Optimal control landscapes for quantum observables

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable finite dimensional quantum systems with no constraints placed on the controls, it is shown that there is only a finite number of distinct values for the extrema, dependent on the spectral degeneracy of the initial and target density matrices. The consequences of these findings for the practical discovery of effective quantum controls in the laboratory is discussed.     

Impact dynamics of colloidal quantum dot solids

We use aerosol techniques to investigate the cohesive and granular properties of solids composed of colloidal semiconductor nanocrystals (quantum dot solids). We form spherical agglomerates of nanocrystals with a nebulizer and direct them toward a carbon substrate at low (~0.01 m/s) or high (~100 m/s) velocities. We then study the morphology of the deposit (i.e., the "splat") after impact. By varying the size of the agglomerate and the spacing between the nanocrystals within it, we observe influences on the mechanical properties of the quantum dot solid. We observe a liquid-to-solid transition as the nanocrystals become more densely packed. Agglomerates with weakly interacting nanocrystals exhibit liquidlike splashing and coalescence of overlapping splats. More dense agglomerates exhibit arching and thickening effects, which is behavior typical of granular materials.     

Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

We use the pair-product approximation to the complex-time quantum mechanical propagator to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. A variety of tests are performed to determine the accuracy of the method and understand its breakdown at longer times. We report quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

Energy transfer among dyes on particulate solids

Absorption and fluorescence properties of methylene blue (MB), a well-known singlet molecular oxygen photosensitizer, and its mixtures with pheophorbide-a (Pheo) sorbed on microgranular cellulose are studied, with emphasis on radiative and nonradiative energy transfer from Pheo to MB. Although pure MB builds up dimeric species on cellulose even at 2 x 10(-8) mol g(-1), addition of 2.05 x 10(-7) mol g(-1) Pheo largely inhibits aggregation up to nearly 10(-6) mol g(-1) MB. At the same time, the absorption spectrum of monomeric MB in the presence of Pheo differs from the spectrum in pure cellulose. Both effects reveal a strong influence of Pheo on the medium properties. A model relying entirely on experimental data is developed, through which energy transfer efficiencies can be calculated for thin and thick layers of dye-loaded cellulose. At the largest concentration of MB assuring no dye aggregation, nonradiative energy transfer efficiencies reach a maximum value of nearly 40%. This value is quite high, taking into account the low fluorescence quantum yield of Pheo, Phi = 0.21, and results from the existence of high local concentrations of the acceptor within the supporting material. These results show that large energy transfer rates can exist in a system devoid of any special molecular organization.     

Temperature-dependent energy transfer in cadmium telluride quantum dot solids

Efficiently luminescing colloidal CdTe quantum dots (QDs) were used for the preparation of monodispersed and mixed size QD solids. Luminescence spectra and decay times of the QD emission were measured as a function of temperature to study energy transfer (ET) processes in the QD solids. In the luminescence decay curves of the emission of the largest QDs (acceptors), a rise time of the luminescence signal is observed due to energy transfer from smaller QDs. Both the rise time (a measure for the energy transfer rate) and the luminescence decay time lengthen upon cooling. This is explained by the decreased dipole strength of the excitonic emission of the QDs in the solid due to the presence of a singlet and a lower lying triplet level. Studies of energy transfer in heteronuclear QD solids reveal that single-step ET dominates.     

Energy landscapes of ion clusters in isotropic quadrupolar and octupolar traps

The energy landscapes of ion clouds confined in isotropic quadrupolar and octupolar traps are characterized for several representative cluster sizes. All clusters exhibit stable multishell structures that belong to separate funnels. Quadrupolar confinement leads to more homogeneous clusters and denser distributions of isomers than octupolar confinement. Statistical analysis of the transition states indicates that the barriers associated with intrashell motion are lower but more asymmetric and more cooperative compared to intershell motion. The relaxation between low-energy funnels with different arrangements of shells mostly exhibits Arrhenius kinetics, with a weak variation of the activation energy at higher temperatures.     

Energy landscapes for water clusters in a uniform electric field

The behavior of small water clusters, (H2O)n, n=2-5 and n=8, in a uniform electric field is investigated for three related rigid-body models. Changes in the properties of the low-lying potential energy minima and the rearrangement pathways between them are examined. Results for certain structural transitions are compared with recent ab initio calculations. The models are found to give qualitatively similar trends, and there is some evidence that as the applied field strength is increased the quantitative differences between the models are also reduced.     

Evaporation of Lennard-Jones clusters

Extensive molecular dynamics simulations have been done to study the evaporation of a 13-atom Lennard-Jones cluster. The survival probability and the evaporative lifetime are calculated as a function of the cluster total energy from a classical trajectory analysis. The results are interpreted in terms of the RRK theory of unimolecular dissociation. The calculation of the binding energy of the evaporated species from the evaporation rate and the average kinetic energy release is discussed.     

