Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Enhanced Tetrahedral Ordering of Water Molecules in Minor Grooves of DNA: Relative Role of DNA Rigidity, Nanoconfinement, and Surface Specific Interactions

Confinement and Surface specific interactions call induce Structures otherwise unstable at that temperature and pressure. Here we Study the groove specific water dynamics ill the nucleic acid sequences, poly-AT and poly-GC, in long B-DNA duplex chains by large scale atomistic molecular dynamics simulations, accompanied by thermodynamic analysis. While water dynamics in the major groove remains insensitive to the sequence differences, exactly the opposite is true for the minor groove water. Much slower water dynamics observed in the minor grooves (especially in the AT minor) call be attributed to all enhanced tetrahedral ordering (< t(h)>) of water. The largest value of < t(h)> in the AT minor groove is related to the spine of hydration found in X-ray Structure. The calculated configurational entropy (S-C) of the water molecules is found to be correlated with the self-diffusion coefficient of water in different region via Adam-Gibbs relation D = A exp(-B/TSC), and also with < t(h)>.

Melting of an Anchored Bilayer: Molecular Dynamics Simulations of the Structural Transition in (CnH2n+1NH3)(2)PbI4 (n=12, 14, 16, 18)

The thermally driven Structural phase transition in the organic-inorganic hybrid perovskite (CnH2n+1NH3)(2)PbI4 has been investigated using molecular dynamics (MD) simulations. This system consists of positively charged alkyl-amine chains anchored to a rigid negatively charged PbI4 sheet with the chains organized as bilayers with a herringbone arrangement. Atomistic simulations were performed using ail isothermal-isobaric ensemble over a wide temperature range from 65 to 665 K for different alkyl chain lengths, n = 12, 14, 16, and 18. The simulations are able to reproduce the essential Features of the experimental observations of this system, including the existence of a transition, the linear variation of the transition temperature with alkyl chain length, and the expansion of the bilayer thickness at the transition. By use of the distance fluctuation Criteria, it is Shown that the transition is associated With a Melting of the alkyl chains of the anchored bilayer. Ail analysis of the conformation of the alkyl chains shows increased disorder in the form of gauche defects above due melting transition. Simulations also show that the melting transition is characterized by the complete disappearance of all-trans alkyl chains in the anchored bilayer, in agreement with experimental observations. A conformationally disordered chain has a larger effective cross-sectional area, and above due transition a uniformly tilted arrangement of the anchored chains call no longer be Sustained. At the melt the angular distribution of the orientation of the chains are 110 longer uniform; the chains are splayed allowing for increased space for individual chains of the anchored bilayer. This is reflected in a sharp rise in the ratio of the mean head-to-head to tail-to-tail distance of the chains of the bilayer at the transition resulting in in expansion of the bilayer thickness. The present MD simulations provide a simple explanation as to how changes in conformation of individual alkyl-chains gives rise to the observed increase in the interlayer lattice spacing of (CnH2n+1NH3)(2)PbI4 at the melting transition.

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

Self-interrupted regenerative metal cutting in turning

A new approach is used to study the global dynamics of regenerative metal cutting in turning. The cut surface is modeled using a partial differential equation (PDE) coupled, via boundary conditions, to an ordinary differential equation (ODE) modeling the dynamics of the cutting tool. This approach automatically incorporates the multiple-regenerative effects accompanying self-interrupted cutting. Taylor's 3/4 power law model for the cutting force is adopted. Lower dimensional ODE approximations are obtained for the combined tool–workpiece model using Galerkin projections, and a bifurcation diagram computed. The unstable solution branch off the subcritical Hopf bifurcation meets the stable branch involving self-interrupted dynamics in a turning point bifurcation. The tool displacement at that turning point is estimated, which helps identify cutting parameter ranges where loss of stability leads to much larger self-interrupted motions than in some other ranges. Numerical bounds are also obtained on the parameter values which guarantee global stability of steady-state cutting, i.e., parameter values for which there exist neither unstable periodic motions nor self-interrupted motions about the stable equilibrium.

