Friedel sum rule for an interacting multiorbital quantum dot

A generalized Friedel sum rule is derived for a quantum dot with internal orbital and spin degrees of freedom. The result is valid when all many-body correlations are taken into account and it links the phase shift of the scattered electron to the displacement of its SPECTRAL density into the dot.Comment: RevTeX 4.0, 5 page

Using GIS to Assess Firearm Thefts, Recoveries and Crimes in Lincoln, Nebraska

Firearm use in the United States has long been of great concern and at the center of many debates. Most research, however, has either focused on the use of firearms in violent crimes or the availability of firearms compared to the violent crime rates. Few studies have focused on the theft of firearms or the relationships between stolen firearms and crime. Using seven years of data collected Lincoln, Nebraska Police Department, this thesis focuses on the geospatial dimensions of firearm thefts and recoveries. Specific attention is given to the relationship firearm thefts and recoveries have with gun-related crimes, violent crimes, and property crimes. Statistical analyses reveal that firearm thefts and recoveries show clear patterns of clustering. Firearm thefts are significantly related to gun-related crimes and property crimes while firearm recoveries are significantly related to gun-related crimes, violent crimes, and property crimes. Findings also reveal that the majority of firearms reported stolen in Lincoln are acquired by the thief in residential neighborhoods (between 70 and 80 percent). The average theft in Lincoln regardless of gang involvement was 1.9 firearms per theft, which is significantly lower than the average for gang involvement at 6.6 firearms per theft. Subsequent spatial analyses revealed a significant southwest directional movement of firearms stolen in relation to gang activity with a large number of firearms being recovered in Phoenix, Arizona. Statistically significant relationships were discovered to exist between gun-related and property crimes. Moreover, firearm recoveries, unlike thefts, were significantly related to violent crimes in addition to gun-related and property crimes. The results have important policy implications. They suggest that a greater amount of attention should be placed on the theft of firearms and their movement away from Lincoln. They also emphasize that gun owners need to put more effort into properly securing firearms in their residences and vehicles. Advisor: James W. Merchan

Using GIS to Assess Firearm Thefts, Recoveries and Crimes in Lincoln, Nebraska

Firearm use in the United States has long been of great concern and at the center of many debates. Most research, however, has either focused on the use of firearms in violent crimes or the availability of firearms compared to the violent crime rates. Few studies have focused on the theft of firearms or the relationships between stolen firearms and crime. Using seven years of data collected Lincoln, Nebraska Police Department, this thesis focuses on the geospatial dimensions of firearm thefts and recoveries. Specific attention is given to the relationship firearm thefts and recoveries have with gun-related crimes, violent crimes, and property crimes. Statistical analyses reveal that firearm thefts and recoveries show clear patterns of clustering. Firearm thefts are significantly related to gun-related crimes and property crimes while firearm recoveries are significantly related to gun-related crimes, violent crimes, and property crimes. Findings also reveal that the majority of firearms reported stolen in Lincoln are acquired by the thief in residential neighborhoods (between 70 and 80 percent). The average theft in Lincoln regardless of gang involvement was 1.9 firearms per theft, which is significantly lower than the average for gang involvement at 6.6 firearms per theft. Subsequent spatial analyses revealed a significant southwest directional movement of firearms stolen in relation to gang activity with a large number of firearms being recovered in Phoenix, Arizona. Statistically significant relationships were discovered to exist between gun-related and property crimes. Moreover, firearm recoveries, unlike thefts, were significantly related to violent crimes in addition to gun-related and property crimes. The results have important policy implications. They suggest that a greater amount of attention should be placed on the theft of firearms and their movement away from Lincoln. They also emphasize that gun owners need to put more effort into properly securing firearms in their residences and vehicles. Advisor: James W. Merchan

A sensitive survey for 13CO, CN, H2CO and SO in the disks of T Tauri and Herbig Ae stars

