Quantum Lunch: Vote Talk – University of Copenhagen

QMath > Events > Quantum Lunch > w 23 Rudner

Quantum Lunch: Vote Talk

Speaker: Mark Rudner, QDEV/NBIA.

Mark will offer to us two titles to choose from.

Berry curvature and a more beautiful classical mechanics.
Abstract: Berry curvature characterizes the geometry of a manifold of quantum states (e.g., the ground state subspace) in a multi-dimensional parameter space. For a gapped system, an adiabatic change of parameters through a cycle may induce a nontrivial phase or unitary transformation on a given state or subspace. This is the so-called Berry's phase. For an electron moving in a periodic crystal, the crystal momentum parametrizes a family of Bloch Hamiltonians, whose eigenvalues and eigenstates comprise the band structure of the system. These bands may feature nontrivial Berry curvature, which leads to dramatic consequences for the semiclassical dynamics of Bloch electrons. The new term -- anomalous velocity -- is a phase space dual to the Lorentz force, and gives rise to many interesting effects such as the anomalous Hall, spin Hall, and valley Hall effects.

Survival, decay, and topological protection in non-Hermitian quantum transport.
Abstract: We discover a new type of robust quantized transport, illustrated with a simple model, which occurs in open systems where particles can decay from a subset of sites on a one-dimensional lattice. The competition between decay and long-time survival, which allows particles to travel to distant regions of the lattice, plays out in an intriguing way in the quantum regime. At special points in parameter space, long-range quantum coherence is established, allowing the particle to avoid all sites of the decaying sublattice. Such "dark states" completely decouple from the environment, and allow the particle to survive in the system for an infinite amount of time. The physical requirement that each injected particle must later be extracted therefore imposes restrictions on the parameter space, which becomes multiply connected. We find that the expected displacement achieved by the particle before it decays is quantized, with its integer value given by a winding number associated with the Bloch Hamiltonian in the multiply-connected parameter space.