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SciPost Physics

SciPost Physics Vol. 2 issue 3 (May - June 2017)

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Emergent Gravity and the Dark Universe

Erik P. Verlinde

SciPost Phys. 2, 016 (2017) · published 16 May 2017 | · pdf

Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional 'dark' gravitational force describing the 'elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale $a_0$ =$cH_0$, and provide evidence for the fact that this additional 'dark gravity force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Multiscale response of ionic systems to a spatially varying electric field

Jesper Schmidt Hansen

SciPost Phys. 2, 017 (2017) · published 27 May 2017 | · pdf

In this paper the response of ionic systems subjected to a spatially varying electric field is studied. Following the Nernst-Planck equation, two forces driving the mass flux are present, namely, the concentration gradient and the electric potential gradient. The mass flux due to the concentration gradient is modelled through Fick's law, and a new constitutive relation for the mass flux due to the potential gradient is proposed. In the regime of low screening the response function due to the potential gradient is closely related to the ionic conductivity. In the large screening regime, on the other hand, the response function is governed by the charge-charge structure. Molecular dynamics simulations are conducted and the two wave vector dependent response functions are evaluated for models of a molten salt and an ionic liquid. In the low screening regime the response functions show same wave vector dependency, indicating that it is the same underlying physical processes that govern the response. In the screening regime the wave vector dependency is very different and, thus, the overall response is determined by different processes. This is in agreement with the observed failure of the Nernst-Einstein relation.
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains

Yingfei Gu, Andrew Lucas, Xiao-Liang Qi

SciPost Phys. 2, 018 (2017) · published 28 May 2017 | · pdf

We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong coupling limit. We find $D\le v_{\text{B}}^2 \tau_{\text{L}}$ from a combination of analytical and numerical approaches. Our example necessitates the sharpening of postulated transport bounds based on quantum chaos.
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 | · 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.
Emergence of quasiparticle Bloch states in artificial crystals crafted atom-by-atom

Jan Girovsky, Jose L. Lado, Floris E. Kalff, Eleonora Fahrenfort, Lucas J. J. M. Peters, Joaquín Fernández-Rossier, Alexander F. Otte

SciPost Phys. 2, 020 (2017) · published 14 June 2017 | · pdf

The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of the tight-binding model, however not many experimental approaches exist that allow to tailor artificial crystal lattices using a bottom-up approach. The ability to engineer and study atomically crafted designer materials by scanning tunnelling microscopy and spectroscopy (STM/STS) helps to understand the emergence of material properties. Here, we use atom manipulation of individual vacancies in a chlorine monolayer on Cu(100) to construct one- and two-dimensional structures of various densities and sizes. Local STS measurements reveal the emergence of quasiparticle bands, evidenced by standing Bloch waves, with tuneable dispersion. The experimental data are understood in terms of a tight-binding model combined with an additional broadening term that allows an estimation of the coupling to the underlying substrate.
Integrable Floquet dynamics

Vladimir Gritsev, Anatoli Polkovnikov

SciPost Phys. 2, 021 (2017) · published 16 June 2017 | · pdf

We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finite-dimensional Lie groups and infinite-dimensional generalization thereof. The second class is related to the row transfer matrices of the 2D statistical mechanics models. The third class of models, called here "boost models", is constructed as a periodic interchange of two Hamiltonians - one is the integrable lattice model Hamiltonian, while the second is the boost operator. The latter for known cases coincides with the entanglement Hamiltonian and is closely related to the corner transfer matrix of the corresponding 2D statistical models. We present several explicit examples. As an interesting application of the boost models we discuss a possibility of generating periodically oscillating states with the period different from that of the driving field. In particular, one can realize an oscillating state by performing a static quench to a boost operator. We term this state a "Quantum Boost Clock". All analyzed setups can be readily realized experimentally, for example in cold atoms.
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 | · 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.