Braid Group and Topological Phase Transitions in Nonequilibrium Stochastic Dynamics

Abstract

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.

4+ pages, 4 figures, published in PRE as a Rapid Communication. See http://pre.aps.org/abstract/PRE/v87/i5/e050101

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• The Theory of Spin Noise Spectroscopy: A Review
• Symmetry classes of open fermionic quantum matter
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Fractional charges in conventional sequential electron tunneling
• Intermittency and dynamical Lee-Yang zeros of open quantum systems
• Quantum Zeno effect as a topological phase transition in full counting statistics and spin noise spectroscopy
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Non-Abelian Braiding of Topological Edge Bands
• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Machine Learning of Knot Topology in Non-Hermitian Band Braids
• Quantum Zeno effect under continuous spin noise measurement in a quantum dot-micropillar cavity
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Random-walk topological transition revealed via electron counting
• Short time dynamics of molecular junctions after projective measurement
• Versatile Braiding of Non-Hermitian Topological Edge States
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Full counting statistics in a Majorana single-charge transistor
• Gain-loss-induced non-Abelian Bloch braids
• Transport fluctuation relations in interacting quantum pumps
• Observation of Braid-Protected Unpaired Exceptional Points
• Fractional positional jumps in stochastic systems with tilted periodic double-well potentials
• Counting interacting electrons in one dimension
• Exceptional topology on nonorientable manifolds