Out-of-equilibrium dynamics of classical and quantum complex systems

Cugliandolo, Leticia F.

doi:10.1016/j.crhy.2013.09.004

Cited by 21 publications

(14 citation statements)

References 78 publications

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“…The continuous spectra of relaxation times appears in many glass models in which the barriers between local minima scale with n. In the limit of n → ∞ at any finite t such glass is trapped in the threshold state characterized by a broad spectrum of relaxation times, the phenomena known as ageing. 3,28,29 . The dynamics discussed in this work occurs in the opposite limit, at the time scales that are exponentially long in n. In this limit the glass is able to explore lower energy states that can be often viewed as deep uncorrelated minima.…”

Section: Discussionmentioning

confidence: 99%

“…Similar phenomenology has been shown in quantum glasses with significant coupling to the environment: as the quantum dynamics is reduced, the system is locked into one of the many metastable states. 3 As a result, for both classical glasses and dissipative quantum glasses, it is believed that the glassy state is not completely frozen at all non-zero temperatures and retains some amount of entropy.…”

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confidence: 99%

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Non-ergodic extended phase of the Quantum Random Energy model

2019

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The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized states is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin-spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a 'hyperglass' in which dynamics is practically absent. We discuss the implications of these finding to quantum information problems. arXiv:1812.06016v2 [cond-mat.dis-nn]

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Non-ergodic extended phase of the Quantum Random Energy model

2019

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“…It can be shown that the remaining identities in Eqs. (D21) and (D22), which involve δS/δx, do not provide additional information [73]. Note that ∆(t, t ) has a cusp at t = t due to the term σ 2 R(t , t), which from (D22) we know it must be of the form…”

Section: G(t S)r(s) Ds − γ(T S)x(s) Dsmentioning

confidence: 98%

Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

2018

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Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigate the effects of partially symmetric connectivity on the dynamics in networks of rate units. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we compute analytically, for an arbitrary degree of symmetry, the autocorrelation of network activity in the presence of external noise. In the chaotic regime, we perform simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

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“…In the case of compaction, it useful to estimate the time it takes for the soil to revert, t R , to the precompacted density. If we assume that soils are below the critical temperature which demarcates the onset of glassy dynamics, then the reversal time is Arrheniusly dependent on the effective temperature and the spatially extensive free energy barrier ( F) between the compacted and un-compacted states (Equation 12) (Cugliandolo, 2013).…”

Section: Soil Memory and Relaxationmentioning

confidence: 99%

Integrating Complex Soil Dynamics Using the Non-equilibrium Effective Temperature

Almquist

2020

Front. Earth Sci.

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Soil dynamics, such as aggregate turnover, play central roles in modulating global cycles of carbon, nitrogen and water. However, understanding soil dynamics, and the role they play in soil system functioning is complicated by the fact that soils naturally exhibit scale-dependent physical and chemical variability across more than a dozen orders of magnitude in both space and time. The arguments herein center on the components of soil variability whose scale dependency emerges because soils are in the larger sense, non-equilibrium thermodynamic systems. Interestingly a ubiquitous process, soil stirring, or pedoturbation, is widely implicated in affecting long-term processes such as aggregation, horizonation, and rates of chemical weathering. This observation aligns well with advancements recently made in theoretical physics. For a variety of non-equilibrium physical systems, the stirring rate has been shown to be equivalent to an effective temperature of the system, and can be used to recover thermodynamic relationships in non-equilibrium settings. This work primarily presents the mathematical basis for calculating the effective temperature, a measurement approach, and discusses the implications of this framework on several outstanding problems within soil science. While effective temperatures have yet to be measured in soils, this framework has the potential to greatly simplify and compliment the modeling of complex soil dynamics, but also potentially provide a new tool to rectify the discordance between small and large scale rates of soil processes.

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Out-of-equilibrium dynamics of classical and quantum complex systems

Cited by 21 publications

References 78 publications

Non-ergodic extended phase of the Quantum Random Energy model

Non-ergodic extended phase of the Quantum Random Energy model

Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

Integrating Complex Soil Dynamics Using the Non-equilibrium Effective Temperature

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