry in the QHE as part of the W∞ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts to taking proper care of the quantum measure. The conseq...

We prove that for a dense G± of shift-invariant measures on AZ d , all d shifts have purely singular continuous spectrum and give a new proof that in the weak topology of measure preserving Zd transformations, a dense G± is generated by transformations with purely singular continuous spectrum. We also give new examples of smooth unitary cocycles over an irrational rotation which have purely sin...

A number of numerical algorithms have been developed for various special classes of DAEs. This paper describes a new variable step size, constraint preserving integrator for general nonlinear fully implicit higher index DAEs. Numerical implementation issues are discussed. Numerical examples illustrate the effectiveness of the new method.

Let G be a finite group having an order preserving and rank preserving action on a finite ranked poset P. Let P/G denote the quotient poset. A well known result in algebraic Sperner theory asserts that an order raising G-linear map on V (P) (the complex vector space with P as basis) satisfying the full rank property induces an order raising linear map on V (P/G), also satisfying the full rank p...

The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge–Kutta numerical integration algorithms, suffers from both severe ineffic...

An impossibility theorem on approximately simulating quantum non-integrable Hamiltonian systems is presented here. This result shows that there is a tradeo between the unitary property and the energy expectation conservation law in time-descretization of quantum non-integrable systems, whose classical counterpart is Ge-Marsden's impossibility result about simulating classically non-integrable H...

A novel Mach-Zehnder interferometer terminated at two different frequencies realizes in a quantum regime the nonlinear frequency conversion of optical quantum superposition states. The information-preserving character of the relevant unitary transformation has been experimentally demonstrated for input qubits and ebits. Besides its own intrinsic fundamental interest, the new scheme is expected ...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

A class of quantum channels and completely positive maps (CPMs) are introduced and investigated. These, which we call subspace preserving (SP) CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve probability weights on a given orthogonal sum decomposition of the Hilbert space of a quantum system. Several equivalent characterizations of SP CPMs are prov...