Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

Radio Frequency Superconducting Quantum Interference Device Meta-atoms and Metamaterials: Experiment, Theory, and Analysis

Metamamterials are 1D, 2D or 3D arrays of articial atoms. The articial atoms, called "meta-atoms", can be any component with tailorable electromagnetic properties, such as resonators, LC circuits, nano particles, and so on. By designing the properties of individual meta-atoms and the interaction created by putting them in a lattice, one can create a metamaterial with intriguing properties not found in nature. My Ph. D. work examines the meta-atoms based on radio frequency superconducting quantum interference devices (rf-SQUIDs); their tunability with dc magnetic field, rf magnetic field, and temperature are studied. The rf-SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. At relatively low rf magnetic field, a magnetic field tunability of the resonant frequency of up to 80 THz/Gauss by dc magnetic field is observed, and a total frequency tunability of 100% is achieved. The macroscopic quantum superconducting metamaterial also shows manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional electromagnetically induced transparency (EIT) or its classical analogs. A near complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bi-stability and can be tuned on/ off easily by altering rf and dc magnetic fields, temperature and history. Hysteretic in situ 100% tunability of transparency paves the way for auto-cloaking metamaterials, intensity dependent filters, and fast-tunable power limiters. An rf-SQUID metamaterial is shown to have qualitatively the same behavior as a single rf-SQUID with regards to dc flux, rf flux and temperature tuning. The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is then studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. This behavior can be understood employing methods in nonlinear dynamics; the sharp onset, and the gap of IM, are due to sudden state jumps during a beat of the two-tone sum input signal. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

Quantum theory beyond the physical : information in context

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum-like model of the human mental lexicon, and shows one set of recent experimental data suggesting that concept combinations can indeed behave non-separably. There is some reason to believe that the human mental lexicon displays entanglement.

Are academics messy? Testing the broken windows theory with a field experiment in the work environment

We test the broken windows theory using a field experiment in a shared area of an academic workplace(the department common room). More specifically, we explore academics’ and postgraduate students’ behavior under an order condition (a clean environment) and a disorder condition (a messy environment). We find strong evidence that signs of disorderly behavior trigger littering: In 59% of the cases, subjects litter in the disorder treatment as compared to 18% in the order condition. These results remain robust in a multivariate analysis even when controlling for a large set of factors not directly examined by previous studies. Overall, when academic staff and postgraduate students observe that others have violated the social norm of keeping the common room clean, all else being equal, the probability of littering increases by around 40%.

A formalization of logical imaging for information retrieval using quantum theory

In this paper we introduce a formalization of Logical Imaging applied to IR in terms of Quantum Theory through the use of an analogy between states of a quantum system and terms in text documents. Our formalization relies upon the Schrodinger Picture, creating an analogy between the dynamics of a physical system and the kinematics of probabilities generated by Logical Imaging. By using Quantum Theory, it is possible to model more precisely contextual information in a seamless and principled fashion within the Logical Imaging process. While further work is needed to empirically validate this, the foundations for doing so are provided.

Increased size selectivity of Si quantum dots on SiC at low substrate temperatures : an ion-assisted self-organization approach

A simple, effective, and innovative approach based on ion-assisted self-organization is proposed to synthesize size-selected Si quantum dots (QDs) on SiC substrates at low substrate temperatures. Using hybrid numerical simulations, the formation of Si QDs through a self-organization approach is investigated by taking into account two distinct cases of Si QD formation using the ionization energy approximation theory, which considers ionized in-fluxes containing Si3+ and Si1+ ions in the presence of a microscopic nonuniform electric field induced by a variable surface bias. The results show that the highest percentage of the surface coverage by 1 and 2 nm size-selected QDs was achieved using a bias of -20 V and ions in the lowest charge state, namely, Si1+ ions in a low substrate temperature range (227-327 °C). As low substrate temperatures (≤500 °C) are desirable from a technological point of view, because (i) low-temperature deposition techniques are compatible with current thin-film Si-based solar cell fabrication and (ii) high processing temperatures can frequently cause damage to other components in electronic devices and destroy the tandem structure of Si QD-based third-generation solar cells, our results are highly relevant to the development of the third-generation all-Si tandem photovoltaic solar cells.

