Table of contents

We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.

We study first-order quantum phase transitions in models where the mean-field treatment is exact, and in particular the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.

We show that the periodic modulation of the Hamiltonian parameters for 1D correlated fermionic systems can be used to parametrically amplify their bosonic collective modes. Treating the problem within the Luttinger-liquid picture, we show how charge and spin density waves with different momenta are simultaneously amplified. We discuss the implementation of our predictions for cold atoms in 1D modulated optical lattices, showing that the fermionic momentum distribution directly provides a clear signature of spin-charge separation.

We propose an analysis of the effects introduced by finite accuracy and round-off arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a model we consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has a power law decay, whereas the decay is exponential if a random perturbation is introduced. For chaotic maps the decay is superexponential after an initial plateau and our method is suitable to identify the reliability threshold of numerical results, i.e. a number of iterations below which global errors can be ignored. The same behaviour is observed if a random perturbation is introduced.

Relativistic thermodynamics is generalized to accommodate four-dimensional rotation in a flat spacetime. An extended body can be in equilibrium when each of its elements moves along a Killing flow. There are three types of basic Killing flows in a flat spacetime, each of which corresponds to translational motion, spatial rotation, and constant linear acceleration; spatial rotation and constant linear acceleration are regarded as four-dimensional rotation. Translational motion has been mainly investigated in the past literature of relativistic thermodynamics. Thermodynamics of the other two is derived in the present paper.

Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion equation (with multiplicative noise) through a Hopf-Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We emphasize the importance of the Lyapunov functional as natural starting point for real-space discretization and, in the light of these findings, challenge the mainstream opinion on the relevance of Galilean invariance.

In the Coulomb gauge, the solution to the Maxwell equations for slowly time-varying homogeneous nondispersive conducting linear media without charge source is obtained. We show that the electromagnetic field acquires the extra geometrical Hannay angle associated to the time-dependent generalized harmonic oscillator. The quantization scheme for the electromagnetic field provides a connection between the classical Hannay angle and the quantum adiabatic Berry phase shifts. We confirm that the interference pattern in the optical system is more or less altered by the existence of the geometric phase.

Recently, Bambi suggested a revision of the generalized uncertainty relation, by introducing a term linear in the Planck length. In this note, the black-hole thermodynamics with this revision is discussed in a heuristic manner. Bambi's suggestion may lead to a -type correction to the black-hole entropy. This is a new result, which is distinct from the existing literature on the generalization of the uncertainty principle.

We report on the nature of the thermal-denaturation transition of homogeneous DNA as determined from a renormalisation group analysis of the Peyrard-Bishop-Dauxois model. Our approach is based on an analogy with the phenomenon of critical wetting that goes further than previous qualitative comparisons, and shows that the transition is continuous for the average base-pair separation. However, since the range of universal critical behaviour appears to be very narrow, numerically observed denaturation transitions may look first-order, as it has been reported in the literature.

We investigate irreversibility in a quantum system subject to unitary dynamics as it results from perturbations of the respective Hamiltonian and from the partitioning of the system into subsystems. We use the quantum fidelity as a distance measure of two states. For the whole system, a perturbation induces instability, but no preferred direction in time. We show that an arrow of time, which is an essential feature of irreversibility, shows up only when focusing on a small enough subsystem. This approach is exemplified by a numerical simulation of a finite spin network, for which we see how irreversibility emerges locally from an appropriate partitioning.

We provide canonically invariant expressions to evaluate diagonal matrix elements of powers of the Hamiltonian in a scar function basis set. As a function of the energy, each matrix element consists of a smooth contribution associated with the central periodic orbit, plus oscillatory contributions given by a finite set of relevant homoclinic orbits. Each homoclinic contribution depends, in leading order, on four canonical invariants of the corresponding homoclinic orbit; a geometrical interpretation of these not well-known invariants is given. The obtained expressions are verified in a chaotic coupled quartic oscillator.

We present a model of a quantum conductive fluid which forms as the molecular crystal hydrogen is subjected to melting at megabar pressures. This model explains the recent experimental observations of anomalies in this melting process. The model is founded on the cell approach that takes the contribution of localized states into consideration. We show that, for temperatures below 13000 K, the fluid produced by the melting process may exist in a metastable state with a density ∼2.3 g/cm³, and may possibly retain this state after the depressurization.

In this letter, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. In the usual approach to color superconductivity, the pairing correlations affect only the quasi-particle states of two colors, the single-particle states of the third color remaining unaffected by the pairing correlations. In the theory of color symmetrical superconductivity here proposed, the pairing correlations affect symmetrically the quasi-particle states of the three colors and vanishing net color charge is automatically insured. We stress that the present note is concerned with the description of quark matter in terms of effective models, such as the NJL model, which are solely expressed in terms of fermion operators, so that in them the gluonic gauge fields are not present.

