Quantum entanglement in a noncommutative system

We explore the effect of two-dimensional position-space noncommutativity on the bipartite entanglement of continuous-variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of commutative systems to the case of noncommutative systems residing in two dimensions. Using the positive partial transpose criterion for separability of bipartite states, we derive a condition on the separability of a noncommutative system that is dependent on the noncommutative parameter theta. We then consider the specific example of a bipartite Gaussian state and show the quantitative reduction in entanglement originating from noncommutative dynamics. We show that such a reduction in entanglement for a noncommutative system arising from the modification of the variances of the phase-space variables (uncertainty relations) is clearly manifested between two particles that are separated by small distances.

NMR relaxation study of disorder in the mixed system BP x GPI(1-x) and the low temperature transition from classical to quantum rotation

1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.

Effect of inter-edge Coulomb interactions on transport through a point contact in nu=5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G(H) = 1/2e(2)/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G(H) = 5/2e(2)/h) and the fully disconnected case (G(H) = 0).

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Effect of Structural Modification on the Quantum-Size Effect in II-VI Semiconducting Nanocrystals

The electronic structure of group II-VI semiconductors in the stable wurtzite form is analyzed using state-of-the-art ab initio approaches to extract a simple and chemically transparent tight-binding model. This model can be used to understand the variation in the bandgap with size, for nanoclusters of these compounds. Results complement similar information already available for same systems in the zinc blende structure. A comparison with all available experimental data on quantum size effects in group II-VI semiconductor nanoclusters establishes a remarkable agreement between theory and experiment in both structure types, thereby verifying the predictive ability of our approach. The significant dependence of the quantum size effect on the structure type suggests that the experimental bandgap change at a given size compared to the bulk bandgap, may be used to indicate the structural form of the nanoclusters, particularly in the small size limit, where broadening of diffraction features often make it difficult to unambiguously determine the structure.

Multiple-quantum artifacts in single-quantum two-dimensional correlated NMR spectra of strongly coupled spins

Artifacts in the form of cross peaks have been observed along two- and three-quantum diagonals in single-quantum two-dimensional correlated (COSY) spectra of several peptides and oligonucleotides. These have been identified as due to the presence of a non-equilibrium state of kind I (a state describable by populations which differ from equilibrium) of strongly coupled spins carried over from one experiment to the next in the COSY algorithm.

Studies of working memory in interrupted human-computer interaction

Distraction in the workplace is increasingly more common in the information age. Several tasks and sources of information compete for a worker's limited cognitive capacities in human-computer interaction (HCI). In some situations even very brief interruptions can have detrimental effects on memory. Nevertheless, in other situations where persons are continuously interrupted, virtually no interruption costs emerge. This dissertation attempts to reveal the mental conditions and causalities differentiating the two outcomes. The explanation, building on the theory of long-term working memory (LTWM; Ericsson and Kintsch, 1995), focuses on the active, skillful aspects of human cognition that enable the storage of task information beyond the temporary and unstable storage provided by short-term working memory (STWM). Its key postulate is called a retrieval structure an abstract, hierarchical knowledge representation built into long-term memory that can be utilized to encode, update, and retrieve products of cognitive processes carried out during skilled task performance. If certain criteria of practice and task processing are met, LTWM allows for the storage of large representations for long time periods, yet these representations can be accessed with the accuracy, reliability, and speed typical of STWM. The main thesis of the dissertation is that the ability to endure interruptions depends on the efficiency in which LTWM can be recruited for maintaing information. An observational study and a field experiment provide ecological evidence for this thesis. Mobile users were found to be able to carry out heavy interleaving and sequencing of tasks while interacting, and they exhibited several intricate time-sharing strategies to orchestrate interruptions in a way sensitive to both external and internal demands. Interruptions are inevitable, because they arise as natural consequences of the top-down and bottom-up control of multitasking. In this process the function of LTWM is to keep some representations ready for reactivation and others in a more passive state to prevent interference. The psychological reality of the main thesis received confirmatory evidence in a series of laboratory experiments. They indicate that after encoding into LTWM, task representations are safeguarded from interruptions, regardless of their intensity, complexity, or pacing. However, when LTWM cannot be deployed, the problems posed by interference in long-term memory and the limited capacity of the STWM surface. A major contribution of the dissertation is the analysis of when users must resort to poorer maintenance strategies, like temporal cues and STWM-based rehearsal. First, one experiment showed that task orientations can be associated with radically different patterns of retrieval cue encodings. Thus the nature of the processing of the interface determines which features will be available as retrieval cues and which must be maintained by other means. In another study it was demonstrated that if the speed of encoding into LTWM, a skill-dependent parameter, is slower than the processing speed allowed for by the task, interruption costs emerge. Contrary to the predictions of competing theories, these costs turned out to involve intrusions in addition to omissions. Finally, it was learned that in rapid visually oriented interaction, perceptual-procedural expectations guide task resumption, and neither STWM nor LTWM are utilized due to the fact that access is too slow. These findings imply a change in thinking about the design of interfaces. Several novel principles of design are presented, basing on the idea of supporting the deployment of LTWM in the main task.

