quote:
Original post by Anonymous Poster
How arrogant!!!
Perhaps you should read the question and the answer again. The question was not asking HOW to do something, but whether anyone knew how to do it. I certainly know that it is possible - since I have some understanding of the problem and the solution method - and I have a close friend that has done it (as his Masters thesis) in the field of Quantum Optics: simulating atoms captured in the potential field created by interacting lasers.
quote:
Original post by bobman312
As a side note to Timkin: I''m pretty sure you need the shape in the first place to define the potential.
Well obviously you are going to define a potential that gives the problem a spatial constraint of a 3D cube... I think that I didn''t explain my point properly. Sorry. What I meant was that you define the constraint in terms of the potential function, rather than in terms of spatial constraints that equate to a cube.
quote:
Original post by bobman312
As a second side note to Tinkin: I was informed by an advisor on Nuclear Physics that to simulate such stuff is inherently exponential, so it would take 2^100 ''size'' locations to simulate all possible reactions.
If you wanted to solve for the interaction of all particles with each other exactly, then yes the complexity of the task is exponential in the number of objects. It''s the same problem faced in performing exact probabilistic inference (it''s exponential in the number of variables). In fact, you have the exact same problem, since the problem you are tring to solve is to find the wave function for 100 objects that are all interacting with strengths dependant on their state.
Your question was whether this could be done efficiently and the answer is yes, in so far as ''efficiently'' implies an approximation to the exact answer. You should consider using a Quantum Monte Carlo Method (the less efficient way) or the Masters Equation (a more efficient way) for simulating state transitions in discrete systems.
The Masters equation is a simple case of the differential Chapman-Kolmogorov equation, of which another simple case is the Fokker-Planck equation (which governs all drift-diffusion processes). The Fokker-Planck equation can be transformed into Schrodinger''s Equation, since they model the same thing.
If you want a reference, try looking up:
R.E.Sholten, T.J.O''Kane, T.R.Mackin, T.A.Hunt and P.M.Farrell,
Aust. J. Phys., 52, pp493-514 (1999) ''Calculating trajectories for atoms in near resonant light fields''.
Good luck,
Timkin
