A solvable model of quantum random optimization problems

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems.Comment: 4 pages, 3 figures, accepted versio

Simultaneous dynamic characterization of charge and structural motion during ferroelectric switching

Monitoring structural changes in ferroelectric thin films during electric field-induced polarization switching is important for a full microscopic understanding of the coupled motion of charges, atoms and domain walls. We combine standard ferroelectric test-cycles with time-resolved x-ray diffraction to investigate the response of a nanoscale ferroelectric oxide capacitor upon charging, discharging and switching. Piezoelectric strain develops during the electronic RC time constant and additionally during structural domain-wall creep. The complex atomic motion during ferroelectric polarization reversal starts with a negative piezoelectric response to the charge flow triggered by voltage pulses. Incomplete screening limits the compressive strain. The piezoelectric modulation of the unit cell tweaks the energy barrier between the two polarization states. Domain wall motion is evidenced by a broadening of the in-plane components of Bragg reflections. Such simultaneous measurements on a working device elucidate and visualize the complex interplay of charge flow and structural motion and challenges theoretical modelling

The Applegate mechanism in Post-Common-Envelope Binaries: Investigating the role of rotation

Eclipsing time variations (ETVs) are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the O-C diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. We explore the feasibility of driving ETVs via the Applegate mechanism for a sample of PCEB systems, including a range of different rotations. Using the MESA code we evolve 12 stars with different masses and rotation rates. We apply a simple dynamo model to their radial profiles to investigate on which scale the predicted activity cycle matches the observed modulation period, and quantify the uncertainty, and further calculate the required energies to drive que Applegate mechanism. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems, and note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star. The results suggest that the ratio of physical to critical rotation in the main sequence star is an important indicator for the feasibility of Applegate's mechanism, but exploring larger samples will be necessary to probe this hypothesis.Comment: 9 pages, 5 figures. Accepted for publication in A&

Landscapes and Fragilities

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.Comment: 17 pages, 10 figures; accepted version, minor correction

AKLT Models with Quantum Spin Glass Ground States

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered N\'eel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate N\'eel ordering despite the lack of randomness in the coupling strengths.Comment: 10 pages, 1 figur

First-order transitions and the performance of quantum algorithms in random optimization problems

We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase transition. We provide evidence that the gap vanishes exponentially with the system size at the transition. This indicates that the Quantum Adiabatic Algorithm requires a time growing exponentially with system size to find the ground state of this problem.Comment: 4 pages, 4 figures; final version accepted on Phys.Rev.Let

Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions

We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the (heuristic-dependent) largest ratio $\alpha_a$ of constraints per variables for which a search algorithm is likely to find solutions is smaller than the critical ratio $\alpha_d$ above which solutions are clustered and highly correlated. In addition we show that the clustering ratio can be reached when the number k of variables per constraints goes to infinity by the so-called Generalized Unit Clause heuristic.Comment: 15 pages, 4 figures, Proceedings of the International Workshop on Statistical-Mechanical Informatics, September 16-19, 2007, Kyoto, Japan; some imprecisions in the previous version have been correcte

Topological Signature of First Order Phase Transitions

We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In particular, we present the thermodynamics of an analytically solvable mean-field model with a k-body interaction which -depending on the value of k- displays no transition (k=1), second order (k=2) or first order (k>2) phase transition. This rich behavior is quantitatively retrieved by the investigation of a topological invariant, the Euler characteristic, of some submanifolds of the configuration space. Finally, we conjecture a direct link between the Euler characteristic and the thermodynamic entropy.Comment: 6 pages, 2 figure

Hyperfine interaction and electronic spin fluctuation study on Sr2−x_{2-x}Lax_xFeCoO6_6 (x = 0, 1, 2) by high-resolution back-scattering neutron spectroscopy

The study of hyperfine interaction by high-resolution inelastic neutron scattering is not very well known compared to the other competing techniques viz. NMR, M\"ossbauer, PACS etc. Also the study is limited mostly to magnetically ordered systems. Here we report such study on Sr$_{2-x}$La$_x$FeCoO$_6$ (x = 0, 1, 2) of which first (Sr$_2$FeCoO$_6$ with x = 0) has a canonical spin spin glass, the second (SrLaFeCoO$_6$ with x = 1) has a so-called magnetic glass and the third (La$_2$FeCoO$_6$ with x = 2) has a magnetically ordered ground state. Our present study revealed clear inelastic signal for SrLaFeCoO$_6$, possibly also inelastic signal for Sr$_2$FeCoO$_6$ below the spin freezing temperatures $T_{sf}$ but no inelastic signal at all for for the magnetically ordered La$_2$FeCoO$_6$ in the neutron scattering spectra. The broadened inelastic signals observed suggest hyperfine field distribution in the two disordered magnetic glassy systems and no signal for the third compound suggests no or very small hyperfine field at the Co nucleus due to Co electronic moment. For the two magnetic glassy system apart from the hyperfine signal due only to Co, we also observed electronic spin fluctuations probably from both Fe and Co electronic moments. \end{abstract

Can the jamming transition be described using equilibrium statistical mechanics?

When materials such as foams or emulsions are compressed, they display solid behaviour above the so-called `jamming' transition. Because compression is done out-of-equilibrium in the absence of thermal fluctuations, jamming appears as a new kind of a nonequilibrium phase transition. In this proceeding paper, we suggest that tools from equilibrium statistical mechanics can in fact be used to describe many specific features of the jamming transition. Our strategy is to introduce thermal fluctuations and use statistical mechanics to describe the complex phase behaviour of systems of soft repulsive particles, before sending temperature to zero at the end of the calculation. We show that currently available implementations of standard tools such as integral equations, mode-coupling theory, or replica calculations all break down at low temperature and large density, but we suggest that new analytical schemes can be developed to provide a fully microscopic, quantitative description of the jamming transition.Comment: 8 pages, 6 figs. Talk presented at Statphys24 (July 2010, Cairns, Australia