Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.Comment: 6 pages, two figures .Presented at the International Symposium on Quantum Fluids and Solids QFS2006 (Kyoto, Japan

Generalized Bose-Einstein Condensation

Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the {}"channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the {}"cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature $T_{c}$ and another "one-dimensional" transition at a lower temperature $T_{1}$ into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, $T_{1}$ merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, $T_{1}$ becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.Comment: 17 pages; 6 figures. Intended for American Journal of Physic

Survival of patients with deficient mismatch repair metastatic colorectal cancer in the pre-immunotherapy era

Contains fulltext : 230109.pdf (Publisher’s version ) (Closed access)BACKGROUND: Metastatic colorectal cancer patients with deficient mismatch repair (dMMR mCRC) benefit from immunotherapy. Interpretation of the single-arm immunotherapy trials is complicated by insignificant survival data during systemic non-immunotherapy. We present survival data on a large, comprehensive cohort of dMMR mCRC patients, treated with or without systemic non-immunotherapy. METHODS: Two hundred and eighty-one dMMR mCRC patients (n = 54 from three prospective Phase 3 CAIRO trials; n = 227 from the Netherlands Cancer Registry). Overall survival was analysed from diagnosis of mCRC (OS), from initiation of first-line (OS1) and second-line (OS2) systemic treatment. Cox regression analysis examined prognostic factors. As comparison for OS 2746 MMR proficient mCRC patients were identified. RESULTS: Of 281 dMMR patients, 62% received first-line and 26% second-line treatment. Median OS was 16.0 months (13.8-19.6) with antitumour therapy and 2.5 months (1.8-3.5) in untreated patients. OS1 was 12.8 months (10.7-15.2) and OS2 6.2 months (5.4-8.9) in treated dMMR patients. Treated dMMR patients had a 7.6-month shorter median OS than pMMR patients. CONCLUSION: Available data from immunotherapy trials lack a control arm with standard systemic treatment. Given the poor outcome compared to the immunotherapy results, our data strongly suggest a survival benefit of immunotherapy in dMMR mCRC patients