Random Walk over Basins of Attraction to Construct Ising Energy Landscapes

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the SK spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.Comment: 2 Figures and 1 Table. To be published in Physical Review Letter

A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

Overlap between Hartree-Fock-Bogoliubov(HFB) vacua is very important in the beyond mean-field calculations. However, in the HFB transformation, the $U,V$ matrices are sometimes singular due to the exact emptiness ($v_i=0$) or full occupation ($u_i=0$) of some single-particle orbits. This singularity may cause some problem in evaluating the overlap between HFB vacua through Pfaffian. We found that this problem can be well avoided by setting those zero occupation numbers to some tiny values (e.g., $u_i,v_i=10^{-8}$). This treatment does not change the HFB vacuum state because $u_i^2,v_i^2=10^{-16}$ are numerically zero relative to 1. Therefore, for arbitrary HFB transformation, we say that the $U,V$ matrices can always be nonsingular. From this standpoint, we present a new convenient Pfaffian formula for the overlap between arbitrary HFB vacua, which is especially suitable for symmetry restoration. Testing calculations have been performed for this new formula. It turns out that our method is reliable and accurate in evaluating the overlap between arbitrary HFB vacua.Comment: 5 pages, 2 figures. Published versio

Theory of resonant spin Hall effect

A biref review is presented on resonant spin Hall effect, where a tiny external electric field induces a saturated spin Hall current in a 2-dimensional electron or hole gas in a perpendicular magnetic field. The phenomenon is attributted to the energy level crossing associated with the spin-orbit coupling and the Zeeman splitting. We summarize recent theoretical development of the effect in various systems and discuss possible experiments to observe the effect.Comment: 5 pages with 1 figure

Comment on 'Note on the dog-and-rabbit chase problem in introductory kinematics'

We comment on the recent paper by Yuan Qing-Xin and Du Yin-Xiao (Eur. J. Phys. 29 (2008) N43-N45).Comment: 2 pages, no figure