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Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterparts are important for the comprehension of posed problems in quantum optics and quantum chemistry. They consist of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. The wave functions are used to obtain the expectation value of the Hamiltonian. Although it is neither Hermitian nor PT symmetric, the Hamiltonian under study exhibits real values of energy.

We would like to solve the following problem: find a mathematical model formulating I) quantum entanglement, II) particle-wave duality, III) universal objects (ur-sub-Planck objects): to be defined in terms of direct or inverse limits (defined by universal mapping properties) giving microcosm behaviors of space-time so as to give the smooth macrocosm space-time, and IV) the "curved" space-time associated with particles with mass in microcosm consistent with the notion of a light cone in macrocosm. Problems I) and II) are treated in Kato G., Europhys. Lett., 68 (2004) 467. In this paper, we will focus on III) and IV). As a candidate for such a model, we have introduced the category of presheaves over a site called a t-topos. During the last several years, the methods of category and sheaf theoretic approaches have been actively employed for the foundations of quantum physics and for quantum gravity. Particles, time, and space are presheafified in the following sense: a fundamental entity is a triple (m,κ,τ) of presheaves so that for an object V in a t-site, a local datum (m(V),κ(V),τ(V)) may provide a local state of the particle m = m(V), i.e., the localization of presheaf m at V, in the neighborhood (κ(V),τ(V)) of m. By presheafifying matter, space, and time, t-topos can provide sheaf-theoretic descriptions of ur-entanglement and ur-particle and ur-wave states formulating the EPR-type non-locality and the duality in a double-slit experiment. Recall that presheaves m and m' are said to be ur-entangled when m and m' behave as one presheaf. Also recall: a presheaf m is said to be in particle ur-state (or wave ur-state) when the presheaf m is evaluated as m(V) at a specified object V in the t-site (or when an object in the t-site is not specified). For more comments and the precise definitions of ur-entanglement and particle and wave ur-states, see the above-mentioned paper. The applications to a double-slit experiment and the EPR-type non-locality are described in detail in the forthcoming papers Kato G. and Tanaka T., Double slit experiment and t-topos, submitted to Found. Phys. and Kafatos M., Kato G., Roy S. and Tanaka T., The EPR-type non-locality and t-topos, to be submitted to Int. J. Pure Appl. Math., respectively. By the notion of decompositions of a presheaf and of an object of the t-site, ur-sub-Planck objects are defined as direct and inverse limits, respectively, in Definitions 2.1 and 2.4 in what will follow.

In this work we investigate the behavior of two-dimensional (2D) cosmological models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A geometrical term, non-linear in the scalar curvature R, is added to the JT dynamics to test if it could play the role of dark energy in a 2D expanding universe. This formulation makes possible, first, the description of an early (inflationary) 2D universe, when the van der Waals (vdW) equation of state is used to construct the energy-momentum tensor of the gravitational sources. Second, it is found that for later times the non-linear term in R can generate an old 2D universe in accelerated expansion, where an ordinary matter-dominated era evolves into a decelerated/accelerated transition, giving to the dark energy effects a geometrical origin. The results emerge through numerical analysis, following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents.

Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. The evolution of these caustic patterns depends upon the Lyapunov exponents λ₁, λ₂ of the suspended particles, as well as the rate J at which particles encounter caustics. We develop a theory determining the quantities J, λ₁, λ₂ from the statistical properties of the gas flow, in the limit of short correlation times.

A new semiclassical mechanism of multi-dimensional tunneling, which originates in the complexified stable and unstable manifolds of the unstable saddle (or unstable periodic orbit) on top of the potential barrier, causes a remarkable plateau-like structure in the tunneling spectrum. Such a mechanism is very universal and works when the instanton mechanism breaks down due to the strong coupling between the degrees of freedom.

The detection of the interrelation between non-stationary time series is a key problem unsolved in the analysis of practical data. Here we present a novel approach to detect the phase locking of time series in non-stationary status, which does not need the reconstruction of the attractor but gets information from the consistence of local rotation speeds. This method can be conveniently used for practical situations, such as the epileptic seizure.

We consider the dynamics of systems of self-propelling particles with kinematic constraints on the velocities. A continuum model for a discrete algorithm used in works by Vicsek et al. is proposed. For a case of planar geometry, finite-flocking behavior is obtained. The circulation of the velocity field is found not to be conserved. The stability of ordered motion with respect to noise is discussed.