We use the IRAM 30-m telescope to perform a sensitive search for CN N=2-1 in 42 T Tauri or Herbig Ae systems located mostly in the Taurus-Auriga region. $^{13}$CO J=2-1 is observed simultaneously to indicate the level of confusion with the surrounding molecular cloud. The bandpass also contains two transitions of ortho-H$_2$CO, one of SO and the C$^{17}$O J=2-1 line which provide complementary information on the nature of the emission. While $^{13}$CO is in general dominated by residual emission from the cloud, CN exhibits a high disk detection rate $> 50$% in our sample. We even report CN detection in stars for which interferometric searches failed to detect $^{12}$CO, presumably because of obscuration by a foreground, optically thick, cloud. Comparison between CN and o-H$_2$CO or SO line profiles and intensities divide the sample in two main categories. Sources with SO emission are bright and have strong H$_2$CO emission, leading in general to [H$_2$CO/CN]$> 0.5$. Furthermore, their line profiles, combined with a priori information on the objects, suggest that the emission is coming from outflows or envelopes rather than from a circumstellar disk. On the other hand, most sources have [H$_2$CO/CN]$< 0.3$, no SO emission, and some of them exhibit clear double-peaked profiles characteristics of rotating disks. In this second category, CN is likely tracing the proto-planetary disks. From the line flux and opacity derived from the hyperfine ratios, we constrain the outer radii of the disks, which range from 300 to 600 AU. The overall gas disk detection rate (including all molecular tracers) is $\sim 68$, and decreases for fainter continuum sources. This study shows that gas disks, like dust disks, are ubiquitous around young PMS stars in regions of isolated star formation, and that a large fraction of them have $R > 300$ AU.Comment: 31 pages (including 59 figures

Probing the spin states of three interacting electrons in quantum dots

We observe a low-lying sharp spin mode of three interacting electrons in an array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic light scattering. The finding is enabled by a suppression of the inhomogeneous contribution to the excitation spectra obtained by reducing the number of optically-probed quantum dots. Supported by configuration-interaction calculations we argue that the observed spin mode offers a direct probe of Stoner ferromagnetism in the simplest case of three interacting spin one-half fermions

Correlated Nanoscopic Josephson Junctions

We discuss correlated lattice models with a time-dependent potential across a barrier and show how to implement a Josephson-junction-like behavior. The pairing occurs by a correlation effect enhanced by the symmetry of the system. In order to produce the effect we need a mild distortion which causes avoided crossings in the many-body spectrum. The Josephson-like response involves a quasi-adiabatic evolution in the time-dependent field. Besides, we observe an inverse-Josephson (Shapiro) current by applying an AC bias; a supercurrent in the absence of electromotive force can also be excited. The qualitative arguments are supported by explicit exact solutions in prototype 5-atom clusters with on-site repulsion. These basic units are then combined in ring-shaped systems, where one of the units sits at a higher potential and works as a barrier. In this case the solution is found by mapping the low-energy Hamiltonian into an effective anisotropic Heisenberg chain. Once again, we present evidence for a superconducting flux quantization, i.e. a Josephson-junction-like behavior suggesting the build-up of an effective order parameter already in few-electron systems. Some general implications for the quantum theory of transport are also briefly discussed, stressing the nontrivial occurrence of asymptotic current oscillations for long times in the presence of bound states.Comment: 12 pages, 2 figures, to appear in J. Phys. - Cond. Ma

The gap exponent of XXZ model in a transverse field

We have calculated numerically the gap exponent of the anisotropic Heisenberg model in the presence of the transverse magnetic field. We have implemented the modified Lanczos method to obtain the excited states of our model with the same accuracy of the ground state. The coefficient of the leading term in the perturbation expansion diverges in the thermodynamic limit (N --> infinity). We have obtained the relation between this divergence and the scaling behaviour of the energy gap. We have found that the opening of gap in the presence of transverse field scales with a critical exponent which depends on the anisotropy parameter (Delta). Our numerical results are in well agreement with the field theoretical approach in the whole range of the anisotropy parameter, -1 < Delta < 1.Comment: 6 pages and 4 figure