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We construct analytic (3+1)-dimensional inhomogeneous and topologically non-trivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing electromagnetic interactions as well as some particular configurations with non-vanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a non-vanishing topological charge that can be identified with baryons surrounded by a cloud of pions. This system supports a topologically protected persistent superflow. When the electromagnetic field is turned on the superflow corresponds to an electromagnetic supercurrent.
When the isospin chemical potential exceeds the pion mass, charged pions condense in the zero-momentum state forming a superfluid. Chiral perturbation theory provides a very powerful tool for studying this phase. However, the formalism that is usuall
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localiz
I discuss the structure of current-induced bottom baryon to charm baryon transitions, and the structure of pion and photon transitions between heavy charm or bottom baryons in the Heavy Quark Symmetry limit as $m_Qrightarrowinfty$. The emphasis is on
We discovered a new class of topological crystals, namely linked rings of crystals. Two rings of tantalum triselenide (TaSe3) single crystals were linked to each other while crystal growing. The topology of the crystal form is called a Hopf link, whi
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symm