Table of contents

Friction induces unexpected dynamical behaviour. In the paradigmatic pendulum and double-well systems with friction, modelled with differential inclusions, distinct trajectories can collapse onto a single point. Transversal homoclinic orbits display collapse and generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.

We study the steady state of a multiply connected system that is driven out of equilibrium by a sparse perturbation. The prototype example is an N-site ring coupled to a thermal bath, driven by a stationary source that induces transitions with log-wide distributed rates. An induced current arises, which is controlled by the strength of the driving, and an associated topological term appears in the expression for the energy absorption rate. Due to the sparsity, the crossover from linear response to saturation is mediated by an intermediate regime, where the current is exponentially small in , which is related to the work of Sinai on "random walk in a random environment".

We derive exact relations between the Rényi entanglement entropies and the particle-number fluctuations of (connected and disjoint) spatial regions in systems of N non-interacting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.

The work discovers a stochastic bifurcation in delayed systems in the presence of both delay and additive noise. To understand this phenomenon we present a stochastic center manifold method to compute a non-delayed stochastic order parameter equation for a scalar delayed system driven by additive uncorrelated noise. The derived order parameter equation includes additive and multiplicative white and coloured noise. An illustrative neural system with delayed self-excitation reveals stationary states that are postponed by combined additive noise and delay. A final brief analytical treatment of the derived order parameter equation reveals analytically the shift of the stationary states which depends on the delay and the noise strength.

Nonlinear dynamics has provided significant insights into the origin of frequency discrimination and signal amplification underlying mammalian hearing. Existing signal amplification models, however, tend to ignore two basic known aspects of the hearing: spontaneous otoacoustic emissions (SOAEs) and intrinsic dynamical coupling in the cochlea. We construct and study a class of coupled-oscillator models to remedy this deficiency. Our analysis and computations reveal that the interplay and balance between the two aspects can naturally explain the phenomena of frequency discrimination and signal amplification and, more strikingly, the origin of hearing loss, all at a quantitative level. In the presence of SOAEs, there exists a critical coupling threshold below which hearing loss can occur, suggesting enhancement of coupling as a potentially effective therapeutic strategy to restore or even significantly enhance hearing.

The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments M_m=Tr[(t^†t)^m], where t is the transmission matrix, which have a known universal expression for systems without time-reversal symmetry. We present a semiclassical derivation of this universality, based on action correlations that exist between sets of long scattering trajectories. Our semiclassical formula for M_m holds for all values of m and an arbitrary number of open channels. This is achieved by mapping the problem into two independent combinatorial problems, one involving pairs of set partitions and the other involving factorizations in the symmetric group.

The improved quark mass density-dependent (IQMDD) model, which has been successfully used to describe the properties of both infinite nuclear matter and finite nuclei, is applied to investigate the properties of quark deconfinement phase transition. By using the finite temperature quantum field theory, we calculate the finite temperature effective potential and extend the IQMDD model to finite temperature and finite nuclear matter density. The critical temperature and the critical density of nuclear matter are given and the QCD phase diagram is addressed. It is shown that this model can not only describe the saturation properties of nuclear matter, but also explain the quark deconfinement phase transition successfully.

Within the superfield approach, we discuss the two-dimensional noncommutative super-QED. Its all-order finiteness is explicitly shown.

van der Waals-Zeeman transitions between magnetic states of metastable rare-gas atoms Ar^*, Kr^* and Xe^* (³P₂) induced by a solid surface in the presence of a magnetic field, are investigated theoretically and experimentally. By use of a Zeeman slower, metastable argon atoms with various velocities ranging from 170 to 560 m/s allow us to investigate the small impact parameter range (3–7 nm) within which these transitions occur, as well as the effect of atom polarisation on the sharing out of the M states.

