Ghost in the machine?

Have you tried to plug the amp to another circuit under another barker?
If nothing changes you may try a different amp.

You may also try to remove everything that's connected in the same circuit. If it happens randomly it may be a freezer or who knows what.

Call an Exorcist.

I would say your amp needs servicing. Something is wrong with the off circuit. Is it remote controlled?

Agree with Erik.
It`s probably amp.
But it doesn't hurt to check the circuit also.

Try unplugging everything and then see if you are getting any noise through the speakers. I have a neighbor with a ham radio, and every so often I will pick up noise from that. If you are using unshielded cables, they may be acting as an antenna.

you have a router, don't you?

Yes. I have a router. 

the noise may be from the router "hunting"

you could turn it off and test

or perhaps move it as far away as you can

Mobile phones.

If you have XENON lights any where in your house, do not put them on the dim setting or at least not while you are listening to your equipment.  Same thing for any dimmers that you may have in your home.  My Krell FPB 300cx was humming and I traced it to the Xenon lights in the kitchen that were on dim.  Undimmed the hum was nonexistent.