Table of contents

We construct multipartite entangled states with underlying W-type structure satisfying positive partial transpose (PPT) condition under any (N- 1)|1 partition. Then we show how to distill a N-partite secure key from the states using two different methods: direct application of local filtering and novel random key distillation scheme in which we adopt the idea from recent results on entanglement distillation. Open problems and possible implications are also discussed.

Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks.

We analyze —for a large set of stocks comprising four financial indices— the annual logarithmic growth rate R and the firm size, quantified by the market capitalization MC. For the Nasdaq Composite and the New York Stock Exchange Composite we find that the probability density functions of growth rates are Laplace ones in the broad central region, where the standard deviation σ(R), as a measure of risk, decreases with the MC as a power law σ(R)∼(MC)^{- β}. For both the Nasdaq Composite and the S&P 500, we find that the average growth rate ⟨R⟩ decreases faster than σ(R) with MC, implying that the return-to-risk ratio ⟨R⟩/σ(R) also decreases with MC. For the S&P 500, ⟨R⟩ and ⟨R⟩/σ(R) also follow power laws. For a 20-year time horizon, for the Nasdaq Composite we find that σ(R) vs. MC exhibits a functional form called a volatility smile, while for the NYSE Composite, we find power law stability between σ(r) and MC.

It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schrödinger equation that reveals how non-Markovian effects are manifested in statistical correlations between different realizations of the process. Moreover, we demonstrate that possible violations of the positivity of approximate master equations are closely connected to singularities of the stochastic Schrödinger equation, which could lead to important insights into the structural characterization of positive non-Markovian equations of motion.

We estimated the polarization contribution of Coulomb energy to the spacing between the ground and first excited state of the ²²⁹Th nucleus as a function of the deformation parameter δ. We show that despite the fact that the odd particle is a neutron, the change in Coulomb energy ΔU_C between these two states can reach several hundreds keV from this contribution. This means that the effect of the variation of the fine-structure constant may be enhanced ΔU_C/E∼10⁴ times in the E=7.6 eV "nuclear clock" transition between the ground and first excited states in the ²²⁹Th nucleus. To extract the full value of ΔU_C, we propose to measure isomeric shift of atomic levels and nuclear electric quadrupole moments in ²²⁹Th.

As a model of decohering environment, we show that a quantum chaotic system behaves equivalently as a many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of the decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is an efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.

We propose an architecture for quantum computing based on superconducting circuits, where on-chip planar microwave resonators are arranged in a two-dimensional grid with a qubit at each intersection. This allows any two qubits on the grid to be coupled at a swapping overhead independent of their distance. We demonstrate that this approach encompasses the fundamental elements of a scalable fault-tolerant quantum-computing architecture.

We considered spin-two gauge boson production in the fermion pair annihilation process and calculated the polarized cross-sections for each set of helicity orientations of initial and final particles. Adding up all sixteen amplitudes and averaging over the initial particle spins, we obtained the unpolarized cross-section. The angular dependence of these cross-sections is compared with the similar annihilation cross-sections in QED with two photons in the final state, with two gluons in QCD and W-pair in the electroweak theory.

We perform a statistical analysis with the prospective results of future experiments on neutrino-less double beta decay, direct searches for neutrino mass (KATRIN) and cosmological observations. Realistic errors are used and the nuclear matrix element uncertainty for neutrino-less double beta decay is also taken into account. Three benchmark scenarios are introduced, corresponding to quasi-degenerate, inverse hierarchical neutrinos, and an intermediate case. We investigate to what extent these scenarios can be reconstructed. Furthermore, we check the compatibility of the scenarios with the claimed evidence of neutrino-less double beta decay.

We present a universal form of the T-matrices renormalized in nonperturbative regime and the ensuing notions and properties that fail conventional wisdoms. A universal scale is identified and shown to be renormalization group invariant. The effective range parameters are derived in a nonperturbative scenario with some new predictions within the realm of contact potentials. Some controversies are shown to be due to the failure of conventional wisdoms.