Structures and molecular-dynamics studies of three active-site mutants of bovine pancreatic phospholipase A(2)

Phospholipase A(2) hydrolyzes phospholipids at the sn-2 position to cleave the fatty-acid ester bond of L-glycerophospholipids. The catalytic dyad (Asp99 and His48) along with a nucleophilic water molecule is responsible for enzyme hydrolysis. Furthermore, the residue Asp49 in the calcium-binding loop is essential for controlling the binding of the calcium ion and the catalytic action of phospholipase A2. To elucidate the structural role of His48 and Asp49, the crystal structures of three active-site single mutants H48N, D49N and D49K have been determined at 1.9 angstrom resolution. Although the catalytically important calcium ion is present in the H48N mutant, the crystal structure shows that proton transfer is not possible from the catalytic water to the mutated residue. In the case of the Asp49 mutants, no calcium ion was found in the active site. However, the tertiary structures of the three active-site mutants are similar to that of the trigonal recombinant enzyme. Molecular-dynamics simulation studies provide a good explanation for the crystallographic results.

Trap-State Dynamics in Visible-Light-Emitting ZnO:MgO Nanocrystals

Oleate-capped ZnO:MgO nanocrystals have been synthesized that are soluble in nonpolar solvents and which emit strongly in the visible region (450−600 nm) on excitation by UV radiation. The visible emission involves recombination of trap states of the nanocrystalline ZnO core and has a higher quantum yield than the band gap UV exciton emission. The spectrally resolved dynamics of the trap states have been investigated by time-resolved emission spectroscopy. The time-evolution of the photoluminescence spectra show that there are, in fact, two features in the visible emission whose relative importance and efficiencies vary with time. These features originate from recombination involving trapped electrons and holes, respectively, and with efficiencies that depend on the occupancy of the trap density of states.

Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within MY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical Molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected self-diffusivity profile for Pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in azeolite system With large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity.Further analysis allowed LIS to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture.

Self-interrupted regenerative turning

A preliminary study of self-interrupted regenerative turning is performed in this paper. To facilitate the analysis, a new approach is proposed to model the regenerative effect in metal cutting. This model automatically incorporates the multiple-regenerative effects accompanying self-interrupted cutting. Some lower dimensional ODE approximations are obtained for this model using Galerkin projections. Using these ODE approximations, a bifurcation diagram of the regenerative turning process is obtained. It is found that the unstable branch resulting from the subcritical Hopf bifurcation meets the stable branch resulting from the self-interrupted dynamics in a turning point bifurcation. Using a rough analytical estimate of the turning point tool displacement, we can identify regions in the cutting parameter space where loss of stability leads to much greater amplitude self-interrupted motions than in some other regions.

An asymptotic analysis of a simple model for the structure and dynamics of the Ramdas layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10(-3), and can therefore be treated as a small parameter (mu). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as mu --> 0 can be written in closed form. Four regimes, consishttp://eprints.iisc.ernet.in/cgi/users/home?screen=EPrint::Edit&eprintid=27192&stage=core#tting of a transient at nominal sunset, a radiative-diffusive boundary ('Ramdas') layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.

Dynamics of ''internal'' interannual variability of the Indian summer monsoon in a GCM

