If you want a process to stay put in a specific core, you need to ask the OS for it, however this might still influence the performance, as naturally there are other processes running there and the OS cannot honour the request if everyone does the same.
However it already improves not copying the process context across all cores.
I used this to good effect back in the Windows NT/2000 days, whose scheduler wasn't that smart about when to move processes across cores.
