For Java you have a choice of three different DBMS:
- HSQLDB (aka HyperSQL): http://hsqldb.org
- H2 Database: http://h2database.com/html/main.html
- Apache Derby (aka. "JavaDB"): http://db.apache.org/derby/
My personal preference is HSQLDB, but H2 is just as good. Both meet the requirements you mentioned.