Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition

The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the λ transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.

Broken symmetry and critical transport properties of random metals

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime.

Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

Mirror symmetry breaking at the molecular level.

Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon.

Regeneration of broken tip links and restoration of mechanical transduction in hair cells

A hair cell’s tip links are thought to gate mechanoelectrical transduction channels. The susceptibility of tip links to acoustic trauma raises questions as to whether these fragile structures can be regenerated. We broke tip links with the calcium chelator 1,2-bis(O-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid and found that they can regenerate, albeit imperfectly, over several hours. The time course of tip-link regeneration suggests that this process may underlie recovery from temporary threshold shifts induced by noise exposure. Cycloheximide does not block tip-link regeneration, indicating that new protein synthesis is not required. The calcium ionophore ionomycin prevents regeneration, suggesting regeneration normally may be stimulated by the reduction in stereociliary Ca2+ when gating springs rupture and transduction channels close. Supporting the equivalence of tip links with gating springs, mechanoelectrical transduction returns over the same time period as tip links; strikingly, adaptation is substantially reduced, even 24 hr after breaking tip links.

Twist fields, the elliptic genus, and hidden symmetry

We combine infinite dimensional analysis (in particular a priori estimates and twist positivity) with classical geometric structures, supersymmetry, and noncommutative geometry. We establish the existence of a family of examples of two-dimensional, twist quantum fields. We evaluate the elliptic genus in these examples. We demonstrate a hidden SL(2,ℤ) symmetry of the elliptic genus, as suggested by Witten.

Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission

The diffraction barrier responsible for a finite focal spot size and limited resolution in far-field fluorescence microscopy has been fundamentally broken. This is accomplished by quenching excited organic molecules at the rim of the focal spot through stimulated emission. Along the optic axis, the spot size was reduced by up to 6 times beyond the diffraction barrier. The simultaneous 2-fold improvement in the radial direction rendered a nearly spherical fluorescence spot with a diameter of 90–110 nm. The spot volume of down to 0.67 attoliters is 18 times smaller than that of confocal microscopy, thus making our results also relevant to three-dimensional photochemistry and single molecule spectroscopy. Images of live cells reveal greater details.

Nanohedra: Using symmetry to design self assembling protein cages, layers, crystals, and filaments

A general strategy is described for designing proteins that self assemble into large symmetrical nanomaterials, including molecular cages, filaments, layers, and porous materials. In this strategy, one molecule of protein A, which naturally forms a self-assembling oligomer, An, is fused rigidly to one molecule of protein B, which forms another self-assembling oligomer, Bm. The result is a fusion protein, A-B, which self assembles with other identical copies of itself into a designed nanohedral particle or material, (A-B)p. The strategy is demonstrated through the design, production, and characterization of two fusion proteins: a 49-kDa protein designed to assemble into a cage approximately 15 nm across, and a 44-kDa protein designed to assemble into long filaments approximately 4 nm wide. The strategy opens a way to create a wide variety of potentially useful protein-based materials, some of which share similar features with natural biological assemblies.

Symmetries in bacterial motility

Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order.

A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.

The role of symmetry in fundamental physics

The role of symmetry in fundamental physics is reviewed.

Symmetry arguments in chemistry

The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.