Biblioteca Digital

Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modelled as one-dimensional elastic objects1. Vortices are a diverse area of study for condensed matter because of the interplay between thermal fluctuations, vortex–vortex interactions and the interaction of the vortex core with the three-dimensional disorder landscape. Although vortex matter has been studied extensively, the static and dynamic properties of an individual vortex have not. Here, we use magnetic force microscopy (MFM) to image and manipulate individual vortices in a detwinned YBa₂Cu₃O_6.991 single crystal, directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and marked enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.; Physics

In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled vs. well-entangled systems and (ii) melts vs. glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary vs. binary and (iv) cooperative vs. nonccoperative relaxation dynamics. I discuss the applicability of (iii-iv) to understanding the functional form of glassy strain hardening. Results from molecular dynamics simulations show that the "dramatic" strain hardening observed in densely entangled systems is associated with a crossover from unary, noncooperative to binary, cooperative relaxation as strain increases; chains stretch between entanglement points, altering the character of local plasticity. Promising approaches for future research along these lines are discussed.; Comment: Results and conclusions same but manuscript extensively edited for clarity. Accepted for publication in J. Polym. Sci. - Polym. Phys

We present a numerical model for the prediction of the rough contact mechanics of a viscoelastic block, with graded rheology, in steady sliding contact with a randomly rough rigid surface. In particular, we derive the effective surface response of a stepwise or continuously-graded block in the Fourier domain, which is then embedded in a Fourier-based residuals molecular dynamic formulation of the contact mechanics. Finally we discuss on the role of small-scale wavelengths on rubber friction and contact area, and we demonstrate that the rough contact mechanics exhibits effective interface properties which converge to asymptotes upon increase of the small-scale roughness content, when a realistic rheology of the confinement is taken into account.

We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a corresponding 10-fold way which has appeared in condensed matter and nuclear physics. We establish a foundation for discussing continuous families of quantum systems. Having done so, topological phases of quantum systems can be defined as deformation classes of continuous families of gapped Hamiltonians. For free particles there is an additional algebraic structure on the deformation classes leading naturally to notions of twisted equivariant K-theory. In systems with a lattice of translational symmetries we show that there is a canonical twisting of the equivariant K-theory of the Brillouin torus. We give precise mathematical definitions of two invariants of the topological phases which have played an important role in the study of topological insulators. Twisted equivariant K-theory provides a finer classification of topological insulators than has been previously available.; Comment: 93 pages, 1 figure; v2 has minor corrections and clarifications for publication in AHP

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the transition to jamming and the nature of the jammed state for disordered packings of particles that act through repulsive contact interactions and are at zero temperature and zero shear stress. We first discuss the breakdown of affine assumptions that underlies the rich mechanics near jamming. We then extensively discuss jamming of frictionless soft spheres. At the jamming point, these systems are marginally stable (isostatic) in the sense of constraint counting, and many geometric and mechanical properties scale with distance to this jamming point. Finally we discuss current explorations of jamming of frictional and non-spherical (ellipsoidal) particles. Both friction and asphericity tune the contact number at jamming away from the isostatic limit, but in opposite directions. This allows one to disentangle distance to jamming and distance to isostaticity. The picture that emerges is that most quantities are governed by the contact number and scale with distance to isostaticity, while the contact number itself scales with distance to jamming.; Comment: Submitted to J Phys Cond Matt 25 pages...

Non-trivial self-adjoint extensions in quantum mechanics have been used in the past to model contact interactions when those interactions are expected a priori. However, real physical systems can only ever be understood to a finite resolution, so there exists a generic ignorance of possible short-range interactions. To address this issue, a real-space approach is described here wherein an artificial boundary is inserted at an intermediate scale to explicitly hide possible short-distance effects. Boundary conditions may then encode physical effects that are hidden behind the boundary, thereby effectively capturing the set of possible UV completions. Using this approach, a non-relativistic analysis is performed of the free particle, harmonic oscillator, and Coulomb potential in three dimensions. Requiring measurable quantities, such as spectra and cross sections, to be independent of the position of the boundary, renormalization group-type equations are derived that determine how the boundary conditions run. Generically, observables differ from their canonical values and symmetries are anomalously broken. Connections are made to well-studied physical systems, such as the deuteron and condensed matter systems that employ Feshbach resonances.; Comment: 6 pages...

