Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

Commensurate and incommensurate correlations in Haldane gap antiferromagnets

We analyze the onset of incommensurabilities around the VBS point of the S=1 bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point $\theta_{\rm vbs}$. Moreover, the theory predicts another special point $\theta_{\rm disp}$, distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.Comment: 8 pages, 2 figures, to appear in PR

Trastuzumab after Adjuvant Chemotherapy in HER2-Positive Breast Cancer

BACKGROUND: Trastuzumab, a recombinant monoclonal antibody against HER2, has clinical activity in advanced breast cancer that overexpresses HER2. We investigated its efficacy and safety after excision of early-stage breast cancer and completion of chemotherapy. METHODS: This international, multicenter, randomized trial compared one or two years of trastuzumab given every three weeks with observation in patients with HER2-positive and either node-negative or node-positive breast cancer who had completed locoregional therapy and at least four cycles of neoadjuvant or adjuvant chemotherapy. RESULTS: Data were available for 1694 women randomly assigned to two years of treatment with trastuzumab, 1694 women assigned to one year of trastuzumab, and 1693 women assigned to observation. We report here the results only of treatment with trastuzumab for one year or observation. At the first planned interim analysis (median follow-up of one year), 347 events (recurrence of breast cancer, contralateral breast cancer, second nonbreast malignant disease, or death) were observed: 127 events in the trastuzumab group and 220 in the observation group. The unadjusted hazard ratio for an event in the trastuzumab group, as compared with the observation group, was 0.54 (95 percent confidence interval, 0.43 to 0.67; P<0.0001 by the log-rank test, crossing the interim analysis boundary), representing an absolute benefit in terms of disease-free survival at two years of 8.4 percentage points. Overall survival in the two groups was not significantly different (29 deaths with trastuzumab vs. 37 with observation). Severe cardiotoxicity developed in 0.5 percent of the women who were treated with trastuzumab. CONCLUSIONS: One year of treatment with trastuzumab after adjuvant chemotherapy significantly improves disease-free survival among women with HER2-positive breast cancer. (ClinicalTrials.gov number, NCT00045032.)published_or_final_versio