Abstract:
As an alternative to conventional magnetic field, the effective spin-orbit field in transition metals, derived from the Rashba field experienced by itinerant electrons confined in a spatial inversion asymmetric plane through the s-d exchange interaction, is proposed for the manipulation of magnetization. Magnetization switching in ferromagnetic thin films with perpendicular magnetocrystalline anisotropy can be achieved by current induced spin-orbit field, with small in-plane applied magnetic field. Spin-orbit field induced by current pulses as short as 10 ps can initiate ultrafast magnetization switching effectively, with experimentally achievable current densities. The whole switching process completes in about 100 ps.

Abstract:
A formula to evaluate the entanglement in an one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-1/2 and spin-s ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when s is sufficiently large. This intriguing result answers unambiguously a fundamental question: ``can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?"

Abstract:
Connection between perennial stream and base flow at the mean annual scale exists since one of the hydrologic functions of perennial stream is to deliver runoff even in low flow seasons. The partitioning of precipitation into runoff and evaporation at the mean annual scale, on the first order, is captured by the ratio of potential evaporation to precipitation (EP/P called climate aridity index) based on Budyko hypothesis. Perennial stream density (DP), which is obtained from the high resolution National Hydrography Dataset, for 185 watersheds declines monotonically with climate aridity index, and an inversely proportional function is proposed to model the relationship between DP and EP/P. The monotonic trend of perennial stream density reconciles with the Abrahams curve since perennial stream density is only a small portion of the total drainage density. The correlation coefficient between the ratio of base flow to precipitation (Qb/P), which follows a complementary Budyko type curve and perennial stream density is found to be 0.74. The similarity between Qb/P and DP reveals the co-evolution between water balance and perennial stream network.

Abstract:
Streams are categorized into perennial and temporal streams based on flow durations. Perennial stream is the basic network, and temporal stream (ephemeral or intermittent) is the expanded network. Connection between perennial stream and runoff generation at the mean annual scale exists since one of the hydrologic functions of perennial stream is to deliver runoff. The partitioning of precipitation into runoff and evaporation at the mean annual scale, on the first order, is represented by the Budyko hypothesis which quantifies the ratio of evaporation to precipitation (E/P) as a function of climate aridity index (Ep/P, ratio of potential evaporation to precipitation). In this paper, it is hypothesized that similarity exists between perennial stream density (Dp) and runoff coefficient (Q/P) as a function of climate aridity index, i.e., DpDp* (EpP) and QP (EpP) where Dp* is a scaling factor and Q is mean annual runoff. To test the hypothesis, perennial stream densities for 185 watersheds in the United States are computed based on the high resolution national hydrography dataset (NHD). The similarity between perennial stream density and runoff coefficient is promising based on the case study watersheds. As a potential application for macroscale hydrological modeling, perennial stream density in ungauged basin can be predicted based on climate aridity index using the complementary Budyko curve.

Abstract:
One dimensional chiral Hubbard model reduces to the Haldane-Shastry spin chain at half-filling with large but finite on-site energy $U$.In this talk, we show that the Gutzwiller-Jastrow wavefunctions are the eigen-states of the Hubbard model at $U=+\infty$ at less than half-filling. The full energy spectrum and an infinite set of mutually commuting constants of motion are also given in this limit for the system.

Abstract:
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order for the theory to be self-consistent. The replicating methods in existing finance literature are shown to violate the self-financing constraint when the underlying asset has stochastic volatility. Correct self-financing hedge is formed in this article.

Abstract:
In this work, the spinless Calogero-Sutherland model with twisted boundary condition is studied. The ground state wavefunctions, the ground state energies, the full energy spectrum are provided in details.

Abstract:
In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$. We construct explicitly the ground states of the system when the number of the electrons $N_e \ge L+1$. In particular, for $N_e=L+1$, the ground state is ferromagnetic with total spin $s_g=(N_e-2)/2$.

Abstract:
In this work we introduce one dimensional multi-component Hubbard model of 1/r hopping and U on-site energy. The wavefunctions, the spectrum and the thermodynamics are studied for this model in the strong interaction limit $U=\infty$. In this limit, the system is a special example of $SU(N)$ Luttinger liquids, exhibiting spin-charge separation in the full Hilbert space. Speculations on the physical properties of the model at finite on-site energy are also discussed.