In the lab, we keep all of the high voltage capacitors shorted when not in use, and rightfully so. They tend to spontaneously charge when left for some time and become extremely dangerous. while the self charge rate is not really of any practical use that i know of, I'm not sure what the main mechanism of this charging is. I have a strong background in EM, the cause is just not evident to me. A good qualitative explanation would be just fine.
The phenomenon you are talking about is called dielectric absorption. The way it works is this:
Let's say you've just discharged a capacitor. An ideal capacitor would remain at zero volts after this. However, in real life, the capacitor will develop a small voltage from time-delayed dipole discharging (also known as dielectric relaxation). Dielectric relaxation is a momentary lag in the dielectric constant of a material. The dielectric constant is the same as the relative permittivity of a material, which is the factor by which the electric field between two points in a material is decreased relative to the permittivity of a vacuum.
A simpler explanation is that since no capacitor is perfect, some of the electrons store energy chemically, and don't move all the way through the dialectric in the capacitor.
This voltage that is developed is can be less than 1-2% of the original voltage, but it can be as much as 15% of the original voltage. This is why you have to keep the capacitors shorted when not in use.
I hope this helps! Here are two websites that might also help:
Capacitors that have been discharged and shorted for a very long time, will still self charge once the short is removed. The energy is coming from an external source, I do believe this is related to the casimir effect, Low voltage capacitors do not exhibit the same effect as high voltage capacitors, probably due to a more leaky di electric being used. There is an idea that Zero point energy is being extracted, due to virtual particles coming into existence on either side of the plates, exerting a force thus creating a charge. Read into the casimir effect for a true answer to this phenomenon , It truly could be the answer to extracting unlimited energy.