Charlie introduces the concept of dissipation early on "Babylon Revisited":
So much for the effort and ingenuity of Montmartre. All the catering to vice and waste was on an utterly childish scale, and he suddenly realized the meaning of the word "dissipate" – to dissipate into thin air; to make nothing out of something. (1.56)
Dissipation is very much a central theme of "Babylon Revisited," both in Charlie's personal life and in the world in which he lives. Nothing has been made out of something in the sense that Charlie's wife is dead, he has lost his daughter, and his fortune is gone. The stock market crash means that much of America's wealth has dissipated as well, disappeared into nothing.
But the idea is somewhat complicated by the second occurrence of the term, towards the end of the text:
His first feeling was one of awe that he had actually, in his mature years, stolen a tricycle and pedaled Lorraine all over the Étoile between the small hours and dawn. In retrospect it was a nightmare. Locking out Helen didn't fit in with any other act of his life, but the tricycle incident did – it was one of many. How many weeks or months of dissipation to arrive at that condition of utter irresponsibility? (4.13)
This is an interesting passage, because we have to reconsider what Charlie means by dissipation. At first, we assumed that Charlie was talking about the dissipation that occurred after, and as a result of, the stock market crash. But here, he talks about dissipation before the crash. He's not just talking about dissipation of his life of wealth and extravagance. Consider Charlie's statement at the end of the story to Paul: he claims that he lost everything he wanted in the boom, not in the crash. For Charlie, the real dissipation – the loss of his wife, his daughter, and his honor – came earlier during the years of extravagance and excess in the 20s.