On the short-range order in Al-Mn quasicrystals during low-temperature ageing

We report the evolution of diffuse intensity during the low-temperature ageing of Al-Mn quasicrystals. This is taken as evidence of short-range order in the icosahedral phase prior to its decomposition. The implication of these diffuse intensities is discussed.

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.

Identity for harmonic oscillator brackets

An identity satisfied by the harmonic oscillator (Talmi-Moshinsky) brackets is derived from two equivalent methods for evaluating an integral often encountered in cluster model studies.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

The short range interactions between two rare gas atoms

The short range interactions in He2, Ne2 and Ar2 have been studied in terms of the electronic forces as functions of their internuclear separations employing their single configuration SCF wave functions. The results show that the constituent molecular orbitals behave differently in terms of the forces they exert on the nuclei during the interaction process. The different behaviour of the orbitals is also reflected in the redistribution of charges.

Electrical switching and short-range order in As-Te glasses

The local structural order in chalcogenide network glasses is known to change markedly at two critical compositions, namely, the percolation and chemical thresholds. In the AsxTe100-x glassy system, both the thresholds coincide at the composition x = 40 (40 at. % of arsenic). It is demonstrated that the electrical switching fields of As-Te glasses exhibit a distinct change at this composition.

Performance metrics in a hybrid MPI-OpenMP based molecular dynamics simulation with short-range interactions

We discuss the computational bottlenecks in molecular dynamics (MD) and describe the challenges in parallelizing the computation-intensive tasks. We present a hybrid algorithm using MPI (Message Passing Interface) with OpenMP threads for parallelizing a generalized MD computation scheme for systems with short range interatomic interactions. The algorithm is discussed in the context of nano-indentation of Chromium films with carbon indenters using the Embedded Atom Method potential for Cr-Cr interaction and the Morse potential for Cr-C interactions. We study the performance of our algorithm for a range of MPI-thread combinations and find the performance to depend strongly on the computational task and load sharing in the multi-core processor. The algorithm scaled poorly with MPI and our hybrid schemes were observed to outperform the pure message passing scheme, despite utilizing the same number of processors or cores in the cluster. Speed-up achieved by our algorithm compared favorably with that achieved by standard MD packages. (C) 2013 Elsevier Inc. All rights reserved.

Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Electric field induced short range to long range structural ordering and its influence on the Eu+3 photoluminescence in the lead-free ferroelectric Na1/2Bi1/2TiO3

Eu+3 was incorporated into the lattice of a lead-free ferroelectric Na1/2Bi1/2TiO3 (NBT) as per the nominal formula Na0.5Bi0.5-xEuxTiO3. This system was investigated with regard to the Eu+3 photoluminescence (PL) and structural behaviour as a function of composition and electric field. Electric field was found to irreversibly change the features in the PL spectra and also in the x-ray diffraction patterns below the critical composition x = 0.025. Detailed analysis revealed that below the critical composition, electric field irreversibly suppresses the structural heterogeneity inherent of the host matrix NBT and brings about a long range ferroelectric state with rhombohedral (R3c) distortion. It is shown that the structural disorder on the nano-scale opens a new channel for radiative transition which manifests as a new emission line branching off from the main D-5(0)-> F-7(0) line along with a concomitant change in the relative intensity of the other crystal field induced Stark lines with different J values. The study suggests that Eu+3 luminescence can be used to probe the relative degree of field induced structural ordering in relaxor ferroelectrics and also in high performance piezoelectric alloys where electric field couples very strongly with the lattice and structural degrees of freedom. (C) 2015 AIP Publishing LLC.

Rotational cut-off and anharmonicity effects on thermodynamic properties of gases at high temperatures

The exact expressions for the partition function (Q) and the coefficient of specific heat at constant volume (Cv) for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100 to 100,000 K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigid-rotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000 K for O2 and N2. Beyond these temperatures the error in Cv will be significant, because of anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000 K.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

Long-range synthon Aufbau modules (LSAM) in crystal structures: systematic changes in C6H6-nFn (0 <= n <= 6) fluorobenzenes

We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

A Study of Long-range Correlations in Schizophrenia EEG using Detrended Fluctuation Analysis

In this paper, we have studied electroencephalogram (EEG) activity of schizophrenia patients, in resting eyes closed condition, with detrended fluctuation analysis (DFA). The DFA gives information about scaling and long-range correlations in time series. We computed DFA exponents from 30 scalp locations of 18 male neuroleptic-naIve, recent-onset schizophrenia (NRS) subjects and 15 healthy male control subjects. Our results have shown two scaling regions in all the scalp locations in all the subjects, with different slopes, corresponding to two scaling exponents. No significant differences between the groups were found with first scaling exponent (short-range). However, the second scaling exponent (long-range) were significantly lower in control subjects at all scalp locations (p<0.05, Kruskal-Wallis test). These findings suggest that the long-range scaling behavior of EEG is sensitive to schizophrenia, and this may provide an additional insight into the brain dysfunction in schizophrenia.

Spin-Selective Correlation Experiment for Measurement of Long-Range J Couplings and for Assignment of (R/S) Enantiomers from the Residual Dipolar Couplings and DFT

We report the C-HETSERF experiment for determination of long- and short-range homo- and heteronuclear scalar couplings ((n)J(HH) and (n)J(XH), n >= 1) of organic molecules with a low sensitivity dilute heteronucleus in natural abundance. The method finds significant advantage in measurement of relative signs of long-range heteronuclear total couplings in chiral organic liquid crystal. The advantage of the method is demonstrated for the measurement of residual dipolar couplings (RDCs) in enantiomers oriented in the chiral liquid crystal with a focus to unambiguously assign R/S designation in a 2D spectrum. The alignment tensor calculated from the experimental RDCs and with the computed structures of enantiomers obtained by DFT calculations provides the size of the back-calculated RDCs. Smaller root-mean-square deviations (rmsd) between experimental and calculated RDCs indicate better agreement with the input structure and its correct designation of the stereogenic center.

Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.