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Abstract:

We develop an analytic theory for the recently demonstrated Josephson Junction laser (Science 355, 939, 2017). By working in the time-domain representation (rather than the frequency-domain) a single non-linear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.

Abstract:

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012)]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

Abstract:

Recent experiments [Banerjee et al, arXiv:1710.00492] have measured thermal conductance of the ν = 5/2 edge in a GaAs electron gas and found it to be quantized as K ≈ 5/2 (in appropriate dimensionless units). This result is unexpected, as prior numerical work predicts that the ν = 5/2 state should be the Anti-Pfaffian phase of matter, which should have quantized K = 3/2. The purpose of this paper is to propose a possible solution to this conflict: if the Majorana edge mode of the Anti-Pfaffian does not thermally equilibrate with the other edge modes, then K = 5/2 is expected. I briefly discuss a possible reason for this nonequilibration, and what should be examined further to determine if this is the case.