One Method to Fit Biexponential Curve by Using Fourier Transform
Many physical phenomena can be described by biexponential curve. To study the physical phenomena, there is a need to obtain their mathematical expressions. Generally, the expressions are acquired based on the fitting of experimental data, and the general method to fit exponential curve is nonlinear least squares (NLLS). In the NLLS method, it is crucial to choose good enough starting values for the parameters, otherwise, the fitting might fail to converge. In this paper, one new method is proposed to solve the problem, which utilizes the Fourier transform to transform the non-linear exponential fitting model into a linear one. It makes the estimation of the parameters independent of the initial values and easy to converge. The fitting result shows that the proposed method can be used to fit the curve expressed by difference of double exponentials.
We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed.