From the Cover…

.. epigraph:: “Townsend is the best book I know for advanced undergraduate quantum mechanics. It is clear, contemporary, and compact. My students used it as a wonderful springboard to graduate school.” -- Ralph D. Amado, University of Pennsylvania .. epigraph:: “With this second edition, Townsend has succeeded in making a clear and pedagogical textbook on undergraduate quantum mechanics even better.” -- Charles Gale, McGill University


The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic filaments. Collectively, our study illuminates the origin of tendril coiling, quantifies Darwin’s original proposal, and suggests designs for biomimetic twistless springs with tunable mechanical responses.


When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. We determine that the D0 branes quickly settle into an incompressible symmetric state—thermalized within a few oscillations through a process driven entirely by internal nonlinear dynamics. Surprisingly, thermal background fluctuations play no role in this mechanism. Signatures of the background fields in this thermal state arise either through fluxes, i.e. black hole hair; or if the probe expands to the size of the horizon—which we see evidence of. We determine simple scaling relations for the D0 branes’ equilibrium size, time to thermalize, lifetime, and temperature in terms of their number, initial energy, and the background fields. Our results are consistent with the conjecture that black holes are the fastest scramblers as seen by matrix theory.


We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer. This geometry is interpreted as a combination of growth-induced mechanical buckling modulated by the growth medium and a simultaneous twisting near the root tip. We study the helical morphology as the modulus of the upper gel layer is varied and demonstrate that the size of the deformation varies with gel stiffness as expected by a mathematical model based on the theory of buckled rods. Moreover, we show that plant-to-plant variations can be accounted for by biomechanically plausible values of the model parameters.


We have studied the Hall effect in superconducting tantalum nitride films. We find a large contribution to the Hall conductivity near the superconducting transition, which we can track to temperatures well above \( T_c \) and magnetic fields well above the upper critical field, \( \mathrm{H}_{c2}(0) \). This contribution arises from Aslamazov-Larkin superconducting fluctuations, and we find quantitative agreement between our data and recent theoretical analysis based on time dependent Ginzburg-Landau theory.


In ion trap quantum information processing, efficient fluorescence collection is critical for fast, high-fidelity qubit detection and ion–photon entanglement. The expected size of future many-ion processors requires scalable light collection systems. We report on the development and testing of a microfabricated surface-electrode ion trap with an integrated high-numerical aperture (NA) micromirror for fluorescence collection. When coupled to a low-NA lens, the optical system is inherently scalable to large arrays of mirrors in a single device. We demonstrate the stable trapping and transport of 40Ca+ ions over a 0.63 NA micromirror and observe a factor of 1.9 enhancement of photon collection compared to the planar region of the trap.


The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone as the driver of spur growth, we find that Aquilegia petal spurs develop via anisotropic cell expansion. Furthermore, changes in cell anisotropy account for 99 per cent of the spur-length variation in the genus, suggesting that the true evolutionary innovation underlying the rapid radiation of Aquilegia was the mechanism of tuning cell shape.


Being able to distinguish light-quark jets from gluon jets on an event-by-event basis could significantly enhance the reach for many new physics searches at the Large Hadron Collider. Through an exhaustive search of existing and novel jet substructure observables, we find that a multivariate approach can filter out over 95% of the gluon jets while keeping more than half of the light-quark jets. Moreover, a combination of two simple variables, the charge track multiplicity and the \( p_T \)-weighted linear radial moment (girth), can achieve similar results. Our study is only Monte Carlo based, so other observables constructed using different jet sizes and parameters are used to highlight areas that deserve further theoretical and experimental scrutiny. Additional information, including distributions of around 10 000 variables, can be found at

Recent Publications

Student authorFaculty author


John S. Townsend

A Modern Approach to Quantum Mechanics, Second Edition

University Science Books, Sausalito, 2012.

Sharon Gerbode, Joshua R. Puzey, A. G. McCormick, and L. Mahadevan

How the cucumber tendril coils and overwinds

Science 337 (2012) 1087.
PDF document

Paul L. Riggins and Vatche Sahakian

Black hole thermalization, D0 brane dynamics, and emergent spacetime

Physical Review D 86 (2012) 046005.
PDF document

J. L. Silverberg, R. N. Noar, M. Packer, M. Harrison, I. Cohen, C. Henley, and Sharon Gerbode

3D Imaging and mechanical modeling of helical buckling in Medicago truncatula plant roots

Proceedings of the National Academy of Sciences 109 (2012) 16794.
PDF document

Nicholas P. Breznay, Karen Michaeli, Konstantin S Tikhonov, Alexander M Finkel'stein, Mihir Tendulkar, and Aharon Kapitulnik

Hall conductivity dominated by fluctuations near the superconducting transition in disordered thin films

Physical Review B 86 (2012) 014514.

J. T. Merrill, C. Volin, D. W. Landgren, J. M. Amini, K. Wright, Charlie Doret, C. -S. Pai, H. Hayden, T. Killian, D. L. Faircloth, K. R. Brown, A. W. Harter, and R. E. Slusher

Demonstration of integrated microscale optics in surface-electrode ion traps

New Journal of Physics 13 (2011) 103005.
PDF document

Joshua R. Puzey, Sharon Gerbode, Scott A. Hodges, Elena M. Kramer, and L. Mahadevan

Evolution of spur-length diversity in Aquilegia petals is achieved solely through cell-shape anisotropy

Proceedings of the Royal Society B 279 (2011) 1640-1645.
PDF document

Jason Gallicchio and Matthew D Schwartz

Quark and Gluon Tagging at the LHC

Physical Review Letters 107 (2011) 172001.
PDF document
Eye candy

Jason Gallicchio and Matthew D Schwartz

Pure samples of quark and gluon jets at the LHC

Journal of High Energy Physics 2011 (2011) .

Donna Phu, Lindsay S. Wray, Robert V. Warren, Richard C. Haskell, and Elizabeth Orwin

Effect of Substrate Composition and Alignment on Corneal Cell Phenotype

Tissue Engineering A 17 (2011) 799–807.