Many-body theory of the quantum mirage

In recent scanning tunneling microscopy experiments, confinement in an elliptical corral has been used to project the Kondo effect from one focus to the other one. I solve the Anderson model at arbitrary temperatures, for an impurity hybridized with eigenstates of an elliptical corral, each of which has a resonant level width delta. This width is crucial. If delta < 20 meV, the Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For particular conditions, a stronger mirage with the impurity out of the foci is predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a reference included to show that the hybridization of the impurity with bulk states can be neglecte

Interaction between Kondo impurities in a quantum corral

We calculate the spectral densities for two impurities inside an elliptical quantum corral using exact diagonalization in the relevant Hilbert subspace and embedding into the rest of the system. For one impurity, the space and energy dependence of the change in differential conductance $\Delta = dI/dV$ observed in the quantum mirage experiment is reproduced. In presence of another impurity, $\Delta = dI/dV$ is very sensitive to the hybridization between impurity and bulk. The impurities are correlated ferromagnetically between them. A hopping $\gtrsim 0.15$ eV between impurities destroy the Kondo resonance.Comment: 4 pages, 4 figure

Role of bulk and surface phonons in the decay of metal surface states

We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening.Comment: 4 pages, 3 figure

One- and many-body effects on mirages in quantum corrals

Recent interesting experiments used scanning tunneling microscopy to study systems involving Kondo impurities in quantum corrals assembled on Cu or noble metal surfaces. The solution of the two-dimensional one-particle Schrodinger equation in a hard wall corral without impurity is useful to predict the conditions under which the Kondo effect can be projected to a remote location (the quantum mirage). To model a soft circular corral, we solve this equation under the potential W*delta(r-r0), where r is the distance to the center of the corral and r0 its radius. We expand the Green's function of electron surface states Gs0 for r<r0 as a discrete sum of contributions from single poles at energies epsilon_i-I*delta_i. The imaginary part delta_i is the half-width of the resonance produced by the soft confining potential, and turns out to be a simple increasing function of epsilon_i. In presence of an impurity, we solve the Anderson model at arbitrary temperatures using the resulting expression for Gs0 and perturbation theory up to second order in the Coulomb repulsion U. We calculate the resulting change in the differential conductance Delta dI/dV as a function of voltage and space, in circular and elliptical corrals, for different conditions, including those corresponding to recent experiments. The main features are reproduced. The role of the direct hybridization between impurity and bulk, the confinement potential, the size of the corral and temperature on the intensity of the mirage are analyzed. We also calculate spin-spin correlation functions.Comment: 13 pages, 12 figures, accepted for publication in Phys. Rev. B. Calculations of spin correlations within an additional approximation adde

Non-Invasive Prostate Cancer Characterization with Diffusion-Weighted MRI: Insight from In silico Studies of a Transgenic Mouse Model

Diffusion-weighted magnetic resonance imaging (DWI) enables non-invasive, quantitative staging of prostate cancer via measurement of the apparent diffusion coefficient (ADC) of water within tissues. In cancer, more advanced disease is often characterized by higher cellular density (cellularity), which is generally accepted to correspond to a lower measured ADC. A quantitative relationship between tissue structure and in vivo measurements of ADC has yet to be determined for prostate cancer. In this study, we establish a theoretical framework for relating ADC measurements with tissue cellularity and the proportion of space occupied by prostate lumina, both of which are estimated through automatic image processing of whole-slide digital histology samples taken from a cohort of six healthy mice and nine transgenic adenocarcinoma of the mouse prostate (TRAMP) mice. We demonstrate that a significant inverse relationship exists between ADC and tissue cellularity that is well characterized by our model, and that a decrease of the luminal space within the prostate is associated with a decrease in ADC and more aggressive tumor subtype. The parameters estimated from our model in this mouse cohort predict the diffusion coefficient of water within the prostate-tissue to be 2.18 × 10−3 mm2/s (95% CI: 1.90, 2.55). This value is significantly lower than the diffusion coefficient of free water at body temperature suggesting that the presence of organelles and macromolecules within tissues can drastically hinder the random motion of water molecules within prostate tissue. We validate the assumptions made by our model using novel in silico analysis of whole-slide histology to provide the simulated ADC (sADC); this is demonstrated to have a significant positive correlation with in vivo measured ADC (r2 = 0.55) in our mouse population. The estimation of the structural properties of prostate tissue is vital for predicting and staging cancer aggressiveness, but prostate tissue biopsies are painful, invasive, and are prone to complications such as sepsis. The developments made in this study provide the possibility of estimating the structural properties of prostate tissue via non-invasive virtual biopsies from MRI, minimizing the need for multiple tissue biopsies and allowing sequential measurements to be made for prostate cancer monitoring

Biomarker discovery using NMR based metabolomics of tissue

NMR-based metabolomics has shown promise in the diagnosis of diseases as it enables identification and quantification of metabolic biomarkers. Using high-resolution magic-angle-spinning (HR-MAS) NMR spectroscopy, metabolic profiles from intact tissue specimens can be obtained with high spectral resolution. In addition, HR-MAS NMR requires minimal sample preparation and the sample is kept intact for subsequent analyses. In this chapter, we describe a typical protocol for NMR-based metabolomics of tissue samples. We cover all major steps ranging from tissue sample collection to determination of biomarkers, including experimental precautions taken to ensure reproducible and reliable reporting of data in the area of clinical application