Personality and social psychological studies on computer-mediated communication in school settings

The present study examined how personality and social psychological factors affect third and fourth graders' computer-mediated communication. Personality was analysed in terms of the following strategies: optimism, pessimism and defensive pessimism. Students worked either individually or in dyads which were paired homogeneously or heterogeneously according to the strategies. Moreover, the present study compared horizontal and vertical interaction. The study also examined the role that popularity plays, and students were divided into groups based on their popularity level. The results show that an optimistic strategy is useful. Optimism was found to be related to the active production and processing of ideas. Although previous research has identified drawbacks to pessimism in achievement settings, this study shows that the pessimistic strategy is not as debilitating a strategy as is usually assumed. Pessimistic students were able to process their ideas. However, defensive pessimists were somewhat cautious in introducing or changing ideas. Heterogeneous dyads were not beneficial configurations with respect to producing, introducing, or changing ideas. Moreover, many differences were found to exist between the horizontal and vertical interaction; specifically, the students expressed more opinions and feelings when teachers took no part in the discussions. Strong emotions were observed especially in the horizontal interaction. Further, group working skills were found to be more important for boys than for girls, while rejected students were not at a disadvantage compared to popular ones. Schools can encourage emotional and social learning. The present study shows that students can use computers to express their feelings. In addition, students who are unpopular in non-computer contexts or students who use pessimism can benefit from computers. Participation in computer discussions can give unpopular children a chance to develop confidence when relating to peers.

Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures

We present a new, generic method/model for multi-objective design optimization of laminated composite components using a novel multi-objective optimization algorithm developed on the basis of the Quantum behaved Particle Swarm Optimization (QPSO) paradigm. QPSO is a co-variant of the popular Particle Swarm Optimization (PSO) and has been developed and implemented successfully for the multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are - the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; Failure Mechanism based Failure criteria, Maximum stress failure criteria and the Tsai-Wu Failure criteria. The optimization method is validated for a number of different loading configurations - uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences as well as fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. Also, the performance of QPSO is compared with the conventional PSO.

Computer simulation of polytypes

Polytypes have been simulated, treating them as analogues of a one-dimensional spin-half Ising chain with competing short-range and infinite-range interactions. Short-range interactions are treated as random variables to approximate conditions of growth from melt as well as from vapour. Besides ordered polytypes up to 12R, short stretches of long-period polytypes (up to 33R) have been observed. Such long-period sequences could be of significance in the context of Frank's theory of polytypism. The form of short-range interactions employed in the study has been justified by carrying out model potential calculations.

Quantum supersymmetric generalisation of Bogomolnyi bounds

We review here classical Bogomolnyi bounds, and their generalisation to supersymmetric quantum field theories by Witten and Olive. We also summarise some recent work by several people on whether such bounds are saturated in the quantised theory.