Water-network percolation transitions in hydrated yeast

Sokołowska, Dagmara; Król-Otwinowska, Agnieszka; Mościcki, Józef K.

doi:10.1103/physreve.70.052901

Cited by 24 publications

(33 citation statements)

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“…They distill the underlying entanglement transition from the complicated epiphenomena associated with globally conserved currents [13,[47][48][49][50][51][52]. Here, we identify disordered Clifford circuits as a tractable semi-classical limit with a delocalization transition that maps precisely to percolation, a well-studied beast [53]. The percolation exponents show up in dynamical properties such as the growth and saturation of entanglement entropy after a global quench.…”

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confidence: 96%

Semiclassical limit for the many-body localization transition

Chandran

Laumann

2015

Phys. Rev. B

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We introduce a semi-classical limit for many-body localization in the absence of global symmetries. Microscopically, this limit is realized by disordered Floquet circuits composed of Clifford gates. In d = 1, the resulting dynamics are always many-body localized with a complete set of strictly local integrals of motion. In d ≥ 2, the system realizes both localized and delocalized phases separated by a continuous transition in which ergodic puddles percolate. We argue that the phases are stable to deformations away from the semi-classical limit and estimate the resulting phase boundary. The Clifford circuit model is a distinct tractable limit from that of free fermions and suggests bounds on the critical exponents for the generic transition.PACS numbers: 05.30. Rt,72.15.Rn The central assumption of statistical mechanics is that interactions between particles establish local equilibrium. It is now believed that this assumption of ergodicity breaks down in isolated quantum systems in the presence of sufficient quenched disorder [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The fundamental feature of such many-body localized (MBL) systems is the slowness of the spread of entanglement [19,20] due to the presence of local integrals of motion (IOM) [8,12,[21][22][23][24]. These local observables remember initial conditions forever and thereby block both equilibration and transport. At lower disorder strengths, the system delocalizes and ergodicity is restored. There is now much theoretical and numerical evidence for this picture in one dimension [4][5][6][7][8][9][10][11][12][13][14][15][16][19][20][21][22][23][24][25][26] and the experimental search in quantum optical and atomic systems is underway [25,[27][28][29].The nature of the two phases and the dynamical transition between them is poorly understood in dimensions greater than one. In this article, we present a semiclassical theory of the delocalization transition in the absence of global symmetries in arbitrary spatial dimension. In the semi-classical limit, the transition maps precisely onto classical site percolation. Each lattice site either blocks the flow of quantum information or permits it to spread. Clusters of unblocked sites form 'ergodic puddles', as such regions locally thermalize. Blockage sites, on the other hand, host local integrals of motion. Thus, at large density of blockage sites p b , the system is localized. As p b decreases, the ergodic puddles grow and eventually percolate (p c b ) leading to delocalization. The sharp distinction between blocked and unblocked sites is a consequence of the lack of quantum tunneling in our semi-classical limit. More precisely, the localization length ξ q of the integrals of motion on blocked sites is identically zero. The delocalization transition is instead driven by the divergence of the percolation length ξ e characterizing the size of ergodic puddles. Perturbing away from the semi-classical limit, both length scales be- * Electronic address: achandran@perimeterinstitute.ca come imp...

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confidence: 96%

Semiclassical limit for the many-body localization transition

Chandran

Laumann

2015

Phys. Rev. B

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“…The increased conductivity decrease rate region is indicative of conductivity percolation phenomenon [11,12,16]. Results of fitting conductivity data in this range with Eq.…”

Section: Resultsmentioning

confidence: 98%

“…All dielectric spectra, recorded at different water content in blue-green algae are typical for hydrated porous materials and showed well-separated contributions from two effects: dc conductivity and a single relaxation process [11,21,22], cf. Fig.…”

Section: Resultsmentioning

confidence: 99%

“…From a simple, model sample geometric considerations of highly porous material it follows that the sample hydration level defined by h = m W /m 0 (where m W and m 0 are the sample water mass and the dry sample mass, respectively), is to within a good approximation proportional to the site occupancy probability of the water-network p, and Eq. (1) becomes [11,12] …”

Section: Theorymentioning

confidence: 99%

“…Several biological systems of increasing complexity, protein powders, biological membranes, seed endosperm, lichens and recently yeasts were found to exhibit conductivity percolation transitions at very low hydration levels [11][12][13][14][15][16][17]. At first glance, these systems have spatial structures similar to abiotic highly porous glass or aerosilicates [16,18,19].…”

Section: Introductionmentioning

confidence: 99%

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