The conventional second-order path-integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of antisymmetric free-fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work we show that optimized fourth-order path-integral Monte Carlo methods, which use no more than five...

n |sn−sn+1|, is presented. This Ising-like model is an interesting example of a graduate-level statistical mechanics problem where the eigenfunctions and eigenvalues of an integral operator, the transfer integral, can be determined exactly. This can be contrasted with the determination of eigenfunctions and eigenvalues of differential operators, such as the quantum mechanical finite-depth squar...

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, tw...

Facial expressions are an integral part of Australian Sign Language (Auslan). This paper presents the implementation and integration of facial expression into the Auslan Tuition System. To incorporate this feature, we use a 3D mesh and animation of an avatar to dynamically display the Auslan signs. Vertex blending is used to improve the aesthetic quality of this model. The mesh provides a basis...

The spin-statistics connection is derived in a simple manner under the postulate that the original and the exchange state vectors are only superposed with the plus sign. The single-particle state vectors must however exhibit dependence on the angle χ of rotations in spin space about the spin-quantization axis. This means that not only a spin-quantization axis but a complete quantization frame m...

Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix, represented in PIMC by open paths. It is demonstrated how the restricted path integral Monte Carlo methods can be extended in order to deal with open paths in fe...

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown...

where now N(x) is integrable in any interval which excludes the origin, O(e') as x -i o and O('/x) as x -O 0. The plus sign in the kernel now changes the entire mode of attack. While Fourier transform methods still play a dominant r6le in our work, we cannot solve the equation (1.2) in one fell swoop as we do equation (1.1). Instead we find it necessary to take advantage of the special assumpti...

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time-integrated) difference between entrance rate and escape rate in mesoscopic jump systems. Such inflow ...