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Updated: May 22, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
Published on: November 11, 2013
Ripples in a string coupled to Glauber spins
L L Bonilla1, A Carpio, A Prados
1G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
Abstract:
Each oscillator in a linear chain (a string) interacts with a local Ising spin in contact with a thermal bath. These spins evolve according to Glauber dynamics. Below a critical temperature, there appears an equilibrium, time-independent, rippled state in the string that is accompanied by a nonzero spin polarization. On the other hand, the system is shown to form "metastable," nonequilibrium long-lived ripples in the string for slow spin relaxation. The system vibrates rapidly about these quasistationary states, which can be described as snapshots of a coarse-grained stroboscopic map. For moderate observation times, ripples are observed irrespective of the final thermodynamically stable state (rippled or not). Interestingly, the system can be considered as a "minimal" model to understand rippling in clamped graphene sheets.
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