Applying POVM to model non-orthogonality in quantum cognition

Much of the work currently occurring in the field of Quantum Interaction (QI) relies upon Projective Measurement. This is perhaps not optimal, cognitive states are not nearly as well behaved as standard quantum mechanical systems; they exhibit violations of repeatability, and the operators that we use to describe measurements do not appear to be naturally orthogonal in cognitive systems. Here we attempt to map the formalism of Positive Operator Valued Measure (POVM) theory into the domain of semantic memory, showing how it might be used to construct Bell-type inequalities.

Influence of Band Non-Parabolicity on Few Ballistic Properties of III-V Quantum Wire Field Effect Transistors Under Strong Inversion

A simplified yet analytical approach on few ballistic properties of III-V quantum wire transistor has been presented by considering the band non-parabolicity of the electrons in accordance with Kane's energy band model using the Bohr-Sommerfeld's technique. The confinement of the electrons in the vertical and lateral directions are modeled by an infinite triangular and square well potentials respectively, giving rise to a two dimensional electron confinement. It has been shown that the quantum gate capacitance, the drain currents and the channel conductance in such systems are oscillatory functions of the applied gate and drain voltages at the strong inversion regime. The formation of subbands due to the electrical and structural quantization leads to the discreetness in the characteristics of such 1D ballistic transistors. A comparison has also been sought out between the self-consistent solution of the Poisson's-Schrodinger's equations using numerical techniques and analytical results using Bohr-Sommerfeld's method. The results as derived in this paper for all the energy band models gets simplified to the well known results under certain limiting conditions which forms the mathematical compatibility of our generalized theoretical formalism.

A quantum chemical investigation of the metal centres in cytochrome c oxidase

Quantum effects are often of key importance for the function of biological systems at molecular level. Cellular respiration, where energy is extracted from the reduction of molecular oxygen to water, is no exception. In this work, the end station of the electron transport chain in mitochondria, cytochrome c oxidase, is investigated using quantum chemical methodology. Cytochrome c oxidase contains two haems, haem a and haem a3. Haem a3, with its copper companion, CuB, is involved in the final reduction of oxygen into water. This binuclear centre receives the necessary electrons from haem a. Haem a, in turn, receives its electrons from a copper ion pair in the vicinity, called CuA. Density functional theory (DFT) has been used to clarify the charge and spin distributions of haem a, as well as changes in these during redox activity. Upon reduction, the added electron is shown to be evenly distributed over the entire haem structure, important for the accommodation of the prosthetic group within the protein. At the same time, the spin distribution of the open-shell oxidised state is more localised to the central iron. The exact spin density distribution has been disputed in the literature, however, different experiments indicating different distributions of the unpaired electron. The apparent contradiction is shown to be due to the false assumption of a unit amount of unpaired electron density; in fact, the oxidised state has about 1.3 unpaired electrons. The validity of the DFT results have been corroborated by wave function based coupled cluster calculations. Point charges, for use in classical force field based simulations, have been parameterised for the four metal centres, using a newly developed methodology. In the procedure, the subsystem for which point charges are to be obtained, is surrounded by an outer region, with the purpose of stabilising the inner region, both electronically and structurally. Finally, the possibility of vibrational promotion of the electron transfer step between haem a and a3 has been investigated. Calculating the full vibrational spectra, at DFT level, of a combined model of the two haems, revealed several normal modes that do shift electron density between the haems. The magnitude of the shift was found to be moderate, at most. The proposed mechanism could have an assisting role in the electron transfer, which still seems to be dominated by electron tunnelling.

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Precipitate growth with composition-dependent diffusivity: Comparison between theory and phase field simulations

We consider the growth of an isolated precipitate when the matrix diffusivity depends on the composition. We have simulated precipitate growth using the Cahn-Hilliard model, and find good agreement between our results and those from a sharp interface theory for systems with and without a dilatational misfit. With misfit, we report (and rationalize) an interesting difference between systems with a constant diffusivity and those with a variable diffusivity in the matrix.