Highly accurate electronic-structure calculations for metastable electronic excited states are needed to supplement scant experimental data in screening possible systems for new higher-precision atomic clocks. We test the suitability of relativistic coupled-cluster methods for the low-lying ²F^o excited states of the Yb II ion by computing the ionization potentials (IP) for the ²S_1/2 and ²F^o states of Yb I and the , j = 5/2, 7/2, electric octupole transition amplitudes. The calculations establish a minimum lifetime of six years and of 10^{− 1} s for the ²F^o_7/2 and ²F^o_5/2 states, respectively. In addition, computations for the lifetimes (τ) of its [Xe]4f¹⁴6p(²P^o) states are compared with high-precision experimental data as tests of the accuracy of our predictions. To our knowledge, this is the first relativistic ab initio estimate of the lifetime and ionization potential for the ²F^o states of Yb II, and the results demonstrate the suitability of these methods to aid in screening other candidates for atomic clocks.

We observe a nonlinear optical process in a gas of cold atoms that simultaneously displays the largest reported fifth-order nonlinear susceptibility χ⁽⁵⁾=1.9×10^{− 12} (m/V)⁴ and high transparency. The nonlinearity results from the simultaneous cooling and crystallization of the gas, and gives rise to efficient Bragg scattering in the form of six-wave mixing at low light levels. For large atom-photon coupling strengths, the back-action of the scattered fields influences the light-matter dynamics. We confirm this interpretation by investigating the nonlinearity for different polarization configurations. In addition, we demonstrate excellent agreement between our experimental measurements and a theoretical model with no free parameters, and compare our results to those obtained using alternative approaches. This system may have important applications in many-body physics, quantum information processing, and multidimensional soliton formation.

We report our observations of localized structures in a thin layer of an emulsion subjected to vertical oscillations. We observe persistent holes, which are voids that span the layer depth, and kinks, which are fronts between regions with and without fluid. These structures form in response to a finite amplitude perturbation. Combining experimental and rheological measurements, we argue that the ability of these structures to withstand the hydrostatic pressure of the surrounding fluid is due to convection within their rim. For persistent holes the oscillatory component of the convection generates a normal stress which opposes contraction, while for kinks the steady component of the convection generates a shear stress which opposes the hydrostatic stress of the surrounding fluid.

A universal process for coherent Ghost Imaging (GI) without phase-sensitive detection is presented in this paper. The process is based on the sparsity constraint of the target, which helps to accelerate the information extraction. By taking advantage of this process, the coherent GI scheme with a point-like detector in the test path is improved to achieve higher efficiency and higher resolution, even though the phase information of the random field is lost. This process will contribute to the practical applications, such as Fourier-transform diffraction GI of X-ray, and remote sensing.

Motivated by a recent experiment (Catani J. et al., Phys. Rev. A, 85 (2012) 023623) we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. The amplitudes of breathing oscillations are suppressed by self-trapping, due to interactions with the Bose gas. Further, exciting phonons in the Bose gas leads to damped oscillations and non-Markovian dynamics of the width of the impurity, the degree of which can be engineered through controllable parameters. Our results, supported by simulations, reproduce the main features of the dynamics observed by Catani et al. despite the temperature of that experiment. Moreover, we predict novel effects at lower temperatures due to self-trapping and the inhomogeneity of the trapped Bose gas.

Quantum turbulence, easily generated in superfluid helium, consists of a disordered tangle of thin, discrete vortex lines of quantised circulation which move in a fluid without viscosity. In this report we show that, in very intense quantum turbulence, the vortex tangle contains small coherent vortical structures (bundles of quantised vortices) which arise from the fundamental Biot-Savart interaction between vortices, and which are similar to the intermittent, coherent structures ("worms") observed in ordinary viscous turbulence. Our result highlights the similarity between quantum turbulence and ordinary turbulence, and sheds new light into the origin of the "worms" in ordinary turbulence.

Einstein first applied Riemannian geometry to develop the general theory of relativity almost one hundred years ago and succeeded in understanding astronomical-scale phenomena such as the straining of time-space by a gravitational field. Whether or not Riemannian space affects the electronic properties of condensed matters on a much smaller scale is of great interest. Although Riemannian geometry has been applied to quantum mechanics since the 1950s, nobody has yet answered this question, because the electronic properties of materials with Riemannian geometry have not been examined experimentally. We report here the first observation of Riemannian geometrical effects on the electronic properties of materials such as Tomononaga-Luttinger liquids, which were previously theoretically predicted by our group. We present in situ high-resolution ultraviolet photoemission spectra of a one-dimensional metallic C₆₀ polymer with an uneven periodic peanut-shaped structure.

