Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson localization, whereby the spread of the walker stays within a finite region even in the infinite time limit. It is therefore important to understand when we can expect a quantum walk to be Anderson localized and when we can expect it to spread to infinity even in the presence of disorder. In this work we analyze the response of a generic one-dimensional quantum walk -- the split-step walk -- to different forms of static disorder. We find that introducing static, symmetry-preserving disorder in the parameters of the walk leads to Anderson localization. In the completely disordered limit, however, a delocalization sets in, and the walk spreads subdiffusively. Using an efficient numerical algorithm, we calculate the bulk topological invariants of the disordered walk, and interpret the disorder-induced Anderson localization and delocalization transitions using these invariants.Comment: version 2, submitted to Phys. Rev.

Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk

Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work on topological phases of quantum walks where the coin operators are spin rotations, in experiments a different coin, the Hadamard operator is often used instead. This was the case in a recent photonic quantum walk experiment, where protected edge states were observed between two bulks whose topological invariants, as calculated by the standard theory, were the same. This hints at a hidden topological invariant in the Hadamard quantum walk. We establish a relation between the Hadamard and the spin rotation operator, which allows us to apply the recently developed theory of topological phases of quantum walks to the one-dimensional Hadamard quantum walk. The topological invariants we derive account for the edge state observed in the experiment, we thus reveal the hidden topological invariant of the one-dimensional Hadamard quantum walk.Comment: 11 pages, 4 figure

Halide binding by the purified halorhodopsin chromoprotein. II. New chloride-binding sites revealed by 35Cl NMR

Halorhodopsin is a light-driven chloride pump in the cell membrane of Halobacterium halobium. Recently, a polypeptide of apparent Mr = 20,000 has been purified that contains the halorhodopsin chromophore. Here we use 35Cl NMR to show that the purified chromoprotein possesses two previously unknown classes of chloride-binding sites. One class exhibits a low affinity (KD much greater than 1 M) for chloride and bromide. The second class exhibits a higher affinity (KD = 110 ± 50 mM) for chloride and also binds other anions according to the affinity series I-, SCN- greater than Br-, NO-3 greater than Cl- greater than F- , citrate. Both classes of NMR site remain intact at pH 11, indicating that the essential positive charges are provided by arginine. Also, both classes are unaffected by bleaching, suggesting that the sites are not in the immediate vicinity of the halorhodopsin chromophore. Although the chromoprotein also appears to contain the chloride- transport site (Steiner, M., Oesterhelt, D., Ariki, M., and Lanyi, J. K. (1984) J. Biol. Chem. 259, 2179-2184), this site was not detected by 35Cl NMR, suggesting that the transport site is in the interior of the protein where it is sampled slowly by chloride in the medium. It is proposed that the purified chromoprotein possesses a channel leading from the medium to the transport site and that the channel contains the high affinity NMR site which facilitates the migration of chloride between the medium and the transport site. We have also used 35Cl NMR to study chloride binding to purified monomeric bacteriorhodopsin; however, this protein contains no detectable chloride-binding sites

Anomalous levitation and annihilation in Floquet topological insulators

Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically-driven, or Floquet systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous Floquet Anderson insulator (AFAI) phase. We show a concrete example for this process, adding disorder via onsite potential "kicks" to a Chern insulator model. By changing the period between kicks, we can tune which type of (conventional or anomalous) levitation-and-annihilation occurs in the system. We expect our results to be applicable to generic Floquet topological systems and to provide an accessible way to realize AFAIs experimentally, without the need for multi-step driving schemes.Comment: 5+4 pages, 5+5 figures, v2: this is the final, published versio

Anion binding to the chloride pump, halorhodopsin, and its implications for the transport mechanism

