Fano resonances and entanglement entropy

We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.Comment: 10 pages, 10 figures, minor change

Quasi-bound states in continuum

We report the prediction of quasi-bound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for a wide region of parameter space. These quasi-bound states are generated in a quantum wire with two channels and an adatom, when the energy bands of the two channels overlap. A would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second QBIC lays above the lower energy band).Comment: 4 pages, 4figures, 1 tabl

Strongly Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide

The decay rate \gam of an excited dipole molecule inside a waveguide is evaluated for the strongly coupled matter-field case near a cutoff frequency \ome_c without using perturbation analysis. Due to the singularity in the density of photon states at the cutoff frequency, we find that \gam depends non-analytically on the coupling constant $\ggg$ as $\ggg^{4/3}$. In contrast to the ordinary evaluation of \gam which relies on the Fermi golden rule (itself based on perturbation analysis), \gam has an upper bound and does not diverge at \ome_c even if we assume perfect conductance in the waveguide walls. As a result, again in contrast to the statement found in the literature, the speed of emitted light from the molecule does not vanish at \ome_c and is proportional to $c\ggg^{2/3}$ which is on the order of $10^3 \sim 10^4$ m/s for typical dipole molecules.Comment: 4 pages, 2 figure

The role of the Van Hove singularity in the time evolution of electronic states in a low-dimensional superlattice semiconductor

textOver the last three decades, the rapid development of efficient synthetic routes for the preparation of expanded porphyrin macrocycles has allowed the exploration of a new frontier involving “porphyrin-like” coordination chemistry. This doctoral dissertation describes the author’s exploratory journey into the area of transition metal cation complexation using oligopyrrolic macrocycles. The reported synthetic findings were used to gain new insights into the factors affecting the observed coordination modes and to probe the emerging roles of counter-anion effects, tautomeric equilibria and hydrogenbonding interactions in regulating the metalation chemistry of expanded porphyrins. The first chapter provides an updated overview of this relatively young coordination chemistry subfield and introduces the idea of expanded porphyrins as a diverse family of ligands for metalation studies. Chapter 2 details the synthesis of a series of binuclear complexes and illustrates the importance of metal oxidation state, macrocycle protonation and counter-anion effects in terms of defining the final structure of the observed metal complexes. The binding study reported in Chapter 3 demonstrates a strong positive allosteric effect for the coordination of silver(I) cations in a Schiff base expanded porphyrin. Chapter 4 introduces the use of oligopyrrolic macrocycles for the stabilization of early transition metal cations. Specifically, the preparation of a series of vanadium complexes illustrates the bimodal (i.e., covalent and noncovalent) recognition of the non-spherical dioxovanadium(V) species within the macrocyclic cavities. Experimental procedures and characterization data are reported in Chapter 5.Physic

(2006-2007) Assembly Resolution 04: In Support of Fiscal Accountability and Equal Access to Campus Recreational Facilities for Students who are Parents

Governmen

Effect of transpiration on plant accumulation and translocation of PPCP/EDCs

The reuse of treated wastewater for agricultural irrigation in arid and hot climates where plant transpiration is high may affect plant accumulation of pharmaceutical and personal care products (PPCPs) and endocrine disrupting chemicals (EDCs). In this study, carrot, lettuce, and tomato plants were grown in solution containing 16 PPCP/EDCs in either a cool-humid or a warm-dry environment. Leaf bioconcentration factors (BCF) were positively correlated with transpiration for chemical groups of different ionized states (p < 0.05). However, root BCFs were correlated with transpiration only for neutral PPCP/EDCs (p < 0.05). Neutral and cationic PPCP/EDCs showed similar accumulation, while anionic PPCP/EDCs had significantly higher accumulation in roots and significantly lower accumulation in leaves (p < 0.05). Results show that plant transpiration may play a significant role in the uptake and translocation of PPCP/EDCs, which may have a pronounced effect in arid and hot climates where irrigation with treated wastewater is common. [Image: see text