Microscopic theory of vibronic dynamics in linear polyenes

We propose a novel approach to calculate dynamical processes at ultrafast time scale in molecules in which vibrational and electronic motions are strongly mixed. The relevant electronic orbitals and their interactions are described by a Hubbard model, while electron-phonon interaction terms account for the bond length dependence of the hopping and the change in ionic radii with valence charge. The latter term plays a crucial role in the non-adiabatic internal conversion process of the molecule. The time resolved photoelectron spectra are in good qualitative agreement with experiments.Comment: 3 figures, other comment

Faster annealing schedules for quantum annealing

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systemsComment: 10 pages, 5 figures, minor correction

SiC(0001): a surface Mott-Hubbard insulator

We present ab-initio electronic structure calculations for the Si-terminated SiC(0001)$\sqrt{3}\times\sqrt{3}$ surface. While local density approximation (LDA) calculations predict a metallic ground state with a half-filled narrow band, Coulomb effects, included by the spin-polarized LDA+U method, result in a magnetic (Mott-Hubbard) insulator with a gap of 1.5 eV, comparable with the experimental value of 2.0 eV. The calculated value of the inter-site exchange parameter, J=30K, leads to the prediction of a paramagnetic Mott state, except at very low temperatures. The observed Si 2p surface core level doublet can naturally be explained as an on-site exchange splitting.Comment: RevTex, 4 pages, 4 eps-figure

Isothermal and cyclic oxidation at 1000 and 1100 deg C of four nickel-base alloys: NASA-TRW VIA, B-1900, 713C, and 738X

The isothermal and cyclic oxidation resistance of four cast Ni-base gamma + gamma prime alloys, NASA-TRW Via, B-1900, 713C, and 738X, was determined in still air at 1000 and 1100 C. The oxidation process was evaluated by specific sample weight change with time, sample thickness change, X-ray diffraction of the scales, and sample metallography. The behavior is discussed in terms of the Cr, Al, and refractory metal contents of the alloys

"Credit Cycle" in an OLG Economy with Money and Bequest

In the late '90s Kiyotaki and Moore (KM) put forward a new framework (Kiyotaki and Moore,1997) to explore the Financial Accelerator hypothesis. The original model was framed in an Infinitely Lived Agent context (ILA-KM economy). As in KM we develop a dynamic model in which the durable asset ("land") is not only an input but also collateralizable wealth to secure lenders from the risk of borrowers' default. In this paper, however, we model an OLG-KM economy whose novel feature is the role of money as a store of value and of bequest as a vehicle of resources to be "invested" in landholding. The dynamics generated by the model are complex. Not only cyclical patterns are routinely generated but the periodicity and amplitude are irregular. A route to chaotic dynamics is open.

Static friction on the fly: velocity depinning transitions of lubricants in motion

The dragging velocity of a model solid lubricant confined between sliding periodic substrates exhibits a phase transition between two regimes, respectively with quantized and with continuous lubricant center-of-mass velocity. The transition, occurring for increasing external driving force F_ext acting on the lubricant, displays a large hysteresis, and has the features of depinning transitions in static friction, only taking place on the fly. Although different in nature, this phenomenon appears isomorphic to a static Aubry depinning transition in a Frenkel-Kontorova model, the role of particles now taken by the moving kinks of the lubricant-substrate interface. We suggest a possible realization in 2D optical lattice experiments.Comment: 5 pages, 4 figures, revtex, in print in Phys. Rev. Let

Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.Comment: 8 pages, 7 figures. (v2) minor revisions, published versio

Lubricated friction between incommensurate substrates

This paper is part of a study of the frictional dynamics of a confined solid lubricant film - modelled as a one-dimensional chain of interacting particles confined between two ideally incommensurate substrates, one of which is driven relative to the other through an attached spring moving at constant velocity. This model system is characterized by three inherent length scales; depending on the precise choice of incommensurability among them it displays a strikingly different tribological behavior. Contrary to two length-scale systems such as the standard Frenkel-Kontorova (FK) model, for large chain stiffness one finds that here the most favorable (lowest friction) sliding regime is achieved by chain-substrate incommensurabilities belonging to the class of non-quadratic irrational numbers (e.g., the spiral mean). The well-known golden mean (quadratic) incommensurability which slides best in the standard FK model shows instead higher kinetic-friction values. The underlying reason lies in the pinning properties of the lattice of solitons formed by the chain with the substrate having the closest periodicity, with the other slider.Comment: 14 pagine latex - elsart, including 4 figures, submitted to Tribology Internationa

Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.Comment: 6 pages, minor correction

Adiabatic quantum dynamics of a random Ising chain across its quantum critical point

We present here our study of the adiabatic quantum dynamics of a random Ising chain across its quantum critical point. The model investigated is an Ising chain in a transverse field with disorder present both in the exchange coupling and in the transverse field. The transverse field term is proportional to a function $\Gamma(t)$ which, as in the Kibble-Zurek mechanism, is linearly reduced to zero in time with a rate $\tau^{-1}$, $\Gamma(t)=-t/\tau$, starting at $t=-\infty$ from the quantum disordered phase ($\Gamma=\infty$) and ending at $t=0$ in the classical ferromagnetic phase ($\Gamma=0$). We first analyze the distribution of the gaps -- occurring at the critical point $\Gamma_c=1$ -- which are relevant for breaking the adiabaticity of the dynamics. We then present extensive numerical simulations for the residual energy $E_{\rm res}$ and density of defects $\rho_k$ at the end of the annealing, as a function of the annealing inverse rate $\tau$. %for different lenghts of the chain. Both the average $E_{\rm res}(\tau)$ and $\rho_k(\tau)$ are found to behave logarithmically for large $\tau$, but with different exponents, $[E_{\rm res}(\tau)/L]_{\rm av}\sim 1/\ln^{\zeta}(\tau)$ with $\zeta\approx 3.4$, and $[\rho_k(\tau)]_{\rm av}\sim 1/\ln^{2}(\tau)$. We propose a mechanism for $1/\ln^2{\tau}$-behavior of $[\rho_k]_{\rm av}$ based on the Landau-Zener tunneling theory and on a Fisher's type real-space renormalization group analysis of the relevant gaps. The model proposed shows therefore a paradigmatic example of how an adiabatic quantum computation can become very slow when disorder is at play, even in absence of any source of frustration.Comment: 10 pages, 11 figures; v2: added references, published versio