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Correction of the Ground State Energy of OneDimensional GrossPitaevskii Equation With GainLoss Term
Oleh:
Prayitno, Teguh Budi
Jenis:
Article from Journal  ilmiah nasional  terakreditasi DIKTI
Dalam koleksi:
Makara Seri Sains vol. 15 no. 2 (Nov. 2011)
,
page 197200.
Topik:
BoseEinstein Condensation
;
GrossPitaevskii
;
Quantum Oscillator
Fulltext:
Teguh Budi Prayitno.pdf
(55.41KB)
Ketersediaan
Perpustakaan Pusat (Semanggi)
Nomor Panggil:
MM65
Nontandon:
1 (dapat dipinjam: 0)
Tandon:
tidak ada
Lihat Detail Induk
Isi artikel
We consider the correction of ground state energy of onedimensional GrossPitaevskii equation by adding a gainloss term as a timedependent external potential. The interesting purpose of this term is that it can be used to explain the experimental results especially in the nonlinear fiber optics regarding the pulse propagation and collapserevival of the condensate in the BoseEinstein condensation. In the BoseEinstein condensation itself, the function can represent that condensate can interact with the normal atomic cloud. Some analytical solutions have been obtained by choosing an ansatz solution of the wave function and its solution can be dark or bright soliton. Since the GrossPitaevskii equation can be treated as a macroscopic quantum oscillator, we can use timedependent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction if we assume other terms to be very small. In addition, timedependent potential allows a transition from one energy level to others. In this case, we expand the solution of nonstationary onedimensional wave function as a linear superposition of harmonic oscillator normalized eigen functions. To get the recursive formulas, we suggest an option to formulate the coefficients after inserting the initial condition which must be satisfied such as in quantum mechanics.
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