Evaporation of Lennard-Jones fluids

Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T/T(c), where T(c) is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.     

Phase locking of molecular two-level quantum systems: Application to ionic solids

Photon locking of optical transitions in molecular systems has been reported recently by Sleva, Xavier, Zewail and Glasbeek. These observations were made on I₂ vapor using phase-coherent multiple pulses and photon echo detection. The same pulse sequence to observe locking in ionic solids using optical detection of triplet state spin coherence is applied here. Agreement between theory and experiment is very satisfactory.     

Electron-conducting quantum dot solids: novel materials based on colloidal semiconductor nanocrystals

We review the optical and electrical properties of solids that are composed of semiconductor nanocrystals. Crystals, with dimensions in the nanometre range, of II-VI, IV-VI and III-V compound semiconductors, can be prepared by wet-chemical methods with a remarkable control of their size and shape, and surface chemistry. In the uncharged ground state, such nanocrystals are insulators. Electrons can be added, one by one, to the conduction orbitals, forming artificial atoms strongly confined in the nanocrystal. Semiconductor nanocrystals form the building blocks for larger architectures, which self-assemble due to van der Waals interactions. The electronic structure of the quantum dot solids prepared in such a way is determined by the orbital set of the nanocrystal building blocks and the electronic coupling between them. The opto-electronic properties are dramatically altered by electron injection into the orbitals. We discuss the optical and electrical properties of quantum dot solids in which the electron occupation of the orbitals is controlled by the electrochemical potential.     

Energy levels in modified quantum statistical potentials

We calculate one-electron energy levels in potentials derived from the solution of the atomic Thomas-Fermi-Dirac equation. A local exchange potential is used. Corrections are made to a previous theory, which joins a TFD density to a quantum mechanical electron density near the nucleus, where the Thomas-Fermi-Dirac density has an incorrect singularity. Use of a potential derived from this theory leads to improvement in inner-shell energies. Changes in the potential, suggested in the literature as being reasonable for valence electrons, do not always give the expected improvement. Nor does naively correcting for self-energy lead to improved one-electron energy levels in general.

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Zusammenfassung Es werden Einelektronen-Energieniveaus bezüglich Potentialen, die sich aus der Thomas-Fermi-Dirac Gleichung ergeben, berechnet, wobei ein lokales Austauschpotential benutzt wird. Es ergeben sich Korrekturen gegenüber einem früheren Verfahren, bei dem einerseits mit einer TFD Dichte und andererseits der quantenmechanischen Dichte in der Umgebung des Kernes, wo das TFD-Modell ein falsches Verhalten liefert, operiert wird. Auf diesem modifizierten Wege erhält man ein Potential, das zu besseren Funktionen für die inneren Schalen führt. Dagegen ergeben üblicherweise benützte Potentialänderungen für die Valenzelektronen, ebenso wenig wie naheliegende Korrekturen für die Selbstwechselwirkung, nicht die erstrebten Verbesserungen.

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Supported by National Science Foundation under grant GP-20718.     

Two-dimensional (17)O multiple quantum magic-angle spinning NMR of organic solids

We report two-dimensional (2D) (17)O multiple-quantum magic-angle spinning (MQMAS) NMR spectra for four (17)O-labeled organic compounds: [(17)O(2)]-D-alanine (1), potassium hydrogen [(17)O(4)]dibenzoate (2), [(17)O(4)]-D,L-glutamic acid.HCl (3) and [2,4-(17)O(2)]uracil (4). The high spectral resolution observed in the 2D (17)O MQMAS NMR spectra allows extraction of precise (17)O NMR parameters for all crystallographically distinct oxygen sites. We demonstrate that rotor synchronization is important in obtaining high-quality (17)O MQMAS spectra for organic compounds. Several issues related to the potential of (17)O MQMAS NMR for large biomolecular systems are also discussed.     

Stability of separation-shifted Lennard-Jones fluids

Ruelle's thermodynamic stability criteria are applied to the separation-shifted Lennard-Jones (SSLJ) fluid, and the domain of its parameters giving "normal" thermodynamic stability in the thermodynamic limit is established. Fluids interacting with the SSLJ both conforming to and breaking these stability criteria were modeled using molecular dynamics computer simulation. For system sizes typical of most simulations, the transition between the two patterns of behavior was found to be smeared out over a range of parameter values. Thermodynamic instability is marked by a collapse of the system into a small "ball" or volume. The collapsed state nevertheless has some statistical mechanical properties typical of systems exhibiting normal thermodynamics (e.g., the kinetic and configurational temperatures were found to be the same in the collapsed state within statistics).