using one random engine for multi distributions in c++11

It's ok.

Reasons to not share the generator:

• threading (standard RNG implementations are not thread safe)

• determinism of random sequences:

  If you wish to be able (for testing/bug hunting) to control the exact sequences generated, you will by likely have fewer troubles by isolating the RNGs used, especially when not all RNGs consumption is deterministic.

You should be careful when using one pseudo random number generator for different random variables, because in doing so they become correlated.

Here is an example: If you want to simulate Brownian motion in two dimensions (e.g. x and y) you need randomness in both dimensions. If you take the random numbers from one generator (noise()) and assign them successively

while(simulating)
    x = x + noise()
    y = y + noise()

then the variables x and y become correlated, because the algorithms of the pseudo number generators only make statements about how good they are, if you take every single number generated and not only every second one like in this example. Here, the Brownian particles could maybe move into the positive x and y directions with a higher probability than in the negative directions and thus introduce an artificial drift.

For two further reasons to use different generators look at sehe's answer.