Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

Noise-assisted preparation of entangled atoms

We discuss the generation of entangled states of two two-level atoms inside an optical cavity. The cavity mode is supposed to be coupled to a white noise with adjustable intensity. We describe how the entanglement between the atoms inside the cavity arise in such a situation. The entanglement is maximized for intermediate values of the noise intensity, while it is a monotonic function of the spontaneous rate. This resembles the phenomenon of stochastic resonance and sheds more light on the idea to exploit white noise in quantum information processing.Comment: 4 pages, 4 figure

Computational Investigation of Novel Tip Leakage Mitigation Methods for High Pressure Turbine Blades

This paper presents preliminary findings on a possible approach to reducing tip leakage losses. In this paper a computational study was conducted on the EEE (Energy Efficient Engine) HPT (High Pressure Turbine) rotor tip geometry using the commercial numerical solver ANSYS FLUENT. The flow solver was validated against aerodynamic data acquired in the NASA Transonic Turbine Blade Cascade facility. The scope of the ongoing study is to computationally investigate how the tip leakage and overall blade losses are affected by 1. injection from the tip near the pressure side, 2. injection from the tip surface at the camber line, and 3. injection from the tip surface into the tip separation bubble. The objective is to identify the locations on the tip surface at which to place appropriately configured blowing keeping in mind the film cooling application of tip blowing holes. The validation was conducted at Reynolds numbers of 85,000, 343,000 and 685,000 and at engine realistic flow conditions. The coolant injection simulations were conducted at a Reynolds number of 343,000 based on blade chord and inlet velocity and utilized the SST turbulence model in FLUENT. The key parameters examined are the number of jets, jet angle and jet location. A coolant to inlet pressure ratio of 1.0 was studied for angles of +30 deg., -30 deg. and 90 deg. to the local free stream on the tip. For the 3 hole configuration, 3 holes spaced 3 hole diameters apart with length to diameter ratio of 1.5 were used. A simulation including 11 holes along the entire mean camber line is also presented (30 degrees toward suction side). In addition, the effect of a single hole is also compared to a flat tip with no injection. The results provide insight into tip flow control methods and can be used to guide further investigation into tip flow control. As noted in past research it is concluded that reducing leakage flow is not necessarily synonymous with reducing losses due to leakage

Quantum trajectory approach to stochastically-induced quantum interference effects in coherently-driven two-level atoms

Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It is shown that in the case of dominant incoherent perturbation, the stochastic noise can unexpectedly create phase correlation between the neighboring atomic dressed states. This phase correlation is responsible for quantum interference between the related transitions resulting in anomalous modifications of the resonance fluorescence spectra.Comment: paper accepted for publicatio

D-branes in PP-wave light cone string field theory

The cubic interaction vertex and the dynamical supercharges are constructed for open strings ending on D7-branes, in light-cone superstring field theory in PP-wave background. In this context, we write down the symmetry generators in terms of the relevant group structure: SU(2) x SU(2) x SO(2) x SO(2), originating from the eight transverse directions in the PP-wave background and use the expressions to explicitly construct the vertex at the level of stringy zero modes. The results are further generalized to include all the stringy excitations as well.Comment: 30 pages, correction in eqn. (4.28), few equations (appendix), Comments (p.17-18) and a reference (no. 58) added, typo is corrected in eqn. (4.5

An alternative formulation of light-cone string field theory on the plane wave

We construct a manifestly SO(4) x SO(4) invariant, supersymmetric extension of the closed string cubic interaction vertex and dynamical supercharges in light-cone string field theory on the plane wave space-time. We find that the effective vertex for states built out of bosonic creation oscillators coincides with the one previously constructed in the SO(8) formalism and conjecture that in general the two formulations are physically equivalent. Further evidence for this claim is obtained from the discrete Z_2-symmetry of the plane wave and by computing the mass-shift of the simplest stringy state using perturbation theory. We verify that the leading non-planar correction to the anomalous dimension of the dual gauge theory operators is correctly recovered.Comment: 28 pages; v2: minor change

Sudden switch of generalized Lieb-Robinson velocity in a transverse field Ising spin chain

The Lieb-Robinson theorem states that the speed at which the correlations between two distant nodes in a spin network can be built through local interactions has an upper bound, which is called the Lieb-Robinson velocity. Our central aim is to demonstrate how to observe the Lieb-Robinson velocity in an Ising spin chain with a strong transverse field. We adopt and compare four correlation measures for characterizing different types of correlations, which include correlation function, mutual information, quantum discord, and entanglement of formation. We prove that one of correlation functions shows a special behavior depending on the parity of the spin number. All the information-theoretical correlation measures demonstrate the existence of the Lieb-Robinson velocity. In particular, we find that there is a sudden switch of the Lieb-Robinson speed with the increasing of the number of spin

Chirality Change in String Theory

It is known that string theory compactifications leading to low energy effective theories with different chiral matter content ({\it e.g.} different numbers of standard model generations) are connected through phase transitions, described by non-trivial quantum fixed point theories. We point out that such compactifications are also connected on a purely classical level, through transitions that can be described using standard effective field theory. We illustrate this with examples, including some in which the transition proceeds entirely through supersymmetric configurations.Comment: 50 pages, 2 figure

Information loss in local dissipation environments

The sensitivity of entanglement to the thermal and squeezed reservoirs' parameters is investigated regarding entanglement decay and what is called sudden-death of entanglement, ESD, for a system of two qubit pairs. The dynamics of information is investigated by means of the information disturbance and exchange information. We show that for squeezed reservoir, we can keep both of the entanglement and information survival for a long time. The sudden death of information is seen in the case of thermal reservoir