I think the object is unique for each user, not to the whole JVM. The only persistent information is the one you put in the user session.
I'm not sure, but I think you can acomplish to have one instance of a Class in the whole Application Server using the ClassLoader class, however I don know how it's done.
UPDATE:
Taken from the Java Article "When is a Singleton not a Singleton?"
Multiple Singletons Simultaneously Loaded by Different Class Loaders
When two class loaders load a class, you actually have two copies of the class, and each one can have its own Singleton instance. That is particularly relevant in servlets running in certain servlet engines (iPlanet for example), where each servlet by default uses its own class loader. Two different servlets accessing a joint Singleton will, in fact, get two different objects.
Multiple class loaders occur more commonly than you might think. When browsers load classes from the network for use by applets, they use a separate class loader for each server address. Similarly, Jini and RMI systems may use a separate class loader for the different code bases from which they download class files. If your own system uses custom class loaders, all the same issues may arise.
If loaded by different class loaders, two classes with the same name, even the same package name, are treated as distinct -- even if, in fact, they are byte-for-byte the same class. The different class loaders represent different namespaces that distinguish classes (even though the classes' names are the same), so that the two MySingleton classes are in fact distinct. (See "Class Loaders as a Namespace Mechanism" in Resources.) Since two Singleton objects belong to two classes of the same name, it will appear at first glance that there are two Singleton objects of the same class.