Boundary Structure and Module Decomposition of the Bosonic Z2Z_2 Orbifold Models with R2=1/2kR^2=1/2k

The $Z_2$ bosonic orbifold models with compactification radius $R^2=1/2k$ are examined in the presence of boundaries. Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, we arrive at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, without resorting to a basis of the extended algebra Ishibashi states. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.Comment: 28 page

Instantons in Four-Fermi Term Broken SUSY with General Potential

It is shown how to solve the Euclidean equations of motion of a point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points $\tau \to \pm \infty$. As an application, the Sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.Comment: 8 page

Boundary States, Extended Symmetry Algebra and Module Structure for certain Rational Torus Models

The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a consistent set of Newmann boundary states. The boundary states are constructed explicitly for these models and the fusion rules are derived from them. These are the ones prescribed by the Verlinde formula from the S-matrix of the theory. In addition, the extended symmetry algebra of these theories is constructed which is responsible for the rationality of these theories. Finally, the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra.Comment: 12 page

Noncommutative Quantization in 2D Conformal Field Theory

The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we rescale the time and change the compactification radius appropriately. The four point function is deformed, preserving, nevertheless, the sl(2,C) invariance. Finally the first Ward identity of the deformed theory is derived.Comment: 5 pages, The solitonic contribution to the partition function has been computed. The parameter $\theta$ has been analytically continued to $-i\theta

Silent versus reading out loud modes: An eye-tracking study

The main purpose of this study is to compare the silent and loud reading ability of typical and dyslexic readers, using eye-tracking technology to monitor the reading process. The participants (156 students of normal intelligence) were first divided into three groups based on their school grade, and each subgroup was then further separated into typical readers and students diagnosed with dyslexia. The students read the same text twice, one time silently and one time out loud. Various eye-tracking parameters were calculated for both types of reading. In general, the performance of the typical students was better for both modes of reading - regardless of age. In the older age groups, typical readers performed better at silent reading. The dyslexic readers in all age groups performed better at reading out loud. However, this was less prominent in secondary and upper secondary dyslexics, reflecting a slow shift towards silent reading mode as they age. Our results confirm that the eye-tracking parameters of dyslexics improve with age in both silent and loud reading, and their reading preference shifts slowly towards silent reading. Typical readers, before 4th grade do not show a clear reading mode preference, however, after that age they develop a clear preference for silent reading

The noncommutative harmonic oscillator in more than one dimensions

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.Comment: 12 page

Closed Bosonic String Partition Function in Time Independent Exact PP-Wave Background

The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp-wave backgrounds is studied. In the absence of an axion field the partition function is found to be modular invariant. In the presence of an axion field modular invariace is broken. This can be attributed to the light-cone gauge which breaks the symmetry in the $\sigma$-, $t$-directions. Recovery of this broken modular invariance suggests the introduction of twists in the world-sheet directions. However, one needs to go beyond the light-cone gauge to introduce such twists.Comment: 17 pages, added reference

Discrete Randomness in Discrete Time Quantum Walk: Study via Stochastic Averaging

The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U(1) coset element. Analysis in terms of quantum statistical moments and generating functions, derived by the completely positive trace preserving (CPTP) map governing evolution, reveals a pronounced eventual transition in walk's diffusion mode, from a quantum ballistic regime with rate O(t) to a classical diffusive regime with rate O(\surdt), when condition (strength of noise parameter)^{2}\times(number of steps)=1, is satisfied. The role of classical randomness is studied showing that the randomized QW, when treated on the stochastic average level by means of an appropriate CPTP averaging map, turns out to be equivalent to a novel quantized classical walk without randomness. This result emphasizes the dual role of quantization/randomization in the context of classical random walk.Comment: Reports on Mathematical Physics, to appea

Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics

Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduced by means of a new rule that treats quantum or classical noise affecting the coin's state, as sources of quantization. The long term asymptotic statistics of QORW walker's position that shows enhanced diffusion rates as compared to classical case, is exactly solved. A quantum optical cavity implementation of the walk provides the framework for quantum simulation of its asymptotic statistics. The simulation utilizes interacting two-level atoms and/or laser randomly pulsating fields with fluctuating parameters.Comment: 18 pages, 3 figure