Archived

This topic is now archived and is closed to further replies.

bobman312

Quantum Mechanics Simulation

Recommended Posts

bobman312    122
Hey you guys. I work at LIGO and I''ve been really into this quantum mechanical stuff. I was thinking about writing a COMPUTER PROGRAM that could perform some sort of approximate simulation of quantum mechanics. So this is my PROBLEM!!! LISTEN CAREFULLY!!!! I want to be able to simulate 100 atoms (all IDENTICAL) in a finite quantum well in a 3-DIMENSIONAL BOX (cube actually, come to think about it). I have all the funky EQUATIONS lined up, but whenever I try and run the THING, I get a SEGMENTATION FAULT. I think it is because I am RUNNING OUT OF MEMORY. Does ANYONE know a way to simulate QUANTUM MECHANICAL effects space-wise efficiently? THANK YOU!!!

Share this post


Link to post
Share on other sites
Guest Anonymous Poster   
Guest Anonymous Poster
Usually a segmentation fault means you''re trying to access memory you haven''t allocated. Maybe you''re trying to access an out of bounds array value, or dereferencing a pointer that points to some random value. I don''t think it means you''re running out of memory, but I could be wrong.

Share this post


Link to post
Share on other sites
Timkin    864
quote:
Original post by bobman312
So this is my PROBLEM!!! LISTEN CAREFULLY!!!! I want to be able to simulate 100 atoms (all IDENTICAL) in a finite quantum well in a 3-DIMENSIONAL BOX (cube actually, come to think about it).



The 3-D box is irrelevant to the problem once you''ve defined your potential function.

quote:
Original post by bobman312
Does ANYONE know a way to simulate QUANTUM MECHANICAL effects space-wise efficiently?



Yes.

Timkin

Share this post


Link to post
Share on other sites
Mordoch Bob    122
quote:

Original post by Timkin
Original post by bobman312
Does ANYONE know a way to simulate QUANTUM MECHANICAL effects space-wise efficiently?

Yes.

Timkin



Our ever mysterious and elusive moderator, folks! Let's all give him a big hand for showing us how to deal with annoying posts with some style .

EDIT: apparently you can't nest quotes

------------------------------------------------
The wind shear alone from a pink golfball can take the head off a 90-pound midget from 300 yards.

-Six String Samurai



[edited by - Mordoch Bob on June 11, 2002 3:14:14 AM]

Share this post


Link to post
Share on other sites
grhodes_at_work    1385
I agree with AP. Regardless of the request for idea on simulating quantum mechanics efficiently, the original post suggests a programming and debugging problem rather than a math/physics problem.

Have you made progress with tracking down the cause of the segmentation fault?

As for quantum mechanics, I''ll leave it to folks who know about that sort of thing to decide whether or not to reply to the efficiency question.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Share this post


Link to post
Share on other sites
bobman312    122
THANK YOU GUYS!!! It turns out it wasn''t the SIMULATION, but the SEGMENTATION FAULT. I was going out of bounds of my assigned memory.

I''ll try and keep the CAPS off (sorry, it''s just a HABIT).

Next time, I''ll use the debugging forum.

As a side note to Tinkin: I''m pretty sure you need the shape in the first place to define the potential. Sure, after you have the potential, the shape is irrelevant, but only because the potential is then specific to the shape.

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. Even if it is possible to completely encode a single interaction by a single bit (that''s a pretty impressive feat!), it would still take 10^20 gigabytes of hard drive space. I''m going to cut it down to 30 atoms instead and see what happens.

P.P.S. Sorry if I sounded pretentious, but I don''t normally interact with people on forums.

Share this post


Link to post
Share on other sites
grhodes_at_work    1385
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. Even if it is possible to completely encode a single interaction by a single bit (that''s a pretty impressive feat!), it would still take 10^20 gigabytes of hard drive space. I''m going to cut it down to 30 atoms instead and see what happens.


I don''t really know the subject matter here, but I do know aerodynamics/CFD and the like, which can have similar (but much less daunting) memory issues. The way we deal with this type of situation is to model only the most important relationships (reactions in your case). Its like a partitioning problem in a way. For example, you can have 100 atoms, but only model reactions of each atom with up to, say, 5 or 10 nearest neighbors .... I have no real idea if this make sense for quantum mechanics!



Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Share this post


Link to post
Share on other sites
Timkin    864
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

Share this post


Link to post
Share on other sites