Universal properties of many-body delocalization transitions

We study the dynamical melting of "hot" one-dimensional many-body localized systems. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics.Comment: 12 pages, 6 figures; major changes from v1, including a modified approach and new emphasis on conventional MBL systems rather than their critical variant

Adiabatic reduction of a model of stochastic gene expression with jump Markov process

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.Comment: 17 page

Localization-protected order in spin chains with non-Abelian discrete symmetries

We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the ${\mathbb{Z}_3}$ clock symmetry or a ${\mathbb{Z}_2}$ chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.Comment: 5 pages, 3 figures main text; 6 pages, 3 figures supplemental material; Version 2 includes a corrected the form of the chiral order parameter, and corresponding data, as well as larger system size numerics, with no change to the phase structur

Loss of PopZ At activity in Agrobacterium tumefaciens by Deletion or Depletion Leads to Multiple Growth Poles, Minicells, and Growth Defects.

Agrobacterium tumefaciens grows by addition of peptidoglycan (PG) at one pole of the bacterium. During the cell cycle, the cell needs to maintain two different developmental programs, one at the growth pole and another at the inert old pole. Proteins involved in this process are not yet well characterized. To further characterize the role of pole-organizing protein A. tumefaciens PopZ (PopZ At ), we created deletions of the five PopZ At domains and assayed their localization. In addition, we created a popZAt deletion strain (ΔpopZAt ) that exhibited growth and cell division defects with ectopic growth poles and minicells, but the strain is unstable. To overcome the genetic instability, we created an inducible PopZ At strain by replacing the native ribosome binding site with a riboswitch. Cultivated in a medium without the inducer theophylline, the cells look like ΔpopZAt cells, with a branching and minicell phenotype. Adding theophylline restores the wild-type (WT) cell shape. Localization experiments in the depleted strain showed that the domain enriched in proline, aspartate, and glutamate likely functions in growth pole targeting. Helical domains H3 and H4 together also mediate polar localization, but only in the presence of the WT protein, suggesting that the H3 and H4 domains multimerize with WT PopZ At , to stabilize growth pole accumulation of PopZ AtIMPORTANCEAgrobacterium tumefaciens is a rod-shaped bacterium that grows by addition of PG at only one pole. The factors involved in maintaining cell asymmetry during the cell cycle with an inert old pole and a growing new pole are not well understood. Here we investigate the role of PopZ At , a homologue of Caulobacter crescentus PopZ (PopZ Cc ), a protein essential in many aspects of pole identity in C. crescentus We report that the loss of PopZ At leads to the appearance of branching cells, minicells, and overall growth defects. As many plant and animal pathogens also employ polar growth, understanding this process in A. tumefaciens may lead to the development of new strategies to prevent the proliferation of these pathogens. In addition, studies of A. tumefaciens will provide new insights into the evolution of the genetic networks that regulate bacterial polar growth and cell division