Chances are doors are not the only problem but you would need to use a solid core door with some rubber or neoprene around the edges for an airtight seal. For windows double pane is usually the trick.
Tex is probably right. What do you mean by "the neighbor next door"? Is this an apartment. Or is he living in the same house? Or is his house 10" away from your wall, or 50' or upstairs or downstairs? Get my drift. You have to TELL us what the conditions are in order to get a concise answer. And there are answers. But every condition is different, and so are the solutions. Information is the key to getting help here. The more the better.
fitZ