Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Influence of composition on the structure, electric and magnetic properties of Pd-Mn-P and Pd-Co-P amorphous alloys

The influence of composition on the structure and on the electric and magnetic properties of amorphous Pd-Mn-P and Pd-Co-P prepared by rapid quenching techniques were investigated in terms of (1) the 3d band filling of the first transition metal group, (2) the phosphorus concentration effect which acts as an electron donor and (3) the transition metal concentration.

The structure is essentially characterized by a set of polyhedra subunits essentially inverse to the packing of hard spheres in real space. Examination of computer generated distribution functions using Monte Carlo random statistical distribution of these polyhedra entities demonstrated tile reproducibility of the experimentally calculated atomic distribution function. As a result, several possible "structural parameters" are proposed such as: the number of nearest neighbors, the metal-to-metal distance, the degree of short-range order and the affinity between metal-metal and metal-metalloid. It is shown that the degree of disorder increases from Ni to Mn. Similar behavior is observed with increase in the phosphorus concentration.

The magnetic properties of Pd-Co-P alloys show that they are ferromagnetic with a Curie temperature between 272 and 399°K as the cobalt concentration increases from 15 to 50 at.%. Below 20 at.% Co the short-range exchange interactions which produce the ferromagnetism are unable to establish a long-range magnetic order and a peak in the magnetization shows up at the lowest temperature range . The electric resistivity measurements were performed from liquid helium temperatures up to the vicinity of the melting point (900°K). The thermomagnetic analysis was carried out under an applied field of 6.0 kOe. The electrical resistivity of Pd-Co-P shows the coexistence of a Kondo-like minimum with ferromagnetism. The minimum becomes less important as the transition metal concentration increases and the coefficients of ℓn T and T^2 become smaller and strongly temperature dependent. The negative magnetoresistivity is a strong indication of the existence of localized moment.

The temperature coefficient of resistivity which is positive for Pd- Fe-P, Pd-Ni-P, and Pd-Co-P becomes negative for Pd-Mn-P. It is possible to account for the negative temperature dependence by the localized spin fluctuation model and the high density of states at the Fermi energy which becomes maximum between Mn and Cr. The magnetization curves for Pd-Mn-P are typical of those resulting from the interplay of different exchange forces. The established relationship between susceptibility and resistivity confirms the localized spin fluctuation model. The magnetoresistivity of Pd-Mn-P could be interpreted in tenns of a short-range magnetic ordering that could arise from the Rudennan-Kittel type interactions.

Narrativas em Libras: análise de processos cognitivos

Palavras ou expressões produzidas em línguas de sinais são conhecidas como sinais. Línguas de sinais são produzidas especificamente em forma visual e o significado dos sinais pode ser compreendido por meio da relação com recursos visuais, do usuário com o mundo e com o corpo. Este estudo, com base na Linguística Cognitiva, propõe-se a analisar essas relações em sinais da Língua Brasileira de Sinais (Libras), produzidos por dez surdos ao narrarem a história em quadrinhos Não chora que eu dou um jeito da Turma da Mônica. Os processos cognitivos foram analisados à luz da gramática cognitiva (LANGACKER, 2008), da corporificação (LAKOFF; JOHNSON, 1980), da metonímia conceptual (LAKOFF; JOHNSON, 2003; EVANS; GREEN, 2006; KÖVECSES, 2010), da categorização (CROFT; CRUSE, 2004; Rosch apud FERRARI, 2011), da iconicidade cognitiva (WILCOX, 2000; QUADROS, 2004; WILCOX, 2004) e da mescla em espaço real (FAUCONNIER; TURNER, 1996, 2003; LIDDELL, 2003; SHAFFER, 2012; DUDIS apud SHAFFER, 2012). Constatou-se que alguns sinais produzidos apresentaram conceptualização de base icônica. A partir dessa fundamentação, postulou-se que esses sinais poderiam receber a seguinte categorização: icônicos (BOLA e CAIXA); icônico metonímicos (INES e CASA); icônico metonímico corporificados (MONICA e CHORAR). Por meio dessa classificação, propôs-se também a categorização de nomes e verbos pessoais. Outro processo cognitivo investigado foi a mescla em espaço real, constatada em seis das dez narrativas, como um recurso cognitivo acionado para expor ao interlocutor a troca de turnos dos participantes da narração. Tendo em vista que esses sinais foram encontrados em narrativas, analisam-se etapas da narrativa (LABOV apud FIGUEIREDO, 2009) e a estrutura das histórias em quadrinhos (SILVA, 2001; SOUZA, 2013). Verificou-se que não houve narrativa com todas as etapas de Labov. Assim, por meio de uma investigação inicial, esta pesquisa fornece questionamentos acerca dos processos cognitivos acionados na produção de sinais da Libras nas narrativas pesquisadas

