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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. Source

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. Source

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. Source

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. Source

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. Source

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