Finite-Temperature Transport in Finite-Size Hubbard Rings in the Strong-Coupling Limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.Comment: 15 pages and 6 figures; accepted for PR

Determination of Radiation Absorbed Dose to Primary Liver Tumors and Normal Liver Tissue Using Post-Radioembolization (90)Y PET.

BACKGROUND: Radioembolization with Yttrium-90 ((90) Y) microspheres is becoming a more widely used transcatheter treatment for unresectable hepatocellular carcinoma (HCC). Using post-treatment (90) Y positron emission tomography/computerized tomography (PET/CT) scans, the distribution of microspheres within the liver can be determined and quantitatively assessed. We studied the radiation dose of (90) Y delivered to liver and treated tumors. METHODS: This retrospective study of 56 patients with HCC, including analysis of 98 liver tumors, measured and correlated the dose of radiation delivered to liver tumors and normal liver tissue using glass microspheres (TheraSpheres(®)) to the frequency of complications with modified response evaluation criteria in solid tumors (mRECIST). (90) Y PET/CT and triphasic liver CT scans were used to contour treated tumor and normal liver regions and determine their respective activity concentrations. An absorbed dose factor was used to convert the measured activity concentration (Bq/mL) to an absorbed dose (Gy). RESULTS: The 98 studied tumors received a mean dose of 169 Gy (mode 90-120 Gy; range 0-570 Gy). Tumor response by mRECIST criteria was performed for 48 tumors that had follow-up scans. There were 21 responders (mean dose 215 Gy) and 27 non-responders (mean dose 167 Gy). The association between mean tumor absorbed dose and response suggests a trend but did not reach statistical significance (p = 0.099). Normal liver tissue received a mean dose of 67 Gy (mode 60-70 Gy; range 10-120 Gy). There was a statistically significant association between absorbed dose to normal liver and the presence of two or more severe complications (p = 0.036). CONCLUSION: Our cohort of patients showed a possible dose-response trend for the tumors. Collateral dose to normal liver is non-trivial and can have clinical implications. These methods help us understand whether patient adverse events, treatment success, or treatment failure can be attributed to the dose that the tumor or normal liver received