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (2nd report, direct numerical simulation using townsend's eddy forcing)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method using 'simple model eddies' (Townsend 1976) for DNS of stationary homogeneous isotropic turbulence is proposed. A force field is obtained in real space by sprinkling many space-filling 'simple model eddies' whose centers are randomly but uniformly distributed in space and whose axes of rotation are random. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects are investigated. The results show that stationary homogeneous isotropic turbulence is generated in real space using the present method. By using different model eddies with different sizes and rotation speeds, we could change the turbulence properties such as the integral and micro scales, the turbulent Reynolds number and the isotropy of turbulence. Turbulence intensities near the wall showed good agreements with the previous measurement and the linear analysis based on a rapid distortion theory (RDT). The splat effect (i.e., turbulence intensities of the components parallel to the boundary are amplified) occurs near the boundary and the viscous effect prohibits the splat effect at the quasi steady state at low Reynolds number.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (3rd report, direct numerical simulation on wall blocking effects for anisotropic turbulence)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method proposed in the second report using Townsend's "simple model eddies" for DNS was extended to generate axisymmetric anisotropic turbulence. A force field is obtained in real space by sprinkling many space-filling "simple model eddies" whose centers are randomly but uniformly distributed in space. The axes of rotation are controlled in this study to generate axisymmetric anisotropic turbulence. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects for anisotropic turbulence are investigated. The results show that stationary axisymmetric anisotropic turbulence is generated using the present method. Turbulence intensities near the wall showed good agreements with the rapid distortion theory (RDT) for small t (t ≪ TL), where TL. is the eddy turnover time. The splat effect (i. e. turbulence intensities of the components parallel to the surface are amplified) occurs near the boundary and the viscous effect attenuates the splat effect at the quasi steady state at low Reynolds number as for Isotropic turbulence. Prandtl's secondary flow of the second kind does not occur for low Reynolds number flows, which qualitatively agrees with previous observetion in a mixing-box.

A time-varying controllable fault-tolerant field associative memory model and its simulation

A time-varying controllable fault-tolerant field associative memory model and the realization algorithms are proposed. On the one hand, this model simulates the time-dependent changeability character of the fault-tolerant field of human brain's associative memory. On the other hand, fault-tolerant fields of the memory samples of the model can be controlled, and we can design proper fault-tolerant fields for memory samples at different time according to the essentiality of memory samples. Moreover, the model has realized the nonlinear association of infinite value pattern from n dimension space to m dimension space. And the fault-tolerant fields of the memory samples are full of the whole real space R-n. The simulation shows that the model has the above characters and the speed of associative memory about the model is faster.

Spectral properties of a double-quantum-dot structure: A causal Green's function approach

Spectral properties of a double quantum dot (QD) structure are studied by a causal Green's function (GF) approach. The double QD system is modeled by an Anderson-type Hamiltonian in which both the intra- and interdot Coulomb interactions are taken into account. The GF's are derived by an equation-of-motion method and the real-space renormalization-group technique. The numerical results show that the average occupation number of electrons in the QD exhibits staircase features and the local density of states depends appreciably on the electron occupation of the dot.

Degenerate four-wave-mixing signals from dc- and ac-driven semiconductor superlattice

Within the one-dimensional tight-binding model;rnd chi-3 approximation, we have calculated four-wave-mixing (FWM) signals for a semiconductor superlattice in the presence of both static and high-frequency electric fields. When the exciton effect is negligible, the time-periodic field dynamically delocalizes the otherwise localized Wannier-Stark states, and accordingly quasienergy band structures are formed, and manifest in the FWM spectra as a series of equally separated continua. The width of each continuum is proportional to the joint width of the valence and conduction minibands and is independent of the Wannier-Stark index. The realistic homogeneous broadening blurs the continua into broad peaks, whose line shapes, far from the Lorentzian, vary with the delay time in the FWM spectra. The swinging range of the peaks is just the quasienergy bandwidth. The dynamical delocalization (DDL) also induces significant FWM signals well beyond the excitation energy window. When the Coulomb interaction is taken into account, the unequal spacing between the excitonic Wannier-Stark levels weakens the DDL effect, and the FWM spectrum is transformed into groups of discrete lines. Strikingly, the groups are evenly spaced by the ac field frequency, reflecting the characteristic of the quasienergy states. The homogeneous broadening again smears out the line structures, leading to the excitonic FWM spectra quite similar to those without the exciton effect. However, all these features predicted by the dynamical theory do not appear in a recent experiment [Phys. Rev. Lett. 79, 301 (1997)], in which, by using the static approximation the observed Wannier-Stark ladder with delay-time-dependent spacing in the FWM spectra is attributed to a temporally periodic dipole field, produced by the Bloch oscillation of electrons in real space. The contradiction between the dynamical theory and the experiments is discussed. In addition, our calculation indicates that the dynamical localization coherently enhances the time-integrated FWM signals. The feasibility of using such a technique to study the dynamical localization phenomena is shown. [S0163-1829(99)10607-6].

Franz-Keldysh effect and dynamical Franz-Keldysh effect of cylindrical quantum wires

We investigate the interband optical absorption spectra near the band edge of a cylindrical semiconductor quantum wire in the presence of a static electric field and a terahertz electric field polarized along the axis. Optical absorption spectra are nonperturbatively calculated by solving the low-density semiconductor Bloch equations in real space and real time. The influence of the Franz-Keldysh (FK) effect and dynamical FK effect on the absorption spectrum is investigated. To highlight the physics behind the FK effect and dynamical FK effect, the spatiotemporal dynamics of the polarization wave packet are also presented. Under a reasonable static electric field, substantial and tunable absorption oscillations appear above the band gap. A terahertz field, however, will cause the Autler-Townes splitting of the main exciton peak and the emergence of multiphoton replicas. The presented results suggest that semiconductor quantum wires have potential applications in electro-optical devices.

