Narrow Results

We compute the resonance energy transfer (RET) in a system composed of two quantum emitters near a host dielectric matrix in which metallic inclusions are inserted until the medium undergoes a dielectric-metal transition at percolation. We show that there is no peak in the RET rate at percolation, in contrast to what happens with the spontaneous emission rate of an emitter near the same critical medium. This result suggests that RET does not strongly correlate with the local density of states.

Tight-binding Hamiltonians with off-diagonal disorder are studied extensively in connection with localization phenomena. For instance, applying a random magnetic field to a square lattice amounts to assigning phases to the off-diagonal entries of H. A gauge transformation simplifies the resulting H to an equivalent Hamiltonian with apparently less disorder. This paper concerns the special case when non-zero entries of a Hamiltonian H are ± 1 between nearest-neighbor sites. Some thought shows that a one-dimensional chain Hamiltonian with this type of randomness can be transformed to that of an ordered chain by flipping the signs of selected basis functions, i.e. by a unitary transformation. Hence such a chain is not disordered at all. On the other hand, whether or not a similar H for a square lattice implies actual disorder is a topological question. The question can be put this way: Can one find a set of simple closed curves such that reversing the signs of basis functions inside the curves will change all non-zero H entries to +1? More generally one can ask about the extent of residual disorder and its effect on electronic properties of the model. We take up these questions on a periodic square lattice.

The formation of chaos in the parametric dependent system of interacting oscillators for both classical and quantum cases has been investigated. The domain in which classical motion is chaotic is defined. It has been shown that for certain values of the parameters from this domain, the form of the classical power spectrum is in a good agreement with the quantum band profile. Local density of states is calculated. The range in which application of perturbation theory is correct has been defined.

Local density of photonic states calculation based on multipole expansion method is a powerful tool for studying spontaneous emission and calculation of photon confinement in photonic crystal cavities. Using multipole expansion method, we calculate local density of states and quality factor of a two-dimensional three angle photonic crystal cavity. We also compare this quality factor result with the one calculated using finite difference time domain of a pulse response. It turns out that the local density of states calculation is more accurate and computationally less expensive. It is shown that shifting and changing the size of neighboring cylinders in the vicinity of photonic crystal cavity has a large impact on the mode volume and confinement. It is also described how the increasing of quality factor can be split up into local optimization of neighboring rods and the effect of increasing the number of photonic crystal layers, which exponentially increases the quality factor. This finding strongly suggests that the number of layers can be excluded from an optimization procedure. We also present structural design rules and geometrical freedom contour plots for the neighboring cylinders. These design rules can be used in further optimization of photonic crystal cavities.

Anisotropic gold nanoparticles (AuNPs) were synthesized using microwave (MW)-assisted route. Lemon extract was used as both reducing and stabilizing agent. Subsequent UV treatment was carried out to modify the particle size and shape. Distribution of triangular and pentagonal-shaped particles were found to increase in number. Moreover, up to 60% increase in particle size was also observed. Change in optical property and appearance of plasmon modes were clear indication of the modification caused. Local density of photonic states (LDOS) and electric field distribution were obtained through computational simulation using MATLAB toolbox. Experimental results were used as the input values for the simulation. Dipolar distribution was observed along the boundaries of the spherical NPs, while for triangular and pentagonal-shaped NPs, they were found to be concentrated along their edges and corners. The results presented here encourage us to choose an alternative eco-friendly, quick and simple route to synthesize gold NPs of various shapes for various application such as in viral detection, nanobiomaterials, biomedical images, detection-therapy, etc.

We study the (Anderson) metal-insulator transition (MIT) in tight binding models (TBM) of disordered systems using the scaling behavior of the typical density of states (GDOS) as localization criterion. The GDOS is obtained as the geometrical mean value of the local density of states (LDOS) averaged over many different lattice sites and disorder realizations. The LDOS can efficiently be obtained within the kernel polynomial method (KPM). To check the validity and accuracy of the method, we apply it here to the standard Anderson model of disordered systems, for which the results (for instance for the critical disorder strength of the Anderson transition) are well known from other methods.

We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble. We quantify the overlap between this single vector with the eigenvectors of the initial matrix and identify precisely a "Cauchy flight" regime. In particular, we compute the local density of this vector in the eigenvalues space of the initial matrix. Our results are obtained in a non-perturbative setting and are derived using the ideas of [O. Ledoit and S. Péché, Eigenvectors of some large sample covariance matrix ensembles, Probab. Theory Related Fields151 (2011) 233]. Finally, we give a robust derivation of a result obtained in [R. Allez and J.-P. Bouchaud, Eigenvector dynamics: General theory and some applications, Phys. Rev. E86 (2012) 046202] to study eigenspace dynamics in a semi-perturbative regime.

We study the (Anderson) metal-insulator transition (MIT) in tight binding models (TBM) of disordered systems using the scaling behavior of the typical density of states (GDOS) as localization criterion. The GDOS is obtained as the geometrical mean value of the local density of states (LDOS) averaged over many different lattice sites and disorder realizations. The LDOS can efficiently be obtained within the kernel polynomial method (KPM). To check the validity and accuracy of the method, we apply it here to the standard Anderson model of disordered systems, for which the results (for instance for the critical disorder strength of the Anderson transition) are well known from other methods.