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2
votes
1answer
177 views

Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
5
votes
0answers
64 views

What is the probability of a Brownian path?

Suppose I have a Brownian particle with a diffusion constant $D$ starting out from a given position at time $0$ and follow it until time $\tau$. What is the probability (distribution) that it takes ...
2
votes
0answers
151 views

Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use $$\sum_{n} ...
1
vote
0answers
41 views

Acceleration by spherical particles (micron-scale) by an external force

I am looking for an expression for the velocity of a micron sized (1 - 10 micron diameter) sized particles under accelerating forces. I have aerosols in mind. This is what I have in mind The ...