We have established a simple process that allows for the one-step synthesis of K_xFe_2−ySe₂ single crystals, which exhibit high critical current density J_c. The post annealing and quenching technique has improved the homogeneity of as-grown crystals, resulting in full shielding of the external magnetic field. The quenched crystals show a superconducting transition at T_c^onset=32.9 K and T_c^zero=32.1 K. The upper critical fields _{μ 0}H₀₂ (0) for H||ab and H||c are estimated to be ∼206 and ∼50 T, respectively. The critical current densities J_c for H||ab and H||c reach as high as 1.0×10⁵ and 3.4×10⁴ A/cm² at 5 K. Furthermore, J_c exhibits a high field performance and a significantly weak temperature dependence up to 5 T, suggesting strong pinning. These results demonstrate that K_xFe_2−ySe₂ would be a promising candidate material for practical applications.

We resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of materials with positive and negative refraction indices. Recently, it was numerically discovered that in such structures with weak fluctuations of refractive indices, the localization length L_loc can be enormously large for small wave frequencies ω. Within a new approach allowing us to go beyond the second order of perturbation theory, we derive the expression for L_loc valid for any ω and small variance of disorder, σ²≪1. In the limit ω→0 one gets a quite specific dependence, L⁻¹_loc∝σ⁴ω⁸. Our approach allows one to establish the conditions under which this effect occurs.

The single-layered manganite Pr_0.22Sr_1.78MnO₄ undergoes structural transition from high temperature tetragonal phase to low temperature orthorhombic phase below room temperature. The orthorhombic phase was reported to have two structural variants with slightly different lattice parameters and Mn-3d levels show orbital ordering within both the variants, albeit having mutually perpendicular ordering axis. In addition to orbital ordering, the orthorhombic variants also order antiferromagnetically with different Néel temperatures. Our magnetic investigation on the polycrystalline sample of Pr_0.22Sr_1.78MnO₄ shows large thermal hysteresis indicating the first-order nature of the tetragonal to orthorhombic transition. We observe magnetic memory, large relaxation, frequency-dependent ac susceptbility and aging effects at low temperature, which indicate spin-glass–like magnetic ground state in the sample. The glassy magnetic state presumably arises from the interfacial frustration of orthorhombic domains with orbital and spin orderings playing crucial role toward the competing magnetic interactions.

We study the correlation-induced deformation of Fermi surfaces by means of a new diagrammatic method which allows for the analytical evaluation of Gutzwiller wave functions in finite dimensions. In agreement with renormalization group results we find Pomeranchuk instabilities in two-dimensional Hubbard models for sufficiently large Coulomb interactions.

Density functional theory is used to investigate the interfaces in the non-polar ATiO₃/SrTiO₃ (A=Pb, Ca, Ba) heterostructures. All TiO₂-terminated interfaces show an insulating behavior. By reduction of the O content in the AO, SrO, and TiO₂ layers, metallic interface states develop, due to the occupation of the Ti 3d orbitals. For PbTiO₃/SrTiO₃, the Pb 6p states cross the Fermi energy. O vacancy formation energies depend strictly on the electronegativity and the effective volume of the A ion, while the main characteristics of the interface electronic states are maintained.

We report ultrahigh dielectric and piezoelectric properties in BaTiO₃-xBaSnO₃ ceramics at its quasi-quadruple point, a point where four phases (Cubic-Tetragonal-Orthorhombic- Rhombohedral) nearly coexist together in the temperature-composition phase diagram. At this point, dielectric permittivity reaches ∼75000, a 6–7-fold increase compared with that of pure BaTiO₃ at its Curie point; the piezoelectric coefficient d₃₃ reaches 697 pC/N, 5 times higher than that of pure BaTiO₃. Also, a quasi-quadruple point system exhibits double morphotropic phase boundaries, which can be used to reduce the temperature and composition sensitivity of its high piezoelectric properties. A Landau-Devonshire model shows that four-phase coexisting leading to minimizing energy barriers for both polarization rotation and extension might be the origin of giant dielectric and piezoelectric properties around this point.

