If we want to look at this from a scientific standpoint, we need to examine the psychology of the situation.
People who do not mind breaking laws, and who use other people to their advantage are termed Anti-Social. People missuse this term in everyday language, but an anti-social person is someone who does harm to society (wikipedia it for the full definition). Criminals are anti-socials. Now a person can be genetically predisposed to be anti-social, or if they grow up in a poor and violent neighborhood, they can pick up the traits from their environments. In the Katrina situation, the people who didn't leave the city were those living in the poorest neighborhoods and projects. So right there basically gives you double the rate of anti-socials running wild (genetically predisposed folks + those who picked up the traits from living in violent neighborhoods). On top of that, once normal people see the anti-social looters looting, they want a piece of the pie too. So basically it was a positive feedback system (snowball effect). The anti-socials started looting, regular people began too, and the cops were somewhere in there too.