Wiegmann P.,James Franck Institute
Physical Review Letters | Year: 2012
We argue that the dynamics of fractional quantum Hall (FQH) edge states is essentially nonlinear and that it features fractionally quantized solitons with charges -νe propagating along the edge. The observation of solitons would be direct evidence of fractional charges. We show that the nonlinear dynamics of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation. Nonlinear dynamics of gapless edge states is determined by gapped modes in the bulk of FQH liquid and is traced to the double boundary layer "overshoot" of FQH states. The dipole moment of the layer η=1-ν4π is obtained in paper. Quantum hydrodynamics of FQH liquid is outlined. © 2012 American Physical Society.
Mazziotti D.A.,James Franck Institute
Physical Review Letters | Year: 2012
We present a constructive solution to the N-representability problem: a full characterization of the conditions for constraining the two-electron reduced density matrix to represent an N-electron density matrix. Previously known conditions, while rigorous, were incomplete. Here, we derive a hierarchy of constraints built upon (i) the bipolar theorem and (ii) tensor decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2, known classical conditions, and new conditions appear naturally. Subsets of the conditions are amenable to polynomial-time computations of strongly correlated systems. © 2012 American Physical Society.
Kleckner D.,James Franck Institute |
Irvine W.T.M.,James Franck Institute
Nature Physics | Year: 2013
Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have been the subject of considerable theoretical study, their creation in the laboratory has remained an outstanding experimental goal. Here we report the creation of isolated trefoil vortex knots and pairs of linked vortex rings in water using a new method of accelerating specially shaped hydrofoils. Using a high-speed scanning tomography apparatus, we measure their three-dimensional topological and geometrical evolution in detail. In both cases we observe that the linked vortices stretch themselves and then deform - as dictated by their geometrically determined energy - towards a series of local vortex reconnections. This work establishes the existence and dynamics of knotted vortices in real fluids. Copyright © 2013 Macmillan Publishers Limited. All rights reserved.
Freed K.F.,James Franck Institute
Accounts of Chemical Research | Year: 2011
Glassy materials have been fundamental to technology since the dawn of civilization and remain so to this day: novel glassy systems are currently being developed for applications in energy storage, electronics, food, drugs, and more. Glass-forming fluids exhibit a universal set of transitions beginning at temperatures often in excess of twice the glass transition temperature T g and extending down to T g, below which relaxation becomes so slow that systems no longer equilibrate on experimental time scales. Despite the technological importance of glasses, no prior theory explains this universal behavior nor describes the huge variations in the properties of glass-forming fluids that result from differences in molecular structure. Not surprisingly, the glass transition is currently regarded by many as the deepest unsolved problem in solid state theory.In this Account, we describe our recently developed theory of glass formation in polymer fluids. Our theory explains the origin of four universal characteristic temperatures of glass formation and their dependence on monomer-monomer van der Waals energies, conformational energies, and pressure and, perhaps most importantly, on molecular details, such as monomer structure, molecular weight, size of side groups, and so forth. The theory also provides a molecular explanation for fragility, a parameter that quantifies the rate of change with temperature of the viscosity and other dynamic mechanical properties at T g. The fragility reflects the fluid's thermal sensitivity and determines the manner in which glass-formers can be processed, such as by extrusion, casting, or inkjet spotting.Specifically, the theory describes the change in thermodynamic properties and fragility of polymer glasses with variations in the monomer structure, the rigidity of the backbone and side groups, the cohesive energy, and so forth. The dependence of the structural relaxation time at lower temperatures emerges from the theory as the Vogel-Fulcher equation, whereas pressure and concentration analogs of the Vogel-Fulcher expression follow naturally from the theory with no additional assumptions. The computed dependence of T g and fragility on the length of the side group in poly(α-olefins) agrees quite well with observed trends, demonstrating that the theory can be utilized, for instance, to guide the tailoring of T g and the fragility of glass-forming polymer fluids in the fabrication of new materials. Our calculations also elucidate the molecular characteristics of small-molecule diluents that promote antiplasticization, a lowering of T g and a toughening of the material. © 2011 American Chemical Society.