Decaying turbulence in a shallow flow is shown to be characterized by the emergence of long-lived meandering currents, which are closely related to pronounced vertical flows inside the shallow layer. These vertical flows are concentrated in regions that are dominated either by vorticity or by strain of the flow field. Upwelling of fluid is observed in patch-like domains near elliptic points. Downward flow takes place close to hyperbolic points where the hyperbolic nature of the streamlines leads to thin, elongated regions of intense downwelling. The latter results in long, contracting regions in the free-surface flow. Particles that float on the liquid surface will congregate in these strain-dominated regions, thus lining out the large-scale meandering streams.

We succeeded in obtaining propulsion of an aluminum bullet by a gigawatt nanosecond pulse Nd:glass laser, in which we demonstrated the effectiveness of a simple double-confined structure that consists of a thin black-paint coat covered with a glass board as a transparent overlay. The black-paint coat not only serves as a substitute for the target to be ablated, but also improves the absorbency of the incident laser energy. Another main feature of this structure is that it can lead to the enhancement of the coupling coefficient due to plasma confinement and impedance mismatch. Adopting this simple double-confined structure, a coupling coefficient up to 160 dyne/W was achieved, which was enhanced by about 20 times with respect to direct ablation.

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddle-splay modulus of a simple fluid interface.

Material-specific atomistic aspects of brittle fracture are studied for the first time for a complex metallic compound with realistic embedded-atom-method potentials. Crack propagation occurs on an atomic level by a successive rupture of cohesive bonds. In many theoretical models of fracture, however, a coarse-grained approach is applied and the explicit influence of the discrete nature of matter is not taken into account. In this paper, numerical experiments on the complex metallic compound NbCr₂ are presented to illustrate why it is necessary to perform atomistic simulations to understand the details of fracture behaviour: the number, strength and orientation of bonds approached by a crack determine whether, where and how it propagates.

We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic one. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with q>2 arises. This observation is used to interpret a number of previous results.

The generation of nanoscale square and stripe patterns is of major technological importance since they are compatible with industry-standard electronic circuitry. Recently, a blend of diblock copolymer interacting via hydrogen bonding was shown to self-assemble in square arrays. Motivated by those experiments we study, using Monte Carlo simulations, the pattern formation in a two-dimensional binary mixture of colloidal particles interacting via isotropic core-corona potentials. We find a rich variety of patterns that can be grouped mainly in aggregates that self-assemble in regular square lattices or in alternate strips. Other morphologies observed include colloidal corrals that are potentially useful as surface templating agents. This work shows the unexpected versatility of this simple model to produce a variety of patterns with high technological potential.

The zero-temperature ferromagnetic phase of distorted perovskite manganites at low doping is studied as a function of lattice parameters and screened ionic charges using the two-orbital model. The dependence in the Mn-O distance of the anisotropic hopping terms is calculated numerically for La_1−xSr_xMnO₃. It is shown that the e_g state is dominated by the 3z²-r² type orbital. For bandwidths comparable to Hund's rule coupling we find partially spin-polarized e_g bands at small doping levels, in agreement with experimental observations using Andreev reflection. We also find small but consistent results for the static Jahn-Teller distortion at small doping. The connection of our solution to electron correlation effects is discussed.

A theory of combined exciton-cyclotron resonance in the quantum well structures is developed for a strong magnetic field. The absorption band structure is calculated for optical quantum transitions with circularly polarized radiation creating a two-dimensional exciton and simultaneously exciting one of the resident electrons from the lowest to the first Landau level. The dipole-active transitions are considered in the second-order perturbation theory taking into account as perturbations the electron-photon interaction and the electron-electron Coulomb interaction. In agreement with the experimental observation it is shown that for σ^- polarized light the probability of quantum transition is four times larger than for σ⁺ light polarization.

On the one hand, in one dimension the coupling of electrons to phonons leads to a transition from a metallic to a Peierls distorted insulated state if the coupling exceeds a critical value. On the other hand, in two dimensions the electron-phonon interaction may also lead to the formation of Cooper pairs. In this letter, we study for two dimensions the competing influence of superconductivity and charge order (in conjunction with a lattice distortion) by means of the projector-based renormalization method (PRM). In this way, we can not only approach correlation functions of superconductivity and charge density wave but also have direct access to the order parameters. Increasing the electron-phonon interaction, we find a crossover behavior between a purely superconducting state and a charge-density wave where a well-defined parameter range of coexistence of superconductivity and lattice distortion exists.

We study the dynamical interplay between ferroelectricity and magnetism in a multiferroic with a helical magnetic order. We show that the dynamical exchange-striction induces a biquadratic interaction between the spins and transverse phonons resulting in quantum fluctuations of the spontaneous ferroelectric polarization P in the ferroelectric phase. The hybridization between the spin wave and the fluctuation of the electric polarization leads to low-lying transverse phonon modes. Those are perpendicular to P and to the helical spins at small wave vector but then turn parallel to P at a wave vector close to the magnetic modulation vector. For helical magnetic structure, the spin chirality which determines the direction of P, also possesses a long-range order. Due to the dynamical Dzyaloshiskii-Moriya interaction, the spin chirality is strongly coupled to the spin fluctuation which implies an on-site inversion of the spin chirality in the ordered spin-(1/2) system and results in a finite scattering intensity of polarized neutrons from a cycloidal helimagnet.

The relativistic Landau levels in the layered organic material α-(BEDT-TTF)₂I₃ (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) are sensitive to the tilt of the Dirac cones, which, as in the case of graphene, determine the low-energy electronic properties under appropriate pressure. We show that an applied in-plane electric field, which happens to be in competition with the tilt of the cones, lifts the twofold valley degeneracy due to a different level spacing. This scenario may be tested in infrared transmission spectroscopy.

For strips of width 2w and height h, with both exchange and the dipole-dipole interaction, we find that Néel and Bloch domain walls are locally stable. As h is increased to h_c, Néel walls evolve continuously to Bloch walls by a second-order transition. It is mediated by a critical mode with , corresponding to motion of the domain wall center. A uniform out-of-plane rf-field couples strongly to this critical mode only in the Néel phase. Local, but not global stability relative to a crosstie phase was established.

Pairing symmetry is important to indentify the pairing mechanism. The analysis becomes particularly timely and important for the newly discovered iron-based multi-orbital superconductors. From the group theory point of view we classified all pairing matrices (in the orbital space) that carry irreducible representations of the system. The quasiparticle gap falls into three categories: full, nodal and gapless. The nodal-gap states show conventional Volovik effect even for on-site pairing. The gapless states are odd in the orbital space, have a negative superfluid density and are therefore unstable. In connection to experiments we proposed possible pairing states and implications for the pairing mechanism.

We present an analysis of waiting time distributions of consecutive single-electron transfers through a double-quantum-dot Aharonov-Bohm interferometer. Waiting time distributions qualitatively indicate the presence of interferences and provide information on orbital-detuning and coherent interdot-electron transfer. The frequencies of interdot-transfer–induced oscillations are Aharonov-Bohm phase sensitive, while those due to level detuning are phase independent. The signature of the quantum interference in the waiting-time distribution is more apparent for weakly coupled electron transfer detectors.

We introduce a valence bond dynamical mean-field theory of doped Mott insulators. It is based on a minimal cluster of two orbitals, each associated with a different region of momentum space and hybridized to a self-consistent bath. The low-doping regime is characterized by singlet formation and the suppression of quasiparticles in the antinodal regions, leading to the formation of Fermi arcs. This is described in terms of an orbital-selective transition in reciprocal space. The calculated tunneling and photoemission spectra are consistent with the phenomenology of the normal state of cuprates. We derive a low-energy description of these effects using a generalization of the slave-boson method.

We investigate the superconducting transition temperature of epitaxial La_0.7Sr_0.3MnO₃/YBa₂Cu₃O₇/ La_0.7Sr_0.3MnO₃ (LSMO/YBCO/LSMO) trilayers as a function of the magnetic field parallel to the layer structure. In these structures, the magnetic moment of the half-metallic ferromagnet LSMO is parallel to the plane of the film. The coercivity- and saturation field of the top and bottom LSMO layer could be independently tuned by adjusting their thickness. The application of a magnetic field increased the superconducting transition temperature by about 1.6 K with respect to the demagnetized state of the LSMO. Three possible mechanisms of the enhancement are considered. These are the stray fields due to domain walls, spin polarization of the current, and the formation of an odd triplet superconducting state.

We study the formation and structure of stable electrostatic complexes between oppositely charged polyelectrolytes, a long polymethacrylic acid and a shorter polyethylenimine, at low pH, where the polyacid is weakly charged. We explore the phase diagram as a function of the charge and concentration ratio of the constituents. In agreement with theory, turbidity and ζ potential measurements show two distinct regimes of weak and strong complexation, which appear successively as the pH is increased and are separated by a well-defined limit. Weak complexes observed by neutron scattering and contrast matching have an open, non-compact structure, while strong complexes are condensed.

We have studied the impact of the hole shape on the growth of Ge dots. Si substrates that have been templated by means of electron beam lithography and reactive ion etching have been used to grow Si buffer layers at different substrate temperatures by molecular-beam epitaxy. Atomic-force-microscopy studies show that for high substrate temperatures, the prepatterned holes are smeared out. A model has been employed to quantitatively analyze the smearing out of the holes. The study further shows that the shape of the holes has a substantial impact on the morphology of the subsequently grown Ge dots, i.e. Ge dots grown in smeared out holes show a tendency towards an inhomogeneous size distribution and the formation of multiple dots in one hole.

Radar-absorbing structures having foam-based honeycomb sandwich structures (FBHSS) were fabricated through a conventional foaming technique. Conductive fillers such as carbonyl iron/nickel fibers (CINF) and magnetic metal micropowder (MMP) were added to polyurethane foams so as to efficiently increase the absorbing capacity of FBHSS. A honeycomb sandwich structure, which was made of composite face sheets and foam cores, was used as a supporter to enhance mechanical strength. A matching layer made of nanotitanium powder and hydrogenation acrylonitrile-butadiene rubber composites was used for the face sheet, which allows the incident electromagnetic wave to enter and largely get attenuated through the absorbing system. Polyurethane foams containing CINFs and MMP of which a suitable content contributing to a broad bandwidth and high loss, were used as the core material. The measurement results show reflection loss was less than -10 dB over the frequency range of 3–18 GHz, which has a minimum value of - 26 dB at 14.2 GHz.

The dynamics of a tri-dimensional dense granular packing under gravity and vertical tapping is numerically investigated in a stationary state. A slowing-down of the dynamics is observed close to the bottom of the packing with a correlation length of 5–6d. In this perturbed zone, the self-intermediate scattering function, decaying slower than exponentially, suggests the existence of a heterogeneous dynamics. A characteristic time scale of the dynamics depending on the distance from the bottom of the packing is extracted. Our numerical results open the way to a systematic study of the influence of external driving force and of boundary conditions on the heterogeneity of the dynamics of granular packings under gravity.

We study the effect of electron-electron interactions in the quasiparticle dispersion of a graphene bilayer within the Hartree-Fock-Thomas-Fermi theory by using a four-bands model. We find that the electronic fluid can be described by a non-interacting–like dispersion but with renormalized parameters. We compare our results with recent cyclotron resonance experiments in this system.

We present results from our simulations of biopolymer translocation in a solvent which explain the main experimental findings. The forced translocation can be described by simple force balance arguments for the relevant range of pore potentials in experiments and biological systems. Scaling of translocation time with polymer length varies with pore force and friction. Hydrodynamics affects this scaling and significantly reduces translocation times.

We analyze handwriting records from several school children with the aim of characterizing the fluctuating behavior of the writing speed. It will be concluded that remarkable differences exist between proficient and dysgraphic handwritings which were unknown so far. It is shown that in the case of proficient handwriting, the variations in handwriting speed are strongly autocorrelated within times corresponding to the completion of a single character or letter, while become uncorrelated at longer times. In the case of dysgraphia, such correlations persist on longer time scales and the autocorrelation function seems to display algebraic time decay, indicating the presence of strong anomalies in the handwriting process. Applications of the results in educational/clinical programs are envisaged.

A Bayesian analysis of rare-event time series is presented. The model space for the description of the time series of Caribbean hurricanes includes a constant Poisson rate, a rate varying linearly in time and a rate described by a change point function. Bayesian model probabilities for the tropical systems of the Bermudas, Bahamas, and East and West Caribbean regions are calculated. For the Bahamas data also model probabilities for the three different hurricane intensity classes (h₃+h₄+h₅), (h₁+h₂) and tropical storms are obtained. All results show that inclusion of a nonlinear not necessarily monotonic model function is mandatory for proper data representation. For the Bahamas we calculate also predictive distributions of the Poisson rate from which the probabilities of H events in the years 2008 and 2015 are deduced. These data find application in future risk assessment in the insurance industry.