In this paper, we discuss the accuracy and complexity of various numerical techniques to solve the stochastic Landau-Lifshitz-Gilbert-Slonczewski (s-LLGS) equation. The s-LLGS equation is widely used by researchers to study the temporal evolution of the macrospin subject to spin torque and thermal noise. The numerical simulation of the s-LLGS equation requires an appropriate choice of stochasti...

I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole, I discuss a perturbative solution of the Heun equation. The analytical results are...

We obtain the nucleation rate of critical droplets for an elastic string moving in a double-well potential and subject to noise and damping forces. We obtain this rate for a class of potentials that includes both the asymmetric straight phi(4) and the straight phi(6) potentials. The frequencies of small oscillations about the critical droplet are obtained from a Heun equation. We solve the Fokk...

The usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with four regular singular points. The identities discussed include ones coming from Möbius automorphisms and F-homotopies, and also quadratic and biqu...

where ℘(x) is the Weierstrass ℘-function with periods (1, τ), ω0 = 0, ω1 = 1 2 , ω2 = − τ+1 2 , ω3 = τ 2 are half-periods, and li (i = 0, 1, 2, 3) are coupling constants. This model is a one-particle version of the BCN Inozemtsev system [6], which is known to be the universal quantum integrable system with BN symmetry [6, 11]. The BCN Calogero-Moser-Sutherland systems are special cases of BCN I...

We study the Pöschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms of the Heun function. At particular values there is a interesting interpretation in terms of finite lattice spin2 XXZ quantum chain with ∆ = cos π L (for free...

Polynomial solutions of the confluent Heun differential equation (CHE) are derived by identifying conditions under which infinite power series expansions around z=0 singular point can be terminated. Assuming a specific structure expansion coefficients, these lead to four non-trivial polynomials that expressed as special cases function Hc(p,β,γ,δ,σ;z). One recovers generalized Laguerre LN(α), an...