Condensed matter systems are potential candidates to realize the integration of quantum information circuits. Surface phonon polariton (SPhP) is a special propagation mode in condensed matter systems. We present an investigation on the entanglement of SPhP modes. The entangled pairs are generated from entangled photons injected to the system. Quantum performances of entangled SPhPs are investigated by using the interaction Hamiltonian and the perturbation theory. The wave mechanics approach is taken to describe the coupling process as a comparison. Finally, the correlation of system is examined. A whole set of descriptions of SPhP entanglement thus are presented.; Comment: 16 pages, 4 figures

We show that the use of momentum-space optical interferometry, which avoids any spatial overlap between two parts of a macroscopic quantum state, presents a unique way to study coherence phenomena in polariton condensates. In this way, we address the longstanding question in quantum mechanics: "\emph{Do two components of a condensate, which have never seen each other, possess a definitive phase?}" [P. W. Anderson, \emph{Basic Notions of Condensed Matter Physics} (Benjamin, 1984)]. A positive answer to this question is experimentally obtained here for light-matter condensates, created under precise symmetry conditions, in semiconductor microcavities taking advantage of the direct relation between the angle of emission and the in-plane momentum of polaritons.; Comment: 6 pages, 3 figures

We systematically check explicit and implicit assumptions of Persson's contact mechanics theory. It casts the evolution of the pressure distribution ${\rm Pr}(p)$ with increasing resolution of surface roughness as a diffusive process, in which resolution plays the role of time. The tested key assumptions of the theory are: (a) the diffusion coefficient is independent of pressure $p$, (b) the diffusion process is drift-free at any value of $p$, (c) the point $p=0$ acts as an absorbing barrier, i.e., once a point falls out of contact, it never reenters again, (d) the Fourier component of the elastic energy is only populated if the appropriate wave vector is resolved, and (e) it no longer changes when even smaller wavelengths are resolved. Using high-resolution numerical simulations, we quantify deviations from these approximations and find quite significant discrepancies in some cases. For example, the drift becomes substantial for small values of $p$, which typically represent points in real space close to a contact line. On the other hand, there is a significant flux of points reentering contact. These and other identified deviations cancel each other to a large degree, resulting in an overall excellent description for contact area...

We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rod-like inclusions. We show that the Poisson's ratio $\nu$ of such a composite evolves with increasing rod density towards a particular value, or {\em fixed point}, independent of the material properties of the matrix, so long as it has a finite initial compressibility. This fixed point is $\nu=1/4$ in three dimensions and $\nu=1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites...

When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model's prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize frictional slip as a fracture phenomenon. We show that predicted precursor lengths depend, within given uncertainty ranges, mainly on the kinetic friction coefficient, and only weakly on other interface and material parameters. By simplifying the fracture mechanics model we also reveal sources for the observed non-linearity in the growth of precursor lengths as a function of the applied force. The discrete nature of precursors as well as the shear tractions caused by frustrated Poisson's expansion are found to be the dominant factors. Finally, we apply our model to a different, symmetric set-up and provide a prediction of the propagation distance of frictional slip for future experiments.

This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are accomplished. First, a rigorous mathematical model is proposed of emergent character, which is conceptually bonded with Quantum Mechanics while apparently non-derivable from the many-body Schr\"{o}dinger equation. I call the resulting conceptual framework the Mesoscopic Mechanics (MeM). Its formulation is space-independent and comprises a nonlinear and holistic extension of the free electron model. Secondly, the question of relevancy of the proposed ``emergent mechanics" to the actually observed phenomena is discussed. In particular, I postulate a probabilistic interpretation, and indicate how the theory could be applied and verified by experiment. The Mesoscopic Mechanics proposed here has been deduced from the Nonlinear Maxwell Theory (NMT)--a classical in character nonlinear field theory. This latter theory has already been shown to provide a consistent phenomenological model of such phenomena as superconductivity, charge stripes, magnetic vortex lattice, and magnetic oscillations. The NMT, which arose from geometric considerations...

Following our discussion [Physica A, 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro- to the micro-domain, we argue that there is a possible connection among normalized probabilities, spacetime geometry (in the form of Schwarzschild radii) and quantum mechanics (in the form of complex wave functions). We show how this association along different (n)-nested surfaces --representing curve space due to an inhomogeneous density of matter-- preserves the postulates of quantum mechanics at different geometrical scales.; Comment: in press

We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly presented, showing how it implies a kind of duality in perturbation theory, from the start. The approach of renormalization group in perturbation theory is then presented. This method permits to resum secularities in perturbation theory and makes fully algorithmical the resummation, transforming the perturbation calculations in a step by step computational procedure. The general theorem on which is founded a proper application of the strong coupling expansion, based on a result in the quantum adiabatic theory, is then exposed. This theorem gives the leading order of a strong coupling expansion. Then, after the introduction of the principle of duality in perturbation theory that puts in a proper context the quantum field theory method, the resulting theory of the strong coupling expansion and the free picture are presented. An algorithm for the computation of the perturbation series is finally given. This approach has a lot of applications in fields as quantum optics, condensed matter and so on, extending the original expectations of the quantum field theory method. So...

Impact craters exist on various solid objects in the planetary system. A simplified analogy of the process of their formation is here analyzed by standard solid state physics and the so called dynamic quantized fracture mechanics. An expression which links the crater volume to the parameters of the impactor and the target is obtained within the two approaches. For low impactor energy, this expression is of the same mathematical form as the one resulting from recent experiments.It is shown that the formation of an impact crater is possible even without heating of the target, if the critical stress in the target satisfies certain conditions. The critical value of the stress needed for the occurence of a fracture is calculated for three craters: two terrestrial and one lunar crater. The approach presented here uses only measurable material parameters, and is therefore more realistic than the treatement of the same problem using the cohesive energy of materials.; Comment: plain LaTeX and 1 EPS file packed together

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.; Comment: Format Revtex4, two columns, 13 pages, 19 pictures. Submitted for publication in the European Physical Journal E. Third revision with minimal changes: Corrected a few mistyping

We present a comprehensive review of the physical behavior of yield stress materials in soft condensed matter, which encompasses a broad range of soft materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear response to an external mechanical forcing, which results from the existence of a finite force threshold for flow to occur, the yield stress. We discuss both the physical origin and the rheological consequences associated with this nonlinear behavior. We give an overview of the different experimental techniques developed to measure the yield stress. We discuss extensively the recent progress concerning a microscopic description of the flow dynamics of yield stress materials, emphasizing in particular the role played by relaxation timescales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and non-local effects in confined geometries. We finally review the status of modeling of the shear rheology of yield stress materials in the framework of continuum mechanics.; Comment: Review article: 58 pages, 38 figs, 487 refs

Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modeled as one-dimensional elastic objects. Vortices are a diverse playground for condensed matter because of the interplay between thermal fluctuations, vortex-vortex interactions, and the interaction of the vortex core with the three-dimensional disorder landscape. While vortex matter has been studied extensively, the static and dynamic properties of an individual vortex have not. Here we employ magnetic force microscopy (MFM) to image and manipulate individual vortices in detwinned, single crystal YBa2Cu3O6.991 (YBCO), directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and dramatic enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.

Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ``exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.; Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Classical soil mechanics results are used to propose the equation of the jamming transition surface in the (stress, specific volume) space. Taking axis-ymmetric conditions, labelling q the deviatoric stress and p' the mean pressure applied on the granular skeleton, and considering normal range of pressure (10 kPa-10MPa) the equation of the surface of jamming transition is v = vo-m ln(p'/p'o)+ md ln(1+q q/(M' M' p' p')); M' is related to the friction angle, m and md are two constants which depend on soil characteristics; p'o is a "unit" pressure.; Comment: 2 pages + 1 page, 0 figure