Brown E.,Yale University |
Jaeger H.M.,James Franck Institute
Reports on Progress in Physics | Year: 2014
Shear thickening is a type of non-Newtonian behavior in which the stress required to shear a fluid increases faster than linearly with shear rate. Many concentrated suspensions of particles exhibit an especially dramatic version, known as Discontinuous Shear Thickening (DST), in which the stress suddenly jumps with increasing shear rate and produces solid-like behavior. The best known example of such counter-intuitive response to applied stresses occurs in mixtures of cornstarch in water. Over the last several years, this shear-induced solid-like behavior together with a variety of other unusual fluid phenomena has generated considerable interest in the physics of densely packed suspensions. In this review, we discuss the common physical properties of systems exhibiting shear thickening, and different mechanisms and models proposed to describe it. We then suggest how these mechanisms may be related and generalized, and propose a general phase diagram for shear thickening systems. We also discuss how recent work has related the physics of shear thickening to that of granular materials and jammed systems. Since DST is described by models that require only simple generic interactions between particles, we outline the broader context of other concentrated many-particle systems such as foams and emulsions, and explain why DST is restricted to the parameter regime of hard-particle suspensions. Finally, we discuss some of the outstanding problems and emerging opportunities. © 2014 IOP Publishing Ltd.
Mazziotti D.A.,James Franck Institute
Physical Review Letters | Year: 2011
The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D.A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.213001]. We illustrate with (i) the dissociation of N2 and (ii) the metal-to-insulator transition of H50. For H50 the SDP problem has 9.4×106 variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics. © 2011 American Physical Society.
Liang Y.,James Franck Institute |
Yu L.,James Franck Institute
Accounts of Chemical Research | Year: 2010
Solar cells based on the polymer-fullerene bulk heterojunction (BHJ) concept are an attractive class of low-cost solar energy harvesting devices. Because the power conversion efficiency (PCE) of these solar cells is still significantly lower than that of their inorganic counterparts, however, materials design and device engineering efforts are directed toward improving their output. A variety of factors limit the performance of BHJ solar cells, but the properties of the materials in the active layer are the primary determinant of their overall efficiency. The ideal polymer in a BHJ structure should exhibit the following set of physical properties: a broad absorption with high coefficient in the solar spectrum to efficiently harvest solar energy, a bicontinuous network with domain width within twice that of the exciton diffusion length, and high donor-acceptor interfacial area to favor exciton dissociation and efficient transport of separated charges to the respective electrodes. To facilitate exciton dissociation, the lowest unoccupied molecular orbital (LUMO) energy level of the donor must have a proper match with that of the acceptor to provide enough driving force for charge separation. The polymer should have a low-lying highest occupied molecular orbital (HOMO) energy level to provide a large open circuit voltage (V oc). All of these desired properties must be synergistically integrated to maximize solar cell performance. However, it is difficult to design a polymer to fulfill all these requirements. In this Account, we summarize our recent progress in developing a new class of semiconducting polymers, which represents the first polymeric system to generate solar PCE greater than 7%. The polymer system is composed of thieno[3,4-b]thiophene and benzodithiophene alternating units. These polymers have low bandgaps and exhibit efficient absorption throughout the region of greatest photon flux in the solar spectrum (around 700 nm). The stabilization of the quinoidal structure from thieno[3,4-b]thiophene is believed to be primarily responsible for these properties. Additionally, the rigid backbone enables the polymer to form an assembly with high hole mobility. Proper side chains on the polymer backbone ensure good solubility and miscibility with fullerene acceptors. The flexibility in structural tuning on the polymer backbone provides the polymers with relatively low-lying HOMO energy levels and enhanced V oc, short-circuit current density (J sc), and fill factor (FF) and, thus, enhanced PCE. All of these features indicate that the polymer system exhibits a host of properties that are indeed synergistically combined, leading to the enhancement in solar cell output. Our preliminary results demonstrate why these polymers are excellent materials for solar energy conversion and represent prime candidates for further improvements through research and development. © 2010 American Chemical Society.
