Possible Lattice Distortions in the Hubbard Model for Graphene

The Hubbard model on the honeycomb lattice is a well known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most six atoms per unit cell as compared to two atoms for the undistorted lattice.Comment: 5 pages, 3 figure

Stability and Absence of Binding for Multi-Polaron Systems

We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fr\"ohlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrt\alpha, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2\alpha, stability of matter does hold for U>2\alpha, that is, the ground state energy per particle has a finite limit as N\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on \alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.Comment: 23 page

Earnings, education and experience

Education ; Wages

Measurement of Fecal Testosterone Metabolites in Mice: Replacement of Invasive Techniques

Testosterone is the main reproductive hormone in male vertebrates and conventional methods to measure testosterone rely on invasive blood sampling procedures. Here, we aimed to establish a non-invasive alternative by assessing testosterone metabolites (TMs) in fecal and urinary samples in mice. We performed a radiometabolism study to determine the effects of daytime and sex on the metabolism and excretion pattern of radiolabeled TMs. We performed physiological and biological validations of the applied EIA to measure TMs and assessed diurnal fluctuations in TM excretions in male and female mice and across strains. We found that males excreted significantly more radiolabeled TMs via the feces (59%) compared to females (49.5%). TM excretion patterns differed significantly between urinary and fecal samples and were affected by the daytime of ³H-testosterone injection. Overall, TM excretion occurred faster in urinary than fecal samples. Peak excretion of fecal TMs occurred after 8 h when animals received the 3H-testosterone in the morning, or after 4 h when they received the 3H-testosterone injection in the evening. Daytime had no effect on the formed TMs; however, males and females formed different types of TMs. As expected, males showed higher fecal TM levels than females. Males also showed diurnal fluctuations in their TM levels but we found no differences in the TM levels of C57BL/6J and B6D2F1 hybrid males. Finally, we successfully validated our applied EIA (measuring 17β-hydroxyandrostane) by showing that hCG (human chorionic gonadotropin) administration increased TM levels, whereas castration reduced them. In conclusion, our EIA proved suitable for measuring fecal TMs in mice. Our non-invasive method to assess fecal TMs can be widely used in various research disciplines like animal behavior, reproduction, animal welfare, ecology, conservation, and biomedicine