NEW FORMATION MECHANISM OF ELECTRIC-FIELD DOMAIN DUE TO GAMMA-X SEQUENTIAL TUNNELING IN GAAS/ALAS SUPERLATTICES

We have studied the sequential tunneling of doped weakly coupled GaAs/ALAs superlattices (SLs), whose ground state of the X valley in AlAS layers is designed to be located between the ground state (E(GAMMA1)) and the first excited state (E(GAMMA2)) of the GAMMA valley in GaAs wells. The experimental results demonstrate that the high electric field domain in these SLs is attributed to the GAMMA-X sequential tunneling instead of the usual sequential resonant tunneling between subbands in adjacent wells. Within this kind of high field domain, electrons from the ground state in the GaAs well tunnel to the ground state of the X valley in the nearest AlAs layer, then through very rapid real-space transfer relax from the X valley in the AlAs layer to the ground state of the GAMMA valley of the next GaAs well.

PHOTOVOLTAIC EFFECT AND ITS POLARITY IN SI DOPING SUPERLATTICES

We have studied the photovoltaic effects in Si doping superlattices (nipi) under different excitation conditions with and without additional cw optical biasing using a He-Ne laser. On the basis of the photovoltaic theory of carrier spatial separation in superlattices, we propose the concept of spatial fixity of the photovoltage polarity in type-II superlattices and examine the experimental results. The photovoltaic effect in Si nipi is found mainly from the direct transitions related with shallow impurities in real space, not the electron-hole band-to-band process as in GaAs nipi.

THE STUDY OF MICROSTRUCTURE IN IRON-DOPED AND SULFUR-DOPED INP CRYSTALS BY MEANS OF HREM AND COMPUTER-SIMULATION

The microstructures in iron- and sulphur-doped InP crystals were studied using both electron microscopy and electron diffraction. A modulated structure has been found in S-doped InP crystal, where the commensurate modulations corresponded to periodicities of 0.68 nm and 0.7 nm in real space and were related to the reflections of the cubic lattice in [111] and [113BAR] directions; they were indexed as q111* = 1/2(a* + b* + c*) and q113BAR* = 1/4(-a* - b* + 3c*), respectively. Single atomic layers of iron precipitate were observed, with preferred orientations along which precipitates are formed. Simulated calculations by means of the dynamical theory of electron diffraction using models for the precipitate structure were in good agreement with our experimental results. The relation between the modulated structure and the precipitates is also discussed.

Observation of N-Shaped Negative Differential Resistance in GaAs-Based Modulation-Doped Field Effect Transistor with InAs Quantum Dots

N-shaped negative differential resistance (NDR) with a high peak-to-valley ratio (PVR) is observed in a GaAs-based modulation-doped field effect transistor (MODFET) with InAs quantum dots (QDs) in the barrier layer (QDFET) compared with a GaAs MODFET. The NDR is explained as the real-space transfer (RST) of high-mobility electrons in a channel into nearby barrier layers with low mobility, and the PVR is enhanced dramatically upon inserting the QD layer. It is also revealed that the QD layer traps holes and acts as a positively charged nano-floating gate after a brief optical illumination, while it acts as a negatively charged nano-floating gate and depletes the adjacent channel when charged by the electrons. The NDR suggests a promising application in memory or high-speed logic devices for the QDFET structure.

Theoretical study of p-d hybridization in Co perovskite

The real-space recursion method and unrestricted Hartree-Fock approximation have been applied to calculate the density of states of various Co perovskite, CeCoO3, SrCoO3 and Sr1-xCexCoO3. We have studied the magnetically ordered states of these Co perovskites in an enlarged double cell, and find its various magnetic structures due to the occupancy of 3d band and its interaction with neighboring Co ions. In this study, we have studied the p-d hybridization of the three Co perovskites, we find t(2g) electrons are localized and the flat e(g) band is responsible for the itinerant behavior, and although the rare earth elements itself contribute little to the DOS at the Fermi energy, the DOS at Fermi energy and the magnetic moment changed consequently because of different valence of Co ions in these compounds and p-d hybridization effect is very important. (C) 2009 Elsevier B.V. All rights reserved.

The phase behavior of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures

The phase behaviors of comblike block copolymer A(m+1)B(m)/homopolymer A mixtures are studied by using the random phase approximation method and real-space self-consistent field theory. From the spinodals of macrophase separation and microphase separation, we can find that the number of graft and the length of the homopolymer A have great effects on the phase behavior of the blend. For a given composition of comblike block copolymer, increasing the number of graft does not change the macrophase separation spinodal curve but decreases the microphase separation region. The addition of a small quantity of long-chain homopolymer A increases the microphase separation of comblike block copolymer/homopolymer A mixture.