Tight-binding electrons on a honeycomb lattice are described by an effective Dirac theory at low energies. Lowering symmetry by an alternate ionic potential (Δ) generates a single-particle gap in the spectrum. We employ the dynamical mean-field theory (DMFT) technique to study the effect of on-site electron correlation (U) on massive Dirac fermions. For a fixed mass parameter Δ, we find that beyond a critical value U_c1(Δ) massive Dirac fermions become massless. Further increasing U beyond U_c2(Δ), there will be another phase transition to the Mott insulating state. Therefore, the competition between the single-particle gap parameter, Δ, and the Hubbard U restores the semi-metallic nature of the parent Hamiltonian. The width of the intermediate semi-metallic regime shrinks by increasing the ionic potential. However, at small values of Δ, there is a wide interval of U values for which the system remains semi-metal. The implication of this result for graphene is that in contrast to a single-particle picture, the on-site Coulomb repulsion makes the Dirac cone spectrum robust against small values of the symmetry breaking parameter Δ.

We investigate the combined effect of Hund's and spin-orbit (SO) coupling on superconductivity in multi-orbital systems. Hund's interaction leads to orbital-singlet spin-triplet superconductivity, where the Cooper pair wave function is antisymmetric under the exchange of two orbitals. We identify three d-vectors describing even-parity orbital-singlet spin-triplet pairings among t_2g-orbitals, and find that the three d-vectors are mutually orthogonal to each other. SO coupling further assists pair formation, pins the orientation of the d-vector triad, and induces spin-singlet pairings with a relative phase difference of π/2. In the band basis the pseudospin d-vectors are aligned along the z-axis and correspond to momentum-dependent inter- and intra-band pairings. We discuss quasiparticle dispersion, magnetic response, collective modes, and experimental consequences in light of the superconductor Sr₂RuO₄.

Metal-ferroelectric-insulator-silicon (MFIS) structures with SrBi₂Ta₂O₉ as ferroelectric thin film and HfO₂ as insulating buffer layer were fabricated by pulsed-laser deposition. The interfaces and memory window of the MFIS structure were investigated. Piezoresponse force microscopy was used to observe the change of domain images in order to investigate the retention characteristics, which demonstrated that the MFIS structure experiences retention loss via a random-walk–type process, identified by a stretched exponential-decay model. The corresponding mechanism was discussed based on the time-dependent depolarization field.

We demonstrate the feasibility to obtain electroluminescence (EL), up to room temperature, from InGaAs self-assembled quantum dots (QDs) included in a forward-biased Schottky diode. Moreover, using a ferromagnet (FM) as the contact layer, sizable circular polarization of the EL emission in the presence of an external magnetic field is obtained. A resonant behavior of the degree of circular polarization (P) as a function of the applied voltage (V), for a given value of magnetic field, is observed. We explain our findings using a model including tunneling of (spin-polarised) holes through the metal-semiconductor interface, transport in the near-surface region of the heterostructure and out-of-equilibrium statistics of the injected carriers occupying the available states in the QD heterostructure. In particular, the resonant P(V) dependence is related to the splitting of the quasi-Fermi level for two spin orientations in the FM.

We present a mode-coupling theory for the dynamics of a tagged particle in a driven granular fluid close to the glass transition. The mean-squared displacement is shown to exhibit a plateau indicating structural arrest. In contrast to elastic hard-sphere fluids, which are solely controlled by volume fraction, the localisation length as well as the critical dynamics depend on the degree of dissipation, parametrized by the coefficient of normal restitution ε. Hence the resulting glassy structure as well as the critical dynamics are nonuniversal with respect to ε.

We propose techniques for computing the angular entropies of DNA sequences, based on the orientations of the dipole moments of the nucleotide bases. The angles of the dipole moment vectors of the bases are used to compute the dipole angular entropy and the Fourier harmonics of the angles are used to compute the dipole angular spectral entropy for a given sequence. We also show that the coding (exons) and noncoding (introns) regions of the DNA can be segregated based on their dipole angular entropies and dipole angular spectral entropies. Segregation using these techniques is found to be computationally faster and more accurate than the previously reported methods. The proposed techniques can also be improvised to use the magnitude of the dipole moments of the bases in addition to the angles.

