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.

Properties of the correlated electronic states of pyrene and hydrogenated pyrene

Approximate calculations are reported on pyrene within the PPP model Hamiltonian using a novel restricted CI scheme which employs both molecular orbital and valence bond techniques. Also reported are detailed full CI results of the PPP model on 2,7-dihydropyrene obtained using the valence bond method. Spectral studies, charge and spin density calculations in ground and excited states, and ring current calculations in the ground state of the molecules are presented. In pyrene, the calculated excitation energies are in good agreement with experiment. The closed structure pi-conjugated molecule pyrene appears to show smaller distortions from the ground state geometry compared with the open structure pi-conjugated molecule 2,7-dihydropyrene. The ground state equilibrium structure of 2,7-dihydropyrene can be viewed as two hexatriene molecules connected by a vinyl crosslink, as is evident from bond order and ring current calculations. This is consistent with the only Kekule resonant structure possible for this molecule.

Coherence and Localization in 2D Luttinger Liquids

Recent measurements on the resistivity of (La-Sr)(2)CuO4 are shown to tit within the general framework of Luttinger liquid transport theory. They exhibit a crossover from the spin-charge separated ''holon nondrag regime'' usually observed, with rho(ab) similar to T, to a ''localizing'' regime dominated by impurity scattering at low temperature. The proportionality of rho(c) and rho(ab) and the giant anisotropy follow directly from the theory.

Defect production due to quenching through a multicritical point

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/tau, where tau is the characteristic timescale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n similar to 1/tau(d nu)/((z nu+1)), where d is the spatial dimension, and. and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n similar to 1/(tau d/(2z2)), where the exponent z(2) determines the behavior of the off-diagonal term of the 2 x 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

Satellite-derived direct radiative effect of aerosols dependent on cloud cover

Aerosols from biomass burning can alter the radiative balance of the Earth by reflecting and absorbing solar radiation(1). Whether aerosols exert a net cooling or a net warming effect will depend on the aerosol type and the albedo of the underlying surface(2). Here, we use a satellite-based approach to quantify the direct, top-of-atmosphere radiative effect of aerosol layers advected over the partly cloudy boundary layer of the southeastern Atlantic Ocean during July-October of 2006 and 2007. We show that the warming effect of aerosols increases with underlying cloud coverage. This relationship is nearly linear, making it possible to define a critical cloud fraction at which the aerosols switch from exerting a net cooling to a net warming effect. For this region and time period, the critical cloud fraction is about 0.4, and is strongly sensitive to the amount of solar radiation the aerosols absorb and the albedo of the underlying clouds. We estimate that the regional-mean warming effect of aerosols is three times higher when large-scale spatial covariation between cloud cover and aerosols is taken into account. These results demonstrate the importance of cloud prediction for the accurate quantification of aerosol direct effects.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Is one-parameter scaling theory of localisation consistent? Comment on Schuh's comment

It is maintained that the one-parameter scaling theory is inconsistent with the physics of Anderson localisation.

Forms of relativistic dynamics with World Line Condition and separability

he Dirac generator formalism for relativistic Hamiltonian dynamics is reviewed along with its extension to constraint formalism. In these theories evolution is with respect to a dynamically defined parameter, and thus time evolution involves an eleventh generator. These formulations evade the No-Interaction Theorem. But the incorporation of separability reopens the question, and together with the World Line Condition leads to a second no-interaction theorem for systems of three or more particles. Proofs are omitted, but the results of recent research in this area is highlighted.

Theory For The Anomalous Hall Constant Of Mixed-Valence Systems

We show that the large anomalous Hall constants of mixed-valence and Kondo-lattice systems can be understood in terms of a simple resonant-level Fermi-liquid model. Splitting of a narrow, orbitally unquenched, spin-orbit split, f resonance in a magnetic field leads to strong skew scattering of band electrons. We interpret both the anomalous signs and the strong temperature dependence of Hall mobilities in CeCu2Si2, SmB6, and CePd3 in terms of this theory.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.