Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.Comment: 15 pages, 6 figures, minor corrections, accepted for publication in JHE

Matrix Product States Algorithms and Continuous Systems

A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be applied to a wide variety of situations. As a first test, we show how it provides reliable results in the computation of fundamental properties of a chain of quantum harmonic oscillators achieving off-critical and critical relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use it to study the ground state properties of the quantum rotor model in one spatial dimension, a model that can be mapped to the Mott insulator limit of the 1-dimensional Bose-Hubbard model. At the quantum critical point, the central charge associated to the underlying conformal field theory can be computed with good accuracy by measuring the finite-size corrections of the ground state energy. Examples of MPS-computations both in the finite-size regime and in the thermodynamic limit are given. The precision of our results are found to be comparable to those previously encountered in the MPS studies of, for instance, quantum spin chains. Finally, we present a spin-off application: an iterative technique to efficiently get numerical solutions of partial differential equations of many variables. We illustrate this technique by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio

Integration of auditory and visual communication information in the primate ventrolateral prefrontal cortex

The integration of auditory and visual stimuli is crucial for recognizing objects, communicating effectively, and navigating through our complex world. Although the frontal lobes are involved in memory, communication, and language, there has been no evidence that the integration of communication information occurs at the single-cell level in the frontal lobes. Here, we show that neurons in the macaque ventrolateral prefrontal cortex (VLPFC) integrate audiovisual communication stimuli. The multisensory interactions included both enhancement and suppression of a predominantly auditory or a predominantly visual response, although multisensory suppression was the more common mode of response. The multisensory neurons were distributed across the VLPFC and within previously identified unimodal auditory and visual regions (O’Scalaidhe et al., 1997; Romanski and Goldman-Rakic, 2002). Thus, our study demonstrates, for the first time, that single prefrontal neurons integrate communication information from the auditory and visual domains, suggesting that these neurons are an important node in the cortical network responsible for communication

Electrical polarization of nuclear spins in a breakdown regime of quantum Hall effect

We have developed a method for electrical polarization of nuclear spins in quantum Hall systems. In a breakdown regime of odd-integer quantum Hall effect (QHE), excitation of electrons to the upper Landau subband with opposite spin polarity dynamically polarizes nuclear spins through the hyperfine interaction. The polarized nuclear spins in turn accelerate the QHE breakdown, leading to hysteretic voltage-current characteristics of the quantum Hall conductor.Comment: 3 pages, 4 figures, submitted to Appl. Phys. Let

Oceanographic implications of radioactive fall-out distributions in the Atlantic Ocean: From 20°N to 25°S, from 1957 to 1961

The patterns of Sr90 distribution in the equatorial Atlantic are described for the years 1957, 1958, 1960, and 1961. Evidence is drawn from analysis of surface samples and of vertical profiles. The concentration distributions bear no resemblance to patterns of fall-out delivery on land; it is concluded that hydrographic processes are responsible for seawater concentration patterns. The data provide evidence for two otherwise unobserved, high fallout incidents over the Atlantic Ocean...

Fission Product Concentration in the Chukchi Sea

Reports on concentrations of strontium-90, cerium-144, and promethium-147 in water samples collected 1959-1962, especially as indicating mass transport of ocean water. The 1959 Sr-90 fallout values were less than those reported from the northwestern Pacific and similar to values for the North Atlantic and mainland Alaska; but the 1960-62 values increased, in contrast to the other areas. No comparable increase was found in the Ce-144 and Pm-147 concentrations, but these radioisotopes may be removed from sea water during passage over shallow seas and analysis of sediment content would be enlightening