Colloquium

Graphene-like materials provide a unique opportunity to explore quantum-relativistic phenomena in a condensed matter laboratory. Interesting phenomena associated with the internal degrees of freedom, spin and valley, including quantum spin-Hall effect, have been theoretically proposed, but could not be observed so far largely due to disorder and density inhonogeneity. We show that weak magnetic field breaks the symmetries that protect flavor (spin, valley) degeneracy, and induces large bulk non-quantized flavor-Hall effect in graphene.

The average quantum physicist on the street believes that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian $H=p^2+ix^3$, which is obviously not Dirac Hermitian, has a real positive discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory.

The gravitational observatory LISA will detect radiation from massive black hole sources at cosmological distances, accurately measure their luminosity distance and help identify the electromagnetic counterparts that such sources may generate. I will describe various astrophysical scenarios for the generation of electromagnetic counterparts and discuss observational strategies aimed at identifying them. Successful identifications will enable novel studies of black hole astrophysics and cosmological physics.

A system of spins with complicated interactions between them can have many possible configurations. Many configurations will be local minima of the energy, and to get from one local minimum to another requires changing the state of very many spins. A system like this is called a spin glass, and at low temperatures tends to get caught for very long times at a local minimum of energy, rather than reaching its true ground state.