AbstractThe light-driven chloride pump, halorhodopsin, binds and transports chloride across the membrane, and to a lesser extent nitrate. Binding and transport kinetics, and resonance Raman spectra of the retinal Schiff base, with these anions suggest the existence of two mutually exclusive binding sites. One of these may be the uptake site, and the other the release site during the transport. Plausible locations can be suggested for these sites, because halorhodopsin is a small protein with few buried positively charged residues, and the primary structure of a second pigment with similar function has recently become available for comparison

Characterization of the Proton-Transporting Photocycle of Pharaonis Halorhodopsin

AbstractThe photocycle of pharaonis halorhodopsin was investigated in the presence of 100mM NaN3 and 1M Na2SO4. Recent observations established that the replacement of the chloride ion with azide transforms the photocycle from a chloride-transporting one into a proton-transporting one. Kinetic analysis proves that the photocycle is very similar to that of bacteriorhodopsin. After K and L, intermediate M appears, which is missing from the chloride-transporting photocycle. In this intermediate the retinal Schiff base deprotonates. The rise of M in halorhodopsin is in the microsecond range, but occurs later than in bacteriorhodopsin, and its decay is more accentuated multiphasic. Intermediate N cannot be detected, but a large amount of O accumulates. The multiphasic character of the last step of the photocycle could be explained by the existence of a HR′ state, as in the chloride photocycle. Upon replacement of chloride ion with azide, the fast electric signal changes its sign from positive to negative, and becomes similar to that detected in bacteriorhodopsin. The photocycle is enthalpy-driven, as is the chloride photocycle of halorhodopsin. These observations suggest that, while the basic charge translocation steps become identical to those in bacteriorhodopsin, the storage and utilization of energy during the photocycle remains unchanged by exchanging chloride with azide

E2F4 regulates transcriptional activation in mouse embryonic stem cells independently of the RB family.

E2F transcription factors are central regulators of cell division and cell fate decisions. E2F4 often represents the predominant E2F activity in cells. E2F4 is a transcriptional repressor implicated in cell cycle arrest and whose repressive activity depends on its interaction with members of the RB family. Here we show that E2F4 is important for the proliferation and the survival of mouse embryonic stem cells. In these cells, E2F4 acts in part as a transcriptional activator that promotes the expression of cell cycle genes. This role for E2F4 is independent of the RB family. Furthermore, E2F4 functionally interacts with chromatin regulators associated with gene activation and we observed decreased histone acetylation at the promoters of cell cycle genes and E2F targets upon loss of E2F4 in RB family-mutant cells. Taken together, our findings uncover a non-canonical role for E2F4 that provide insights into the biology of rapidly dividing cells

Application of the operator product expansion to the short distance behavior of nuclear potentials

We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.Comment: 40 pages, no figure

Neuroinflammation by cytotoxic T-lymphocytes impairs retrograde axonal transport in an oligodendrocyte mutant mouse

Mice overexpressing proteolipid protein (PLP) develop a leukodystrophy-like disease involving cytotoxic, CD8+ T-lymphocytes. Here we show that these cytotoxic T-lymphocytes perturb retrograde axonal transport. Using fluorogold stereotactically injected into the colliculus superior, we found that PLP overexpression in oligodendrocytes led to significantly reduced retrograde axonal transport in retina ganglion cell axons. We also observed an accumulation of mitochondria in the juxtaparanodal axonal swellings, indicative for a disturbed axonal transport. PLP overexpression in the absence of T-lymphocytes rescued retrograde axonal transport defects and abolished axonal swellings. Bone marrow transfer from wildtype mice, but not from perforin- or granzyme B-deficient mutants, into lymphocyte-deficient PLP mutant mice led again to impaired axonal transport and the formation of axonal swellings, which are predominantly located at the juxtaparanodal region. This demonstrates that the adaptive immune system, including cytotoxic T-lymphocytes which release perforin and granzyme B, are necessary to perturb axonal integrity in the PLP-transgenic disease model. Based on our observations, so far not attended molecular and cellular players belonging to the immune system should be considered to understand pathogenesis in inherited myelin disorders with progressive axonal damage