THEORY OF QUANTUM LIQUIDS: WHERE WE ARE AND WHERE WE ARE GOING

Abstract

The present status of the microscopic understanding of quantum liquids is reviewed. We take a conservative approach and focus thoroughly on two examples: the neutral quantum liquids 4 He and 3 He . The first part of this contribution reviews the present state of the microscopic theory of these systems. Results of both simulation methods and semi-analytic theories are discussed and compared. Quantum liquids in non-uniform geometries lead, due to symmetry breaking, to a number of new and interesting effects and also to new experimental possibilities and theoretical challenges. Finally, we highlight a number of yet open problems where present microscopic approaches have so far been unsuccessful.