Introduction

Toom, Tarmo

doi:10.1017/cbo9781107588967.001

Patristic Theories of Biblical Interpretation 2016

DOI: 10.1017/cbo9781107588967.001

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Introduction

Tarmo Toom¹

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2020

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“…More generally, one can also consider coupling to a non-equilibrium bath, which presumably leads to a larger space of stochastic systems including probabilistic cellular automata [41]. In this more general context, remarkable results from Gács [42][43][44] and Toom [45][46][47] suggest that rigid subharmonic entrainment can arise in all dimensions d > 0 [48].…”

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Classical discrete time crystals

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The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions, and the breakdown of ergodicity. However, subharmonic responses [1] are also a well-known feature of classical dynamical systems ranging from predator-prey models [2] to Faraday waves [3] and AC-driven charge density waves [4]. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finitetemperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially-long time scales. Power-law correlations are present along a first-order line which terminates at a critical point. We analyze the transition by mapping it to the locked-to-sliding transition of a DCdriven charge density wave. Our work points to a classical limit for quantum time crystals, and raises several intriguing questions concerning the non-equilibrium universality class of the CDTC critical point. arXiv:1801.02628v1 [cond-mat.stat-mech]

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Classical discrete time crystals

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Introduction

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References 8 publications

Classical discrete time crystals

Classical discrete time crystals

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