We theoretically investigate the mechanical effect of the light-induced dipole-dipole interaction potential on the atoms in a Bose-Einstein condensate. We present numerical calculations on the magnitude and shape of the induced potentials for different experimentally accessible geometries. It is shown that the mechanical effect can be distinguished from the effect of incoherent scattering for an experimentally feasible setting.

By quantitative studies of statistics of polymer stretching in an elastic turbulence and the statistical properties of this random flow itself that are characterized by the average Lyapunov exponents of particle pair separations, , we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition. The experimental value of the onset of the coil-stretch transition, _cr·τ = 0.77 ± 0.20, where τ is the polymer relaxation time, is found to be rather close to the theoretically predicted one.

High-pressure X-ray diffraction, Mössbauer, and Raman studies in the antiferromagnetic insulators RFeO₃ orthorhombic perovskites (R = Pr, Eu, Lu) disclose an unusual phenomena of a reversible first-order isostructural phase transition around 50 GPa concurring with an abrupt ∼ 5% volume decrease. It is shown experimentally that this transformation concurs with, and is driven by, a high-to-low-spin transition taking place in Fe³⁺; a manifestation of a new kind of isostructural phase transition. These studies suggest that the RFeO₃ perovskite is a rather sturdy oxide-structure, maintaining its original structural symmetry beyond 125 GPa.

The dynamic dislocation-solute interaction is studied through a system integration method where a feedback mechanism is introduced to characterize the competition of pinning and depinning effects. The results self-consistently exhibit three branches of the interaction, two stable branches at low and high strain rate (or dislocation velocity) which correspond to the effective pinning or unpinning of dislocation, respectively, and a metastable one at the intermediate strain rate where negative strain rate sensitivities result from dynamic strain ageing. This unified description should be helpful to the studies of rate-softening plastic instability.

We study experimentally the slow growth of a single crack in polycarbonate films submitted to uniaxial and constant imposed stress. The specificity of fracture in polycarbonate films is the appearance of flame-shaped macroscopic process zones at the tips of the crack. Supported by an experimental study of the mechanical properties of polycarbonate films, an analysis of the stress dependence of the mean ratio between the process zone and crack lengths, during the crack growth, shows a quantitative agreement with the Dugdale-Barenblatt model of the plastic process zone. We find that the fracture growth curves obey strong scaling properties that lead to a well-defined growth master curve.

Relaxor ferroelectrics (RF) are characterized by diffuse ferroelectric transitions and high and frequency-dependent dielectric susceptibilities. Non-RFs show high dielectric responses only in the direct vicinity of the transition temperature whereas RFs exhibit high responses over a large temperature range. Despite their long history, the microscopic origin of RFs is still unknown due to their structural complexity. RF behaviour is exclusively observed in nonstoichiometric, mixed ion systems, and represents a composite of dielectrically soft matrix and highly polarizable doped ions. Here we propose a multi-component scenario with intrinsic inhomogeneity, which shows that spatially localized excitations (discrete breathers) coupled to the soft matrix yield a self-consistent multi-length scale response and successfully explains the relaxor ferroelectric behaviour.

Numerical simulation is employed to study dynamical heterogeneities in model monoatomic harmonic glasses, whose atoms interact trough the Lennard-Jones potential. Soft and hard vibrational heterogeneities are observed, and a temperature effect on these heterogeneities is found. A method is proposed to evaluate the size of the heterogeneities.

We present molecular-dynamics simulations on 1,4-polybutadiene performed ≈ 20 K above the glass transition T_g and relate them to measurements of the dynamic structure factor obtained by neutron spin echo spectroscopy. In real space the simulation data display two well-separated dynamical processes: anomalous diffusion and local hopping. A real-space analysis allows a unique identification of both processes. The obtained results lead to a rationalization of most of the various and very different experimental results reported so far in this system and facilitate a general understanding of why close to T_g the local dynamics may globally dominate the dynamic structure factor.

Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi–two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-sphere suspension using a Monte Carlo method to evaluate thermodynamic equations of state. Coexisting phases are determined for systems in constrained- and full-equilibrium states that correspond to different stages of film relaxation.