1] The poor predictability of the Indian summer monsoon ( ISM) appears to be due to the fact that a large fraction of interannual variability (IAV) is governed by unpredictable "internal'' low frequency variations. Mechanisms responsible for the internal IAV of the monsoon have not been clearly identified. Here, an attempt has been made to gain insight regarding the origin of internal IAV of the seasonal ( June - September, JJAS) mean rainfall from "internal'' IAV of the ISM simulated by an atmospheric general circulation model (AGCM) driven by fixed annual cycle of sea surface temperature (SST). The underlying hypothesis that monsoon ISOs are responsible for internal IAV of the ISM is tested. The spatial and temporal characteristics of simulated summer intraseasonal oscillations ( ISOs) are found to be in good agreement with those observed. A long integration with the AGCM forced with observed SST, shows that ISO activity over the Asian monsoon region is not modulated by the observed SST variations. The internal IAV of ISM, therefore, appears to be decoupled from external IAV. Hence, insight gained from this study may be useful in understanding the observed internal IAV of ISM. The spatial structure of the ISOs has a significant projection on the spatial structure of the seasonal mean and a common spatial mode governs both intraseasonal and interannual variability. Statistical average of ISO anomalies over the season ( seasonal ISO bias) strengthens or weakens the seasonal mean. It is shown that interannual anomalies of seasonal mean are closely related to the seasonal mean of intraseasonal anomalies and explain about 50% of the IAV of the seasonal mean. The seasonal mean ISO bias arises partly due to the broad-band nature of the ISO spectrum allowing the time series to be aperiodic over the season and partly due to a non-linear process where the amplitude of ISO activity is proportional to the seasonal bias of ISO anomalies. The later relation is a manifestation of the binomial character of rainfall time series. The remaining 50% of the IAV may arise due to land-surface processes, interaction between high frequency variability and ISOs, etc.

The dynamics of solvation of an electron in the image potential state by a layer of polar adsorbates

Recently, ultrafast two-photon photoemission has been used to study electron solvation at a two-dimensional metal/polar adsorbate interfaces [A. Miller , Science 297, 1163 (2002)]. The electron is bound to the surface by the image interaction. Earlier we have suggested a theoretical description of the states of the electron interacting with a two-dimensional layer of the polar adsorbate [K. L. Sebastian , J. Chem. Phys. 119, 10350 (2003)]. In this paper we have analyzed the dynamics of electron solvation, assuming a trial wave function for the electron and the solvent polarization and then using the Dirac-Frenkel variational method to determine it. The electron is initially photoexcited to a delocalized state, which has a finite but large size, and causes the polar molecules to reorient. This reorientation acts back on the electron and causes its wave function to shrink, which will cause further reorientation of the polar molecules, and the process continues until the electron gets self-trapped. For reasonable values for the parameters, we are able to obtain fair agreement with the experimental observations. (c) 2005 American Institute of Physics.

Analysis of dynamics and mechanism of ligand binding to Artocarpus integrifolia agglutinin. A 13C and 19F NMR study

Binding of 13C-labeled N-acetylgalactosamine (13C-GalNAc) and N-trifluoroacetylgalactosamine (19F-GalNAc) to Artocarpus integrifolia agglutinin has been studied using 13C and 19F nuclear magnetic resonance spectroscopy, respectively. Binding of these saccharides resulted in broadening of the resonances, and no change in chemical shift was observed, suggesting that the alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc experience a magnetically equivalent environment in the lectin combining site. The alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc were found to be in slow exchange between free and protein bound states. Binding of 13C-GalNAc was studied as a function of temperature. From the temperature dependence of the line broadening, the thermodynamic and kinetic parameters were evaluated. The association rate constants obtained for the alpha-anomers of 13C-GalNAc and 19F-GalNAc (k+1 = 1.01 x 10(5) M-1.s-1 and 0.698 x 10(5) M-1.s-1, respectively) are in close agreement with those obtained for the corresponding beta-anomers (k+1 = 0.95 x 10(5) M-1.s-1 and 0.65 x 10(5) M-1.s-1, respectively), suggesting that the two anomers bind to the lectin by a similar mechanism. In addition these values are several orders of magnitude slower than those obtained for diffusion controlled processes. The dissociation rate constants obtained are 49.9, 56.9, 42, and 43 s-1, respectively, for the alpha- and beta-anomers of 13C-GalNAc and 19F-GalNAc. A two-step mechanism has been proposed for the interaction of 13C-GalNAc and 19F-GalNAc with A. integrifolia lectin in view of the slow association rates and high activation entropies. The thermodynamic parameters obtained for the association and dissociation reactions suggest that the binding process is entropically favored and that there is a small enthalpic contribution.

Lattice dynamics of hexagonal ice

The lattice dynamics of hexagonal ice is worked out with the force constants deduced from the experimental elastic constants.