Gutzwiller Approximation in Degenerate Hubbard Models

Degenerate Hubbard models are studied using the Generalized-Gutzwiller-Approximation. It is found that the metal-insulator transition occurs at a finite correlation $U_c$ when the average number of electrons per lattice site is an integer. The critical $U_c$ depends sensitively on both the band degeneracy $N$ and the filling $x$. A derivation is presented for the general expression of $U_c(x,N)$ which reproduces all previously known Gutzwiller solutions, including that of the Boson Hubbard model. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed.Comment: RevTex file with 2 figures included, 12 page

Immune targets in the tumor microenvironment treated by radiotherapy.

Radiotherapy (RT), the major anti-cancer modality for more than half of cancer patients after diagnosis, has the advantage of local tumor control with relatively less systematic side effects comparing to chemotherapy. However, the efficacy of RT is limited by acquired tumor resistance leading to the risks of relapse and metastasis. To further enhance the efficacy of RT, with the renaissances of targeted immunotherapy (TIT), increasing interests are raised on RT combined with TIT including cancer vaccines, T-cell therapy, and antibody-based immune checkpoint blockers (ICB) such as anti-CTLA-4 and anti-PD1/PD-L1. In achieving a significant synergy between RT and TIT, the dynamics of radiation-induced response in tumor cells and stromal cells, especially the cross-talk between tumor cells and immune cells in the irradiated tumor microenvironment (ITME) as highlighted in recent literature are to be elucidated. The abscopal effect refereeing the RT-induced priming function outside of ITME could be compromised by the immune-suppressive factors such as CD47 and PD-L1 on tumor cells and Treg induced or enhanced in the ITME. Cell surface receptors temporally or permanently induced and bioactive elements released from dead cells could serve antigenic source (radiation-associated antigenic proteins, RAAPs) to the host and have functions in immune regulation on the tumor. This review is attempted to summarize a cluster of factors that are inducible by radiation and targetable by antibodies, or have potential to be immune regulators to synergize tumor control with RT. Further characterization of immune regulators in ITME will deepen our understanding of the interplay among immune regulators in ITME and discover new effective targets for the combined modality with RT and TIT