Determining topological order from a local ground state correlation function

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological insulators and the Z index of the integer quantum Hall effect manifest themselves locally. We do so by providing an algorithm for determining these indices from a local equal time ground-state correlation function at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder and can be naturally generalized to include weak interactions. The locality of these topological indices implies bulk-edge correspondence theorem.Comment: 7 pages, 3 figures. Major changes: the paper was divided into sections, the locality of the order in 3D topological insulators is also discusse

Universal Uncertainty Principle in the Measurement Operator Formalism

Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulas for the noise and disturbance of measurements given by the measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals the square root of 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.Comment: 11 pages. Based on the author's invited talk at the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005), Besancon, France, May 2-6, 200

Low Frequency VLA Observations of Abell 754: Evidence for a Cluster Radio Halo and Possible Radio Relics

We present 74 MHz and 330 MHz VLA observations of Abell 754. Diffuse, halo-like emission is detected from the center of the cluster at both frequencies. At 330 MHz the resolution of 90'' distinguishes this extended emission from previously known point sources. In addition to the halo and at a much lower level, outlying steep-spectrum emission regions straddle the cluster center and are seen only at 74 MHz. The location, morphology and spectrum of this emission are all highly suggestive of at least one, and possibly two cluster radio relics. Easily obtained higher resolution, higher sensitivity VLA observations at both frequencies are required to confirm the extended nature of the halo-like emission and the 74 MHz relic detections. However, since there is prior evidence that this cluster is or has recently been in the process of a major merger event, the possible discovery of relics in this system is of great interest in light of recent observational and theoretical evidence in favor of a merger-relic connection. We discuss the possible role the merger shock waves, which are seen in the X-ray emission, may have played in the formation of the halo and radio relics in A754.Comment: 15 pages including 4 figures. Accepted for publication by Ap

Correlated interaction fluctuations in photosynthetic complexes

The functioning and efficiency of natural photosynthetic complexes is strongly influenced by their embedding in a noisy protein environment, which can even serve to enhance the transport efficiency. Interactions with the environment induce fluctuations of the transition energies of and interactions between the chlorophyll molecules, and due to the fact that different fluctuations will partially be caused by the same environmental factors, correlations between the various fluctuations will occur. We argue that fluctuations of the interactions should in general not be neglected, as these have a considerable impact on population transfer rates, decoherence rates and the efficiency of photosynthetic complexes. Furthermore, while correlations between transition energy fluctuations have been studied, we provide the first quantitative study of the effect of correlations between interaction fluctuations and transition energy fluctuations, and of correlations between the various interaction fluctuations. It is shown that these additional correlations typically lead to changes in interchromophore transfer rates, population oscillations and can lead to a limited enhancement of the light harvesting efficiency

2-Player Nash and Nonsymmetric Bargaining Games: Algorithms and Structural Properties

The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are ``small'', then its solution can be found in strongly polynomial time. We also give a non-succinct linear game whose solution can be found in strongly polynomial time

How to detect level crossings without looking at the spectrum

We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians representable by matrices. This approach provides a pedagogical introduction to (avoided) crossings, is capable of handling realistic Hamiltonians analytically, and offers a way to visualize crossings which is sometimes superior to that provided by the spectrum. We illustrate the method using the Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground state hydrogen atom in a uniform magnetic field.Comment: Accepted for publication in the American Journal of Physic

A Theory of Errors in Quantum Measurement

It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an observable are distributed normally. We obtain the probability distribution this implies for the outcome of a measurement, exactly for the case of 2x2 matrices and in the steepest descent approximation in general. Due to the phenomenon of `level repulsion', the probability distributions obtained are quite different from the Gaussian.Comment: Based on talk at "Spacetime and Fundamental Interactions: Quantum Aspects" A conference to honor A. P. Balachandran's 65th Birthda