Hybrid Monte Carlo simulation of polymer chains

We develop the hybrid Monte Carlo method for simulations of single off-lattice polymer chains. We discuss implementation and choice of simulation parameters in some detail. The performance of the algorithm is tested on models for homopolymers with short- or long-range self-repulsion, using chains with $16\le N\le 512$ monomers. Without excessive fine tuning, we find that the computational cost grows as $N^{2+z^\prime}$ with $0.64<z^\prime<0.84$. In addition, we report results for the scaling of the end-to-end distance, $r_{1N}\sim N^\nu(\ln N)^{-\alpha}$.Comment: 13 pages, single postscript file, uuencoded form, Lund Preprint LU-TP 93-2

Local unitary versus local Clifford equivalence of stabilizer states

We study the relation between local unitary (LU) equivalence and local Clifford (LC) equivalence of stabilizer states. We introduce a large subclass of stabilizer states, such that every two LU equivalent states in this class are necessarily LC equivalent. Together with earlier results, this shows that LC, LU and SLOCC equivalence are the same notions for this class of stabilizer states. Moreover, recognizing whether two given stabilizer states in the present subclass are locally equivalent only requires a polynomial number of operations in the number of qubits.Comment: 8 pages, replaced with published versio

Moment-angle complexes from simplicial posets

We extend the construction of moment-angle complexes to simplicial posets by associating a certain T^m-space Z_S to an arbitrary simplicial poset S on m vertices. Face rings Z[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen--Macaulay rings. Our primary motivation is to study the face rings Z[S] by topological methods. The space Z_S has many important topological properties of the original moment-angle complex Z_K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z_S is isomorphic to the Tor-algebra of the face ring Z[S]. This leads directly to a generalisation of Hochster's theorem, expressing the algebraic Betti numbers of the ring Z[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z_S from below by proving the toral rank conjecture for the moment-angle complexes Z_S.Comment: 17 pages, 2 pictures; v2 revised, v3 minor correction

Solving Separable Nonlinear Equations Using LU Factorization

Separable nonlinear equations have the form F(y,z) ≡ A (y)z + b(y) = 0, where the matrix A(y)∈ R m × N and the vector b(y) ∈ Rmare continuously differentiable functions of y ∈ Rn and z ∈ RN. We assume that m ≥ N + n, and F\u27(y,z) has full rank. We present a numerical method to compute the solution (y∗, z∗) for fully determined systems (m = N+ n) and compatible overdetermined systems (m \u3e N+ n). Our method reduces the original system to a smaller system f(y) = 0 of m − N ≥ n equations in y alone. The iterative process to solve the smaller system only requires the LU factorization of one m × m matrix per step, and the convergence is quadratic. Once y∗ has been obtained, z∗ is computed by direct solution of a linear system. Details of the numerical implementation are provided and several examples are presented

Azimuthal angle dependence of di-jet production in unpolarized hadron scattering

We study the azimuthal angular dependence of back-to-back di-jet production in unpolarized hadron scattering $H_A+H_B \to J_1 + J_2 +X$, arising from the product of two Boer-Mulders functions, which describe the transverse spin distribution of quarks inside an unpolarized hadron. We find that when the di-jet is of two identical quarks ($J_q+J_q$) or a quark-antiquark pair ($J_q+J_{\bar{q}}$), there is a $\cos \delta \phi$ angular dependence of the di-jet, with $\delta \phi=\phi_1-\phi_2$, and $\phi_1$ and $\phi_2$ are the azimuthal angles of the two individual jets. In the case of $J_q+J_q$ production, we find that there is a color factor enhancement in the gluonic cross-section, compared with the result from the standard generalized parton model. We estimate the $\cos \delta \phi$ asymmetry of di-jet production at RHIC, showing that the color factor enhancement in the angular dependent of $J_q+J_q$ production will reverse the sign of the asymmetry.Comment: 10 pages, 7 figures, version accepted by Physical Review

An SL(2, Z) Multiplet of Type IIB Super Five-Branes

It is well-known that the low energy string theory admits a non-singular solitonic super five-brane solution which is the magnetic dual to the fundamental string solution. By using the symmetry of the type IIB string theory, we construct an SL(2, Z) multiplet of magnetically charged super five-branes starting from this solitonic solution. These solutions are characterized by two integral three-form charges $(q_1, q_2)$ and are stable when the integers are coprime. We obtain an expression for the tension of these $(q_1, q_2)$ five-branes as envisaged by Witten. The SL(2, Z) multiplets of black strings and black fivebranes and the existence of similar magnetic dual solutions of strings in type II string theory in $D < 10$ have also been discussed.Comment: 13 pages, LaTeX, no figures, Eqs.(18)-(26) have been corrected, some important changes have been made, replaces the withdrawn versio

Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)\gamma^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is $p=2.5$, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming $k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres