Publications

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• Liu-Nagel phase diagrams in infinite dimension

  Giulio Biroli, Pierfrancesco Urbani

  SciPost Phys. 4, 020 (2018) · published 27 April 2018 | Toggle abstract · pdf

  We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous solid as found for Hard Spheres systems. A general outcome of our results is that a reduced stability of the glass favors the appearance of the Gardner transition. Therefore using strong perturbations, e.g. shear and compression, on standard glasses or using weak perturbations on weakly stable glasses, e.g. the ones prepared close to the jamming point, are the generic ways to induce a Gardner transition. The formalism that we discuss allows to study general perturbations, including strain deformations that are important to study soft glassy rheology at the mean field level.

  24 citations

• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench

  Axel Cortes Cubero

  SciPost Phys. 4, 016 (2018) · published 27 March 2018 | Toggle abstract · pdf

  At thermal equilibrium, the concept of effective central charge for massive deformations of two-dimensional conformal field theories (CFT) is well understood, and can be defined by comparing the partition function of the massive model to that of a CFT. This temperature-dependent effective charge interpolates monotonically between the central charge values corresponding to the IR and UV fixed points at low and high temperatures, respectively. We propose a non-equilibrium, time-dependent generalization of the effective central charge for integrable models after a quantum quench, $c_{\rm eff}(t)$, obtained by comparing the return amplitude to that of a CFT quench. We study this proposal for a large mass quench of a free boson, where the charge is seen to interpolate between $c_{\rm eff}=0$ at $t=0$, and $c_{\rm eff}\sim 1$ at $t\to\infty$, as is expected. We use our effective charge to define an "Ising to Tricritical Ising" quench protocol, where the charge evolves from $c_{\rm eff}=1/2$ at $t=0$, to $c_{\rm eff}=7/10$ at $t\to\infty$, the corresponding values of the first two unitary minimal CFT models. We then argue that the inverse "Tricritical Ising to Ising" quench is impossible with our methods. These conclusions can be generalized for quenches between any two adjacent unitary minimal CFT models. We finally study a large mass quench into the "staircase model" (sinh-Gordon with a particular complex coupling). At short times after the quench, the effective central charge increases in a discrete "staircase" structure, where the values of the charge at the steps can be computed in terms of the central charges of unitary minimal CFT models. When the initial state is a pure state, one always finds that $c_{\rm eff}(t\to\infty)\geq c_{\rm eff}(t=0)$, though $c_{\rm eff}(t)$, generally oscillates at finite times. We explore how this constraint may be related to RG flow irreversibility.

• Fluctuations of observables for free fermions in a harmonic trap at finite temperature

  Aurélien Grabsch, Satya N. Majumdar, Grégory Schehr, Christophe Texier

  SciPost Phys. 4, 014 (2018) · published 24 March 2018 | Toggle abstract · pdf

  We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of certain observables of the form of sums of a function of the fermions' positions, $\mathcal{L}=\sum_n h(x_n)$. Such observables are also called linear statistics of the positions. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations. We discuss the universality of the results with respect to the nature of the confinement.

  11 citations

• (Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional

  Camille Aron, Giulio Biroli, Leticia F. Cugliandolo

  SciPost Phys. 4, 008 (2018) · published 31 January 2018 | Toggle abstract · pdf

  We unveil the universal (model-independent) symmetry satisfied by Schwinger-Keldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the Schwinger-Keldysh path-integral formalism in which the physical time can be re-parametrized to arbitrary contours in the complex plane. Strong relations between correlation functions, such as the fluctuation-dissipation theorems, are derived as immediate consequences of this symmetry of equilibrium. In this view, quantum non-equilibrium dynamics -- e.g. when driving with a time-dependent potential -- are seen as symmetry-breaking processes. The symmetry-breaking terms of the action are identified as a measure of irreversibility, or entropy creation, defined at the level of a single quantum trajectory. Moreover, they are shown to obey quantum fluctuation theorems. These results extend stochastic thermodynamics to the quantum realm.

  27 citations

• Drude Weight for the Lieb-Liniger Bose Gas

  Benjamin Doyon, Herbert Spohn

  SciPost Phys. 3, 039 (2017) · published 15 December 2017 | Toggle abstract · pdf

  Based on the method of hydrodynamic projections we derive a concise formula for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our formula contains only quantities which are obtainable from the thermodynamic Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear functional: it is bilinear in the currents, and each current may refer to a general linear combination of the conserved charges of the model. As a by-product we obtain the dynamical two-point correlation functions involving charge and current densities at small wavelengths and long times, and in addition the scaled covariance matrix of charge transfer. We expect that our formulas extend to other integrable quantum models.

  142 citations

• RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles

  Nicholas P. Bailey, Trond S. Ingebrigtsen, Jesper Schmidt Hansen, Arno A. Veldhorst, Lasse Bøhling, Claire A. Lemarchand, Andreas E. Olsen, Andreas K. Bacher, Lorenzo Costigliola, Ulf R. Pedersen, Heine Larsen, Jeppe C. Dyre, Thomas B. Schrøder

  SciPost Phys. 3, 038 (2017) · published 14 December 2017 | Toggle abstract · pdf

  RUMD is a general purpose, high-performance molecular dynamics (MD) simulation package running on graphical processing units (GPU's). RUMD addresses the challenge of utilizing the many-core nature of modern GPU hardware when simulating small to medium system sizes (roughly from a few thousand up to hundred thousand particles). It has a performance that is comparable to other GPU-MD codes at large system sizes and substantially better at smaller sizes.RUMD is open-source and consists of a library written in C++ and the CUDA extension to C, an easy-to-use Python interface, and a set of tools for set-up and post-simulation data analysis. The paper describes RUMD's main features, optimizations and performance benchmarks.

  73 citations

• Exploring the jamming transition over a wide range of critical densities

  Misaki Ozawa, Ludovic Berthier, Daniele Coslovich

  SciPost Phys. 3, 027 (2017) · published 12 October 2017 | Toggle abstract · pdf

  We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of jamming densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical "J-line", our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.

  52 citations

• Unifying description of the damping regimes of a stochastic particle in a periodic potential

  Antonio Piscitelli, Massimo Pica Ciamarra

  SciPost Phys. 3, 018 (2017) · published 4 September 2017 | Toggle abstract · pdf

  We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Il'in and Khasminskii model, with a novel semi-analytical approach. Our approach gives access to the transient and the asymptotic dynamics in all damping regimes, which are difficult to investigate in the usual Brownian model. We show that the crossover from the overdamped to the underdamped regime is associated with the loss of a typical time scale and of a typical length scale, as signaled by the divergence of the probability distribution of a certain dynamical event. In the underdamped regime, normal diffusion coexists with a non Gaussian displacement probability distribution for a long transient, as recently observed in a variety of different systems. We rationalize the microscopic physical processes leading to the non-Gaussian behavior, as well as the timescale to recover the Gaussian statistics. The theoretical results are supported by numerical calculations and are compared to those obtained for the Brownian model.

  1 citation

• Variation along liquid isomorphs of the driving force for crystallization

  Ulf R. Pedersen, Karolina Adrjanowicz, Kristine Niss, Nicholas P. Bailey

  SciPost Phys. 2, 022 (2017) · published 21 June 2017 | Toggle abstract · pdf

  We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent $\gamma$ in these cases is an increasing function of density, although this cannot be seen in measurements of viscosity or relaxation time.

  2 citations

• Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

  Silvio Franz, Giorgio Parisi, Maksim Sevelev, Pierfrancesco Urbani, Francesco Zamponi

  SciPost Phys. 2, 019 (2017) · published 2 June 2017 | Toggle abstract · pdf

  Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.

  83 citations