The ground-state properties of one-dimensional 3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicit...

We construct an e cient proof of knowledge protocol for the demonstration of Monte-Carlo evidence that a number n is the product of two odd primes of roughly equal size without the prime factors being disclosed. The cost for a proof amounts to 12k log 2 n multiplications of integers of size of n where k is a security parameter which controls the error probability of the proof under 2 . With the...

In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact ...