Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrödinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, the Chebyshev polynomial technique, four Suzuki-formula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by ...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

For the oscillator-like systems, connected with the Laguerre, Legendre and Chebyshev polynomials coherent states of Glauber-Barut-Girardello type are defined. The suggested construction can be applied to each system of orthogonal polynomials including classical ones as well as deformed ones.

A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with thermodynamically fluctuating fields. Using moment expansions of the density of states with Chebyshev polynomials, the algorithm provides an efficient calculation on large ...

Abstract. In this paper, we propose efficient algorithms for approximating particular solutions of second and fourth order elliptic equations. The approximation of the particular solution by a truncated series of Chebyshev polynomials and the satisfaction of the differential equation lead to upper triangular block systems, each block being an upper triangular system. These systems can be solved...

Amongst satisfactory techniques for the numerical solution of differential equations, the use of Chebyshev series is often avoided because of the tedious nature of the calculations. A systematic application of the Chebyshev method is given for certain fourth order boundary value problems in which the derivatives have polynomial coefficients. Numerical results for various problems using the Cheb...

In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev–Ga...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

presents a modiied Chebyshev pseudospec-tral method, involving mapping of the Chebyshev points, for solving rst-order hyperbolic initial boundary value problems. It is conjectured that the time step restriction for the modiied method is O(N ?1) compared to O(N ?2) for the standard Chebyshev pseudospectral method, where N is the number of discretization points in space. In the present paper we s...

This note, written for the NIC Winter School ”Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms”, discusses and compares – in theoretical respects – various old and new approaches to numerical time integration for quantum dynamics: implicit vs. exponential midpoint rule; splitting, Chebyshev and Lanczos approximations to the exponential; Magnus integrators; integrators...