Recently, Li et al. (Phys. Rev. Lett., 104 (2010) 018701) studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability P_ij∼r_ij^−α, where r_ij is the Manhattan length of the long-range edges. The total length of the additional edges is subject to a cost constraint (). This spatial network model displays an optimal exponent α for transportation (measured by the average shortest-path length). However, we observe that the degree in such spatial networks is homogeneously distributed, which is different from some real networks. In this letter, we propose a method to introduce degree heterogeneity in spatial networks with total cost constraint. Results show that with degree heterogeneity the optimal exponent shifts to a smaller value and the average shortest-path length can further decrease. Moreover, we find the optimal degree heterogeneity for transportation. We further consider the synchronization on the spatial networks and related results are discussed. Our new model may better explain the features of real transportation systems.

Many models are put forward to mimic the evolution of real networked systems. A well-accepted way to judge the validity is to compare the modeling results with real networks subject to several structural features. Even for a specific real network, we cannot fairly evaluate the goodness of different models since there are too many structural features while there is no criterion to select and assign weights on them. Motivated by the studies on link prediction algorithms, we propose a unified method to evaluate the network models via the comparison of the likelihoods of the currently observed network driven by different models, with an assumption that the higher the likelihood is, the more accurate the model is. We test our method on the real Internet at the Autonomous System (AS) level, and the results suggest that the Generalized Linear Preferential (GLP) model outperforms the Tel Aviv Network Generator (Tang), while both two models are better than the Barabási-Albert (BA) and Erdös-Rényi (ER) models. Our method can be further applied in determining the optimal values of parameters that correspond to the maximal likelihood. The experiment indicates that the parameters obtained by our method can better capture the characters of newly added nodes and links in the AS-level Internet than the original methods in the literature.

The recent financial crisis has caused extensive world-wide economic damage, affecting in particular those who invested in companies that eventually filed for bankruptcy. A better understanding of stocks that become bankrupt would be helpful in reducing risk in future investments. Economists have conducted extensive research on this topic, and here we ask whether statistical physics concepts and approaches may offer insights into pre-bankruptcy stock behavior. To this end, we study all 20092 stocks listed in US stock markets for the 20-year period 1989–2008, including 4223 (21 percent) that became bankrupt during that period. We find that, surprisingly, the distributions of the daily returns of those stocks that become bankrupt differ significantly from those that do not. Moreover, these differences are consistent for the entire period studied. We further study the relation between the distribution of returns and the length of time until bankruptcy, and observe that larger differences of the distribution of returns correlate with shorter time periods preceding bankruptcy. This behavior suggests that sharper fluctuations in the stock price occur when the stock is closer to bankruptcy. We also analyze the cross-correlations between the return and the trading volume, and find that stocks approaching bankruptcy tend to have larger return-volume cross-correlations than stocks that are not. Furthermore, the difference increases as bankruptcy approaches. We conclude that before a firm becomes bankrupt its stock exhibits unusual behavior that is statistically quantifiable.

Two-step decay of relaxation functions, i.e., time scale separation between microscopic dynamics and structural relaxation, is the defining signature of the structural glass transition. We show that for glass-forming polymer melts at an attractive surface slow desorption kinetics introduces an additional time scale separation among the relaxational degrees of freedom leading to a three-step decay. The inherent length scale of this process is the radius of gyration in contrast to the segmental scale governing the glass transition. We show how the three-step decay can be observed in incoherent scattering experiments and discuss its relevance for the glass transition of confined polymers by analogy to surface critical phenomena.

Using a combination of first-principles calculations and Monte Carlo simulations, we show that Fe-containing silicates such as olivines naturally offer a way for visualizing tracks left by diffusing vacancies. Fe in its 2+ and 3+ valency states prefers two distinct cation sites in the olivine structure. Vacancies formed at the cationic M sites, cause neighboring Fe ions in their normally occurring Fe²⁺ state to change valency to Fe³⁺, compensating for the charge imbalance and reducing energy costs, consequently altering the local site preference of Fe. Once the vacancy diffuses away, Fe atoms remain stuck in their metastable location producing a microscopic record of the vacancy's trajectory. Our results may be verified using high-resolution transmission electron microscopy, combined with electron energy-loss spectroscopy.