Knight C.,James Franck Institute |
Voth G.A.,James Franck Institute
Accounts of Chemical Research | Year: 2012
Understanding the hydrated proton is a critically important problem that continues to engage the research efforts of chemists, physicists, and biologists because of its involvement in a wide array of phenomena. Only recently have several unique properties of the hydrated proton been unraveled through computer simulations. One such process is the detailed molecular mechanism by which protons hop between neighboring water molecules, thus giving rise to the anomalously high diffusion of protons relative to other simple cations. Termed Grotthuss shuttling, this process occurs over multiple time and length scales, presenting unique challenges for computer modeling and simulation. Because the hydrated proton is in reality a dynamical electronic charge defect that spans multiple water molecules, the simulation methodology must be able to dynamically readjust the chemical bonding topology. This reactive nature of the chemical process is automatically captured with ab initio molecular dynamics (AIMD) simulation methods, where the electronic degrees of freedom are treated explicitly. Unfortunately, these calculations can be prohibitively expensive for more complex proton solvation and transport phenomena in the condensed phase. These AIMD simulations remain extremely valuable, however, in validating empirical models, verifying results, and providing insight into molecular mechanisms.In this Account, we discuss recent progress in understanding the solvation and transport properties of the hydrated excess proton. The advances are based on results obtained from reactive molecular dynamics simulations using the multistate empirical valence bond (MS-EVB) methodology. This approach relies on a dynamic linear combination of chemical bond topologies to model charge delocalization and dynamic bonding environments. When parametrized via a variational force-matching algorithm from AIMD trajectories, the MS-EVB method can be viewed as a multiscale bridging of ab initio simulation results to a simpler and more efficient representation. The process allows sampling of longer time and length scales, which would normally be too computationally expensive with AIMD alone.With the MS-EVB methodology, the statistically important components of the excess proton solvation and hopping mechanisms in liquid water have been identified. The most likely solvation structure for the hydrated proton is a distorted Eigen-type complex (H 9O 4 +). In this state, the excess proton charge defect rapidly resonates between three possible distorted Eigen-type structures until a successful proton hop occurs. This process, termed the "special-pair dance", serves as a kind of preparatory phase for the proton hopping while the neighboring water hydrogen-bonding network fluctuates and ultimately rearranges to facilitate a proton hop.The modifications of the solvation structure and transport properties of the excess proton in concentrated acid solutions were further investigated. The Eigen-type solvation structure also possesses both "hydrophilic" and "hydrophobic" sides, which accounts for the affinity of the hydrated proton for the air-water interface. This unusual " amphiphilic" character of the hydrated proton further leads to the metastable formation of contact ion pairs between two hydrated protons. It also engenders a surprisingly constant degree of solubility of hydrophobic species as a function of acid concentration, which contrasts with a markedly variable solubility as a function of salt (such as NaCl or KCl) concentration. © 2011 American Chemical Society.
Guyot-Sionnest P.,James Franck Institute
Journal of Physical Chemistry Letters | Year: 2012
In nanocrystal solids, the small density of states of quantum dots makes it difficult to achieve metallic conductivity without band-like transport. However, to achieve band-like transport, the energy scale of the disorder should be smaller than the coupling energy. This is unlikely with the present systems due to the size polydispersivity. Transport by hopping may nevertheless lead to an increased mobility with decreasing temperature for some temperature range, and such behavior at finite temperature is not proof of band-like conduction. To date, at low temperature, variable range hopping in semiconductor or weakly coupled metal nanocrystal solids dominates transport, as in disordered semiconductors. © 2012 American Chemical Society.
Mazziotti D.A.,James Franck Institute
Chemical Reviews | Year: 2012
Recent advances in new approaches to the study of electron correlation, the direct calculation of the two-electron reduced density matrix, are reviewed. The ACSE and the cumulant reconstruction of the 3-RDM from the 2-RDM is combined to solve the ACSE for the 2-RDM. Calculations demonstrate that the ACSE yields a balanced description of single- and multireference correlation effects in both the presence and absence of strong electron correlation. The systematic hierarchy of N-representability constraints for the 2-RDM known as the p-positivity conditions is also developed. The efficiency of the matrix factorization has been confirmed by studying a dual formulation of the problem. Greenman applied the variational 2-RDM method with 2-positivity conditions to studying the convergence of the ground-state potential energy surface of dioxetanone with active-space size. Kamarchik extended the variational 2-RDM method for electronic systems to compute ground-state distributions of electrons and hydrogen nuclei in molecules beyond the Born-Oppenheimer approximation.