We present theoretical and experimental data concerning the possibility of inducing in Pd properties characteristic of a noble metal. A free-standing Pd(100) monolayer expanded to the lattice constant of 3.30 Å exhibits an atomic-like electronic structure, having its d-valence states almost full, like the noble metals Cu, Ag or Au. To prevent de-population of the d-states, we deposit the Pd ML on a Nb(100) substrate passivated by a pseudomorphic S monolayer. The weak interaction with the S-capped Nb(100) surface causes the centre of the d-states of the Pd monolayer to lie much closer to the Fermi level than in bulk Pd. As a result, the weakly bonded Pd monolayer becomes more reactive than bulk Pd. However, when Pd is deposited directly on the Nb(100) surface, the strong, direct bonds between Pd and Nb push the d-band centre of the monolayer toward lower binding energies, resulting in Pd reactivity comparable to that of the noble metal Ag.

The transport properties of a homogenous perovskite oxide p-n junction composed of the p-type In-doped SrTiO₃ and n-type Nb-doped SrTiO₃ have been studied by solving one-dimensional steady-state carrier-transport equations based on the drift-diffusion model. The energy band profile, electric-field intensity, and charge density are obtained for the space charge region at various bias voltages. Furthermore, the rectifying characteristics of the I-V curves are calculated and analyzed as a function of doping density. The theoretical results are in good agreement with the experimental data, and more details in the understanding of transport mechanism for oxide p-n junctions have been gained.

Using one-loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits non-trivial two-time dynamical regimes with exponents and scaling functions obtained in a dimensional expansion. The aging and equilibrium dynamics of the super-rough glass phase of the random Sine-Gordon model at low temperature is found to be characterized by a single dynamical exponent z ≈ c/T, where c compares well with recent numerical work. This agrees with the thermal boundary layer picture of pinned systems.

When a ferromagnet is in proximity to an antiferromagnet, lateral length scales such as the respective magnetic domain sizes drastically affect the exchange bias. Bilayers of FeF₂ and either Ni, Co or Fe are studied using SQUID and spatially resolved MOKE. When the antiferromagnetic domains are larger than or comparable to the ferromagnetic domains, a local, non-averaging exchange bias is observed. This gives rise to unusual and tunable magnetic hysteresis curves.

Upon the addition of multivalent cations, a giant DNA chain exhibits a large discrete transition from an elongated coil into a folded compact state. We performed single-chain observation of long DNAs in the presence of a tetravalent cation (spermine), at various temperatures and monovalent salt concentrations. We confirmed that the compact state is preferred at higher temperatures and at lower monovalent salt concentrations. This result is interpreted in terms of an increase in the net translational entropy of small ions due to ionic exchange between higher and lower valence ions.

This experiment presents a new approach to measure elasticity parameters of lipid bilayers. We have deposited a stack of phospholipid bilayers on a silicon surface grating defined by e-beam lithography. The periodic surface profile acts as a boundary condition which imposes a controlled strain in the smectic film. Probing this distortion field by neutron reflectometry, we determine the smectic penetration length Λ = (K/B)^1/2 from the relative intensity of the satellite peaks.

We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time causing local overloads that drive the dynamic evolution of the network topology. Our model displays a transition from a fully connected network to a configuration with a non-trivial topology and where global failures are suppressed. The most efficient topology is characterized by an exponential degree distribution, in agreement with the topology of the real electric grid. The model intrinsically presents self-induced break-down events, which can be thought as representative of real black-outs.

We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show that whether the transition from a low-traffic regime to a congested phase is of first- or second-order type is determined by the protocol at work. The microscopic dynamics reveals that these two radically different behaviors are due to the way in which traffic jams propagate through the network. Our results are discussed in the context of Internet dynamics and other transport processes that take place on complex networks and provide insights for the design of routing policies based on traffic awareness in communication systems.

We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power law profile, as opposed to a fractal model, can account for the observed power law galaxy-galaxy correlations. We conclude that such model, which can actually be considered as a degenerate multifractal model, is not realistic but suggests a new picture of multifractal models, namely, as sets of fractal distributions of haloes. We analyse, according to this picture, the properties of the matter distribution produced in cosmological N-body simulations, with affirmative results; namely, haloes of similar mass have a fractal distribution with a given dimension, which grows as the mass diminishes.