@inproceedings {cosme-spp-2013, title = {Thomas-Fermi approach on the particle density of a Tonks-Girardeau gas in harmonic confinement with multiple δ-perturbations}, booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress}, year = {2013}, month = {23{\textendash}25 Oct 2013}, pages = {SPP2013-3B-2}, address = {University of San Carlos, Cebu City}, abstract = {
We investigate the Thomas-Fermi approach on the single particle density of a strongly interacting one dimensional bose gas under harmonic confinement with multiple localized δ barriers. We compare the resulting approximate of the density profile to exact density profiles that can be calculated for finite number of bosons. From the ground state energy, the corresponding chemical potential at T=0 is used to find the radius or extent of the density cloud.
}, author = {Jayson G Cosme and Francis N. C. Paraan and Jose Perico H Esguerra} } @article {Paraan2008, title = {Brownian motion of a charged particle driven internally by correlated noise}, journal = {Phys. Rev. E}, volume = {77}, number = {2}, year = {2008}, note = {cited By 12}, pages = {022101}, abstract = {
We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.
}, doi = {10.1103/PhysRevE.77.022101}, author = {Francis N. C. Paraan and Mikhail P Solon and Jose Perico Esguerra} } @article {Paraan2006, title = {Exact moments in a continuous time random walk with complete memory of its history}, journal = {Phys. Rev. E}, volume = {74}, number = {3}, year = {2006}, pages = {032101}, abstract = {
We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.
}, doi = {10.1103/PhysRevE.74.032101}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.74.032101}, author = {Francis N. C. Paraan and Jose Perico Esguerra} }