James P. Sethna

Coulomb blockade and the Kondo effect in single-atom transistors

Using molecules as electronic components is a powerful new direction in the science and technology of nanometre-scale systems. Experiments to date have examined a multitude of molecules conducting in parallel, or, in some cases, transport through single molecules. The latter includes molecules probed in a two-terminal geometry using mechanically controlled break junctions or scanning probes as well as three-terminal single-molecule transistors made from carbon nanotubes, C60 molecules, and conjugated molecules diluted in a less-conducting molecular layer. The ultimate limit would be a device where electrons hop on to, and off from, a single atom between two contacts. Here we describe transistors incorporating a transition-metal complex designed so that electron transport occurs through well-defined charge states of a single atom. We examine two related molecules containing a Co ion bonded to polypyridyl ligands, attached to insulating tethers of different lengths. Changing the length of the insulating tether alters the coupling of the ion to the electrodes, enabling the fabrication of devices that exhibit either single-electron phenomena, such as Coulomb blockade, or the Kondo effect.

Universally Sloppy Parameter Sensitivities in Systems Biology Models

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters.

Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present results of numerical simulations in three dimensions.

Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states

In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO2 unit cell. We analyse spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8 + δ and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90°-rotational symmetry within every CuO2 unit cell.

Universal properties of the transition from quasi-periodicity to chaos in dissipative systems

Monitoring the peak temperature of a moving mass, such as a flowing stream of molten material, has in the past been plaqued with problems. The present system and method overcomes these problems by oscillating a temperature sensor, spaced from the moving mass, such that the sensor scans back and forth across the moving mass during each cycle of oscillation. The output signal from the sensor is fed to device that preferably puts out a signal proportional to the peak temperature sensed by the sensor on each half cycle of oscillation, which output signal is caused to decay at a desired rate between peak temperature measurements. This slightly sawtooth shaped output signal can be recorded and/or used for control purposes.

DISORDER-DRIVEN PRETRANSITIONAL TWEED PATTERN IN MARTENSITIC TRANSFORMATIONS

Defying the conventional wisdom regarding first-order transitions, {ital solid{minus}solid} {ital displacive} {ital transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates`` the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed`` pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two-dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.

AVALANCHES, BARKHAUSEN NOISE, AND PLAIN OLD CRITICALITY

We explain Barkhausen noise in magnetic systems in terms of avalanches of domains near a plain old critical point in the hysteretic zero-temperature random-field Ising model. The avalanche size distribution has a universal scaling function, making nontrivial predictions of the shape of the distribution up to 50{percent} above the critical point, where two decades of scaling are still observed. We simulate systems with up to 1000{sup 3} domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2D and 6{minus}{epsilon} predictions, and compare to a variety of experiments. {copyright} {ital 1995 The American Physical Society.}

Imaging Atomic Rearrangements in Two-Dimensional Silica Glass: Watching Silica’s Dance

Glassy Eyed In crystalline materials, the collective motion of atoms in one- and two-dimensional defects—like dislocations and stacking faults—controls the response to an applied strain, but how glassy materials change their structure in response to strain is much less clear. Huang et al. (p. 224; see the Perspective by Heyde) used advanced-transmission electron microscopy to investigate the structural rearrangements in a two-dimensional glass, including the basis for shear deformations and the atomic behavior at the glass/liquid interface. Dynamics of individual atoms in a two-dimensional silicate glass have been observed using transmission electron microscopy. [Also see Perspective by Heyde] Structural rearrangements control a wide range of behavior in amorphous materials, and visualizing these atomic-scale rearrangements is critical for developing and refining models for how glasses bend, break, and melt. It is difficult, however, to directly image atomic motion in disordered solids. We demonstrate that using aberration-corrected transmission electron microscopy, we can excite and image atomic rearrangements in a two-dimensional silica glass—revealing a complex dance of elastic and plastic deformations, phase transitions, and their interplay. We identified the strain associated with individual ring rearrangements, observed the role of vacancies in shear deformation, and quantified fluctuations at a glass/liquid interface. These examples illustrate the wide-ranging and fundamental materials physics that can now be studied at atomic-resolution via transmission electron microscopy of two-dimensional glasses.

Parameter Space Compression Underlies Emergent Theories and Predictive Models

Information Physics Multiparameter models, which can emerge in biology and other disciplines, are often sensitive to only a small number of parameters and robust to changes in the rest; approaches from information theory can be used to distinguish between the two parameter groups. In physics, on the other hand, one does not need to know the details at smaller length and time scales in order to understand the behavior on large scales. This hierarchy has been recognized for a long time and formalized within the renormalization group (RG) approach. Machta et al. (p. 604) explored the connection between two scales by using an information-theoretical approach based on the Fisher Information Matrix to analyze two commonly used physics models—diffusion in one dimension and the Ising model of magnetism—as the time and length scales, respectively, were progressively coarsened. The expected “stiff” parameters emerged, in agreement with RG intuition. An information-theoretical approach is used to distinguish the important parameters in two archetypical physics models. The microscopically complicated real world exhibits behavior that often yields to simple yet quantitatively accurate descriptions. Predictions are possible despite large uncertainties in microscopic parameters, both in physics and in multiparameter models in other areas of science. We connect the two by analyzing parameter sensitivities in a prototypical continuum theory (diffusion) and at a self-similar critical point (the Ising model). We trace the emergence of an effective theory for long-scale observables to a compression of the parameter space quantified by the eigenvalues of the Fisher Information Matrix. A similar compression appears ubiquitously in models taken from diverse areas of science, suggesting that the parameter space structure underlying effective continuum and universal theories in physics also permits predictive modeling more generally.

Bayesian Error Estimation in Density-Functional Theory

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.