Quantum first-passage problem

Formulation of quantum first passage problem is attempted in terms of a restricted Feynman path integral that simulates an absorbing barrier as in the corresponding classical case. The positivity of the resulting probability density, however, remains to be demonstrated.

State space formulation of ammonia reactor dynamics

The specific objective of this paper is to develop a state space model of a tubular ammonia reactor which is the heart of an ammonia plant in a fertiliser complex. A ninth order model with three control inputs and two disturbance inputs is generated from the nonlinear distributed model using linearization and lumping approximations. The lumped model is chosen such that the steady state temperature at the exit of the catalyst bed computed from the simplified state space model is close enough to the one computed from the nonlinear steady state model. The model developed in this paper is very useful for the design of continuous/discrete versions of single variable/multivariable control algorithms.

Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A Molecular Dynamics Study

Molecular dynamics (MD) simulations are reported for an anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) and CH3(CH2)15N+(CH3) ions in a layered solid, CdPS3. The intercalated CTA ions are organized with the cationic headgroups tethered to the inorganic sheet and the hydrocarbon tails arranged as bilayers. Simulations were performed at three temperatures, 65, 180, and 298 K, using an isothermal−isobaric ensemble that was subsequently switched once macroscopic parameters had converged to a canonical isothermal−isochoric ensemble. The simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and layer-to-layer separation distance. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained a planar all-trans conformation, and that gauche bonds occurred as part of a “kink” (gauche+−trans−gauche−) sequence and not as isolated gauche bonds. Trans−gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. A two-dimensional periodic Voronoi tessellation analysis was performed to obtain the single-molecular area of an alkyl chain in the bilayer. The single-molecular area relaxation times are an order of magnitude longer than the trans−gauche isomerization times. The results indicate that the trans−gauche isomerization is associated with the creation and annihilation of a kink defect sequence. The results of the present MD simulation explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C nuclear magnetic resonance measurements.

Dynamics of the ammonium ion in the ferroelectric transition in sodium ammonium selenate, NaNH4SeO4·2H2O-an E.S.R. study

E.S.R. investigations of γ-irradiated ferroelectric Sodium ammonium selenate, NaNH4SeO4•2H2O and its deuteriated analogue in powder and single crystal forms have led to a deeper understanding of the nature of the ferroelectric transition of 180 K. A number of paramagnetic species formed due to γ-irradiation have been identified on the basis of their g-factors and hyperfine features from 77Se. The radical SeO4 has been used as a microprobe in studying the phase transition.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Effect of inter-edge Coulomb interactions on transport through a point contact in nu=5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, we show that the stable fixed point corresponds to a point contact that is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G(H) = 1/2e(2)/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G(H) = 5/2e(2)/h) and the fully disconnected case (G(H) = 0).

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.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Conserved water-mediated H-bonding dynamics of catalytic Asn 175 in plant thiol protease

The role of invariant water molecules in the activity of plant cysteine protease is ubiquitous in nature. On analysing the 11 different Protein DataBank (PDB) structures of plant thiol proteases, the two invariant water molecules W I and W2 (W220 and W222 in the template 1PPN structure) were observed to form H-bonds with the Ob atom of Asn 175. Extensive energy minimization and molecular dynamics simulation studies up to 2 ns on all the PDB and solvated structures clearly revealed the involvement of the H-bonding association of the two water molecules in fixing the orientation of the asparagine residue of the catalytic triad. From this study, it is suggested that H-bonding of the water molecule at the W1 invariant site better stabilizes the Asn residue at the active site of the catalytic triad.

Dynamics Of Thermotropic Liquid Crystals Across The Isotropic-Nematic Transition And Their Similarity With Glassy Relaxation In Supercooled Liquids

No abstract.

Proton magnetic resonance study of molecular dynamics in (NH4)2CdI4

Proton magnetic resonance and spin-lattice relaxation studies have been carried out on (NH4)2CdI4 as a function of temperature (77–400 K) and Larmor frequency (10, 20 and 30 MHz). The T1 data indicate isotropic tumbling of ammonium ions at equivalent sites till 160 K. There is an indication of a phase transition at 265 K, the activation energy for molecular reorientation increases from 2.8 kcal/mole to 4.6 kcal/mole. The relaxation results and the linewidth data support the presence of two inequivalent sites at low temperatures, one having an environment corresponding to near-rigid-lattice limit and the other undergoing fast reorientations. The behaviour of the free induction decay with temperature below 120 K suggests a coherent motion for the faster species.

Effect of Structural Modification on the Quantum-Size Effect in II-VI Semiconducting Nanocrystals

The electronic structure of group II-VI semiconductors in the stable wurtzite form is analyzed using state-of-the-art ab initio approaches to extract a simple and chemically transparent tight-binding model. This model can be used to understand the variation in the bandgap with size, for nanoclusters of these compounds. Results complement similar information already available for same systems in the zinc blende structure. A comparison with all available experimental data on quantum size effects in group II-VI semiconductor nanoclusters establishes a remarkable agreement between theory and experiment in both structure types, thereby verifying the predictive ability of our approach. The significant dependence of the quantum size effect on the structure type suggests that the experimental bandgap change at a given size compared to the bulk bandgap, may be used to indicate the structural form of the nanoclusters, particularly in the small size limit, where broadening of diffraction features often make it difficult to unambiguously determine the structure.

Multiple-quantum artifacts in single-quantum two-dimensional correlated NMR spectra of strongly coupled spins

Artifacts in the form of cross peaks have been observed along two- and three-quantum diagonals in single-quantum two-dimensional correlated (COSY) spectra of several peptides and oligonucleotides. These have been identified as due to the presence of a non-equilibrium state of kind I (a state describable by populations which differ from equilibrium) of strongly coupled spins carried over from one experiment to the next in the COSY algorithm.