The Lieb-Schultz-Mattis theorem is a powerful theorem that puts nonperturbative restriction on possible phases of quantum many-body systems based on the filling fraction. We review recent extensions of the theorem to the systems with nonsymmorphic space groups and /or strong spin–orbit interactions, emphasizing their applications in searching for Dirac / Weyl semimetals and quantum spin liquids.

Relativistic jets are collimated plasma outflows with speeds close to the light speed from the vicinities of black holes. They are associated with some fraction of active galaxies and with the most luminous transient phenomena, gamma-ray bursts. There are several basic problems on formation of relativistic jets; mechanisms of energy injection, mass injection, acceleration, collimation, stability, and dissipation. This article reviews the current theoretical framework for solving those problems and a recent development on understanding physics of Blandford-Znajek process, i.e. steady electromagnetic energy injection by rotating black holes. The relationships are also mentioned among studies of relativistic jets, stellar evolution, galaxy evolution, high-energy cosmic-rays, neutrinos, gravitational waves, observational cosmology, and fundamental physics.

The superfluid ³He serves as a rich repository of novel topological quantum phenomena. The quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase and the A-phase as a Weyl superfluid. With a focus on the ³He-B confined to a restricted geometry, we here show that the interplay of topology and symmetry brings about a new type of topological phase transition concomitant with spontaneous symmetry breaking.

We formulate a variational principle for dissipative systems in terms of optimal control theory by regarding the generalized coordinate, generalized velocity and action functional as the state variable, control variable, and cost functional, respectively. The nonholonomic constraint in a dissipative system is given by the equation of entropy, which should be consistent with symmetry, the second law of thermodynamics, and well-posedness. In this formulation, we can derive equations of motion for various dissipative systems. We describe the detailed derivation for a damped harmonic oscillator, a Newtonian fluid, and a viscoelastic material.

A nano-scale molecular switch conventionally utilizes its conductance change induced by conformational transformation. Controlling the spin degree of freedom in addition to the charge of a single molecule is the key concept to realize molecular spintronics devices. We here show the complementary study of iron-based spin-crossover (SCO) single molecules, Fe(1,10-phenanthroline)₂(NCS)₂ molecules, by scanning tunneling microscope and synchrotron-based techniques. Decoupling from a metallic Cu(100) substrate by introducing an insulating Cu₂N layer, we have demonstrated that individual SCO molecules can be reproducibly and deterministically switched between a combined high-spin, high-conductance state and a low-spin, low-conductance state. These results will pave the way to confer multifunctional spintronic properties on molecular devices at the single-molecular level.

A giant resonance is a typical collective mode emerging in finite systems such as atomic nuclei. The giant monopole resonance, being the compressive mode of excitation, has attracted a lot of interest because it can tell us about the incompressibility of nuclear matter. From the monopole-transition strength distributions, the state-of-the-art experimental techniques as well as the microscopic nuclear-structure model further extract the deformation of nuclear shape that occurs in a short period of time due to the spontaneous breaking of the rotational symmetry of the nuclear many-body Hamiltonian.