Spatially dependent correlation functions in the Anderson model

We report results from a first principles calculation of spatially dependent correlation functions around a magnetic impurity in metals described by the nondegenerate Anderson model. Our computations are based on a combination of perturbative scaling theory and numerical renormalization group methods. Results for the conduction election charge density around the impurity and correlation functions involving the conduction electron and impurity charge and spin densities will be presented. The behavior in various regimes including the mixed valent regime will be explored.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Origin of the insulating state in NaCuO2

We study the electronic structure of NaCuO2 by analysing experimental core level photoemission and X-ray absorption spectra using a cluster as well as an Anderson impurity Hamiltonian including the band structure of the oxygen sublattice. We show that the X-ray absorption results unambiguously establish a negative value of the charge transfer energy, A. Further, mean-field calculations for the edge-shared one-dimensional CuO2 lattice of NaCuO2 within the multiband Hubbard Hamiltonian show that the origin of the insulating nature lies in the band structure rather than in the correlation effects. LMTO-ASA band structure calculations suggest that NaCuO2 is an insulator with a gap of around 1 eV.

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called 'symplectic condition' (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Anderson transitions in Ln1-x Sr x CoO3 (Ln═Pr or Nd)

Electrical conductivity measurements show that Ln1-x Sr x CoO3, (Ln = Pr or Nd) undergoes a non-metal-metal transition when x≈0 3. The d.c. conductivity of compositions with 0Anderson localized.

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Geographic variation of the Anderson's Niviventer (Niviventer andersoni) (Thomas, 1911) (Rodentia: Muridae) of two new subspecies in China verified with cranial morphometric variables and pelage characteristics

A total of 66 specimens of Niviventer andersoni with intact skulls was investigated on pelage characteristics and cranial morphometric variables. The data were subjected to principal component analyses as well as to discriminant analyses, and measurement

A TAXONOMIC REVIEW OF TYLOTOTRITON VERRUCOSUS ANDERSON (AMPHIBIA, CAUDATA, SALAMANDRIDAE)

Generally it has not been recognized that salamanders of two distinctive color morphs currently are assigned to Tylototriton verrucosus Anderson. One form is uniformly dark brown dorsally, with bright orange coloration confined to the ventral edge of the tail; the other has a dark brown to black dorsal ground color with orange dorsolateral warts, an orange vertebral crest, and orange lateral and medial crests on the head. In addition, the limbs and ventrolateral surfaces of the second form have a variable pattern of orange coloration. The brown form occurs in northeastern India, Nepal, northern Burma, Bhutan, northern Thailand, the type locality in extreme western Yunnan, and perhaps in northern Vietnam. The orange-patterned form occurs only in western Yunnan Province, People's Republic of China. The two forms appear to be allopatric but occur close together in the area of the type locality near the Burma border in western Yunnan. There is no evidence of color intergradation in specimens from this region. Analyses of morphometric and meristic characters, however, suggest the possibility of limited genetic exchange between adjacent populations of brown and orange-patterned forms in western Yunnan. The genetic and taxonomic relationships between the two forms is not fully resolved. However, these two highly distinctive forms obviously have evolved along independent trajectories and merit taxonomic recognition. We therefore propose to restrict the concept of Tylototriton verrucosus to the brown form and designate a neotype for that purpose, and we describe a new species to receive the orange-patterned form.

New type of Fano resonant tunneling via Anderson impurities in superlattice

The spectrum of differential tunneling conductance in Si-doped GaAs/AlAs superlattice is measured at low electric fields. The conductance spectra feature a zero-bias peak and a low-bias dip at low temperatures. By taking into account the quantum interference between tunneling paths via superlattice miniband and via Coulomb blockade levels of impurities, we theoretically show that such a peak-dip structure is attributed to a Fano resonance where the peak always appears at the zero bias and the line shape is essentially described by a new function \xi\/\xi\+1 with the asymmetry parameter q approximate to 0. As the temperature increases, the peak-dip structure fades out due to thermal fluctuations. Good agreement between experiment and theory enables us to distinguish the zero-bias resonance from the usual Kondo resonance.

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.