Abstract

Superfluidity and superconductivity are among the most exotic phenomena of certain quantum states of matter. Their physical understanding, however, are primarily based on mean-field approximations that generate Bogoliubov-type number fluctuation, in direct contradiction to the strict number conservation of the system. Based on rigorous analytical studies of quantum many-body systems, this talk will cover three fundamental issues against standard lore: 1) how to completely suppress quantum coherence in a homogeneous system to defeat superfluidity and produce the long-sought “quantum Bose metal”, 2) why the low-temperature fluctuation of modern superconductors irreparably invalidates standard theories and inspires qualitative correction to the standard theory of bosonic superfluidity, and 3) why superfluidity and superconductivity should not be regarded with spontaneously broken U(1) symmetry and why the zero modes in the vortex cores cannot be Majorana particles capable of braiding quantum information.