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.

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.

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.

Proton NMR studies of dihalogenated phenyl benzamides: two-dimensional higher quantum methodologies

The scalar coupled proton NMR spectra of many organic molecules possessing more than one phenyl ring are generally complex due to degeneracy of transitions arising from the closely resonating protons, in addition to several short- and long- range couplings experienced by each proton. Analogous situations are generally encountered in derivatives of halogenated benzanilides. Extraction of information from such spectra is challenging and demands the differentiation of spectrum pertaining to each phenyl ring and the simplification of their spectral complexity. The present study employs the blend of independent spin system filtering and the spin-state selective detection of single quantum (SO) transitions by the two-dimensional multiple quantum (MQ) methodology in achieving this goal. The precise values of the scalar couplings of very small magnitudes have been derived by double quantum resolved experiments. The experiments also provide the relative signs of heteronuclear couplings. Studies on four isomers of dilhalogenated benzanilides are reported in this work.

Visualization of enantiomers using natural abundant 13C-filtered single and double quantum selective refocusing experiments: Application to small chiral molecules

The routine use of proton NMR for the visualization of enantiomers, aligned in the chiral liquid crystal solvent poly-γ-benzyl-l-glutamate (PBLG), is restricted due to severe loss of resolution arising from large number of pair wise interaction of nuclear spins. In the present study, we have designed two experimental techniques for their visualization utilizing the natural abundance 13C edited selective refocusing of single quantum (CH-SERF) and double quantum (CH-DQSERF) coherences. The methods achieve chiral discrimination and aid in the simultaneous determination of homonuclear couplings between active and passive spins and heteronuclear couplings between the excited protons and the participating 13C spin. The CH-SERF also overcomes the problem of overlap of central transitions of the methyl selective refocusing (SERF) experiment resulting in better chiral discrimination. Theoretical description of the evolution of magnetization in both the sequences has been discussed using polarization operator formalism.

The interaction of quantum dots with plasmons supported by metal waveguides

Plasmonics is a recently emerged technology that enables the compression of electromagnetic waves into miniscule metallic structures, thus enabling the focusing and routing of light on the nanoscale. Plasmonic waveguides can be used to miniaturise the size of integrated chip circuits while increasing the data transmission speed. Plasmonic waveguides are used to route the plasmons around a circuit and are a major focus of this thesis. Also, plasmons are highly sensitive to the surrounding dielectric environment. Using this property we have experimentally realised a refractive index sensor to detect refractive index change in solutions.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Quantum diffusion in thin disordered wires

Quantum Ohmic residual resistance of a thin disordered wire, approximated as a one-dimensional multichannel conductor, is known to scale exponentially with length. This nonadditivity is shown to imply (i) a low-frequency noise-power spectrum proportional to -ln(Ω)/Ω, and (ii) a dispersive capacitative impedance proportional to tanh(√iΩ )/ √iΩ. A deep connection to the quantum Brownian motion with linear dynamical frictional coupling to a harmonic-oscillator bath is pointed out and interpreted in physical terms.

Classical solitons with no quantum counterparts and their supersymmetric revival

We demonstrate the phenomenon stated in the title, using for illustration a two-dimensional scalar-field model with a triple-well potential {fx837-1}. At the classical level, this system supports static topological solitons with finite energy. Upon quantisation, however, these solitons develop infinite energy, which cannot be renormalised away. Thus this quantised model has no soliton sector, even though classical solitons exist. Finally when the model is extended supersymmetrically by adding a Majorana field, finiteness of the soliton energy is recovered.

Topological Quantum Computation - An Analysis of an Anyon Model Based on Quantum Double Symmetries

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

Noncommutative Quantum Field Theories and UV/IR Mixing

Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.