Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Wigner distribution for angle coordinates in quantum mechanics

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase‐space language is much clarified by this extension.

Paradoxical reflection in quantum mechanics

This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.

Compressible MHD boundary layer in the stagnation region of a sphere

The steady laminar compressible boundary layer flow of an electrically conducting fluid in the stagnation region of a sphere with an applied magnetic field has been studied. The effects of the induced magnetic field, mass transfer, and viscous dissipation have been taken into account. Both isothermal and adiabatic wall conditions have been considered. The governing equations have been solved numerically using a shooting method. The skin friction and heat transfer are found to be strongly affected by the magnetic field, mass transfer, wall temperature and Mach number. It is found that the magnetic field reduces the heat transfer. This is a significant result which can be used in controlling the heat transfer rate. The boundary layer solutions break down as the magnetic parameter tends to a certain critical value.

Patterning Nanoroads and Quantum Dots on Fluorinated Graphene

Using ab initio methods we have investigated the fluorination of graphene and find that different stoichiometric phases can be formed without a nucleation barrier, with the complete “2D-Teflon” CF phase being thermodynamically most stable. The fluorinated graphene is an insulator and turns out to be a perfect matrix-host for patterning nanoroads and quantum dots of pristine graphene. The electronic and magnetic properties of the nanoroads can be tuned by varying the edge orientation and width. The energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO) of quantum dots are size-dependent and show a confinement typical of Dirac fermions. Furthermore, we study the effect of different basic coverage of F on graphene (with stoichiometries CF and C4F) on the band gaps, and show the suitability of these materials to host quantum dots of graphene with unique electronic properties.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Quantification of enantiomeric excess by H-1-detected heteronuclear refocusing and homonuclear multiple quantum NMR experiments

The omega(1)-heterodecoupled-C-13-filtered proton detected NMR experiments are reported for the accurate quantification of enantiomeric excess in chiral molecules embedded in chiral liquid crystal. The differential values of both H-1-H-1 and C-13-H-1 dipolar couplings in the direct dimension and only H-1-H-1 dipolar couplings in the indirect dimension enable unraveling of overlapped enantiomeric peaks. The creation of unequal C-13-bound proton signal for each enantiomer in the INEPT block and non-uniform excitation of coherences in homonuclear multiple quantum experiments do not yield accurate quantification of enantiomeric excess. In circumventing these difficulties, a coupling dependent intensity correction factor has been invoked. (C) 2010 Elsevier B.V. All rights reserved.

Ion probing with Luminescent PbS Quantum dots in PVA

The PbS quantum dots synthesized in PVA are used to investigate their photoluminescence (PL) response to various ions such as Zn, Cd, Hg, Ag, Cu, Fe, Mn, Co, Cr and Ni ions. The enhancement in the photoluminescence intensity is observed with specific ions namely Zn, Cd, Hg and Ag. Among these four ions, the PL response to Hg and Ag even at sub-micro-molar concentrations is quite high, approximately an order of magnitude higher than Zn and Cd. It is interesting to observe that the change in Pb and S molar ratio has profound effect on the selectivity of these ions. The samples prepared under excess of S are quite effective compared to Pb. Indeed, the later one has hardly any effect on the photoluminescence response. These results also indicate that the sensitivity of these QDs could be fine-tuned by controlling the S concentration at the surface. Contrary to the above, Cu, Fe and Co quenches the photoluminescence. Another interesting property of PbS in PVA observed is photo-brightening mechanism due to the curing of the polymer with laser. However, the presence of excess ions at the surface changes its property to photo-darkening/brightening that depends on the direction of carrier transfer mechanism (from QDs to the surface adsorbed metal ions or vice-versa), which is an interesting feature for metal ion detectivity.

Quantum Properties in Transport Through Nanoscopic Rings:Charge-Spin Separation and Interference Effects

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems. Charge-spin separation was predicted theoretically in one-dimensional strongly inter-acting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohmrings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential. These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z(2) invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent nu being different in different sectors. Copyright (C) EPLA, 2010

Experimental Test of the Quantum No-Hiding Theorem

The no-hiding theorem says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the Universe with no information being hidden in the correlation between these two subsystems. Here, we report an experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance. We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits.

Two beam photoluminescence of PbS quantum dots in polyvinyl alcohol

We report the effect of dual beam excitation on the photoluminescence (PL) from PbS quantum dots in polyvinyl alcohol by using two excitation lasers, namely Ar+ (514.5 nm) and He-Ne laser (670 nm). Both sources of excitation gave similar PL spectra around 1.67 eV (related to shallow traps) and 1.1 eV (related to deep traps). When both lasers were used at the same time, we found that the PL induced by each of the lasers was partly quenched by the illumination of the other laser. The proposed mechanism of this quenching effect involves traps that are populated by one specific laser excitation, being photo-ionized by the presence of the other laser. Temperature, laser intensity and modulation frequency dependent quenching efficiencies are presented in this paper. This reversible modulation has potential for optical switching and memory device applications. (C) 2010 Elsevier B.V. All rights reserved.

Photoluminescence enhancement and quenching in metal-semiconductor quantum dot hybrid arrays

Hybrid monolayer arrays of metal and semiconductor quantum dots have been prepared to study the exciton-plasmon interaction. We observed crossover from strong quenching to enhancement in photoluminescence of the quantum dots as a function of the emission wavelength for fixed interparticle spacings. Remarkably, the enhancement is observed even for extremely short separation at which strong quenching has been observed and predicted earlier. A significant redshift in emission maxima is also observed for quantum dots with quenched emission. The possible role of collective phenomena as well as strong interactions in such ordered hybrid arrays in controlling the emission is discussed. (C) 2011 American Institute of Physics. doi:10.1063/1.3553766]