Some time ago I had an idea that, as the unitary evolution of the wavefunction is described by a deterministic equation (PDE, simply), could be the collapse of it be described by some kind of a stochastic differential equation? Was this question posed before (I suppose yes...), and what kind of an SDE could it be?
Answer
This idea was suggested by Richard Feynman during his computational phase in the mid 1980s. Feynman asked whether you could simulate a decohering quantum system by stochastically projecting the quantum state whenever decoherence is sufficiently large, and produce a viable classical-quantum hybrid method, where you would only take into account quantum interference for non-decohered trajectories (I am paraphrasing from memory).
I don't think anyone has thought up such a scheme, and it is technically nontrivial. I used to think about it from time to time. None of this is in the literature, even Feynman's remark was off-the-cuff (I don't even remember where I read it), and if you come up with a way of doing it, I personally think it would be a very worthwhile thing.
Simulations people do
Nobody does honest simulations of a quantum system. They are always either stochastic simulations in imaginary time, designed to extract ground state correlation functions, or else density function calculations which are very far removed from the actual many-body wavefunction. The reason is that it is just plain impossible to simulate a quantum system classically, because it requires exponential resources in the general case.
But we know that we can understand most quantum systems at room temperature, because decoherence gets rid of the true exponential-resources quantum effects. Is there a way of actually projecting the wavefunction stochastically so that you get a hybrid quantum-classical-stochastic simulation?
The answer should be yes, but it has never been done to my knowledge. I had some ideas about this, which I will try to sketch out here later.
No comments:
Post a Comment