We investigate nanoflows through dilute disordered media by means of joint lattice Boltzmann (LB) and molecular dynamics (MD) simulations —when the size of the obstacles is comparable to the size of the flowing particles— for randomly located spheres and for a correlated particle-gel. In both cases at sufficiently low solid fraction, Φ<0.01, LB and MD provide similar values of the permeability. However, for Φ>0.01, MD shows that molecular-size effects lead to a decrease of the permeability, as compared to the Navier-Stokes predictions. For gels, the simulations highlights a surplus of permeability, which can be accommodated within a rescaling of the effective radius of the gel monomers.

We propose a scheme to generate hyper-entangled photon pairs from single quantum dots (SQDs). Single photons emitted by SQD are manipulated to be entangled after post-selection. Crucially, exciton fine-structure splitting, which was previously deemed undesirable in similar schemes, is used here to produce photon pairs entangled in both frequency and polarization degrees of freedom. This hyper-entangled two-photon state is potentially more powerful than a normal entangled state for quantum state engineering and quantum information processing.

We present a detailed bifurcation structure and associated flow patterns for low–Prandtl-number (P=0.0002, 0.002, 0.005, 0.02) Rayleigh-Bénard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low–Prandtl-number (low-P) convection exhibits similar patterns and chaos as zero-P convection (Pal P. et al., EPL, 87 (2009) 04003) namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier.

Complex shapes can occur through successions of instabilities, like in the growth of chemical gardens, where a semi-permeable membrane precipitates at the interface between a sodium silicate solution and a metal salt. Instead of letting the osmotic pressure during the metal salt dissolution lead the dynamics of the growth, we inject a ferric sulfate solution into a sodium silicate solution, both of controlled concentration, controlling also the other hydrodynamical parameters. Although qualitatively distinct regimes can be obtained, we focus here on a previously unobserved regime where the reactive interface grows in tubular fingering patterns with ocean-ridge-like dynamics: the tubes grow evenly on both sides of a central fracture where the silica deposits continuously. Our experiments show that the whole dynamics is intrinsically related to the precipitation occurring at the interface: the tubes elongation rate remains constant even when the injection rate is varying, but strongly depends on the limiting concentration in injected solution, thus on the reaction rate.

We demonstrate numerically that armchair graphene nanoribbons can support vibrational localized states in the form of surface solitons. Such localized states appear through self-localization of the vibrational energy along the edge of the graphene nanoribbon, and they decay rapidly inside the structure. We find five types of such solitary waves including in-plane and out-of-plane edge breathers and moving envelope solitons.

We address generic behavior of quantum dislocations in almost ideal crystals. It is proven that the combination of arbitrary small Peierls potential and Coulomb-type elastic interaction between dislocation kinks prevents quantum roughening of dislocations. Thermally created kinks induce classical roughening which leads to softening of crystal shear modulus at temperatures comparable to the kink energy. This effect is discussed in the context of the shear modulus softening observed by Day & Beamish in solid ⁴He.

Motivated by experimental results on the dynamic buckling and fragmentation of a vertical column impacted by a falling mass, results from an analytical model for dynamic buckling which considers the dynamic interaction between the axial column deformation and the out-of-plane buckling displacements are used to interpret the fragmentation process and the resulting fragment lengths. It is shown that a critical time exists for the rod to undergo fragmentation. At this critical time, the rod deforms in a modulated pattern of waves, setting up the stage for the ensuing fragmentation as a result of induced large curvatures that exceed the critical bending strain of the rod material. The resulting fragment length distributions, which show two characteristics peaks at and , where λ is a characteristic half-wavelength, are found to compare favorably with the experimental results.

The clustering of elastic-energy density has been investigated when electro hydrodynamic instabilities occur in a nematic liquid crystal, under the action of an external electric field. Statistical properties of clustering have been investigated for different applied voltages and, for the first time, at different depths inside the sample using a confocal fluorescence microscopy technique. The spatial inhomogeneities of elastic-energy density have been characterized through the multifractal evolving set of a coarse-graining energy density in the position space. We found that the probability density of energy fluctuations at small scales strongly deviates from homogeneity, mainly at high applied voltages and far from the surface of the sample, where small-scale structures tend to concentrate due to the lower influence of the anchoring energy, at boundary plates.

The thermal rectification (TR) effect in a topological system, Möbius graphene strip, is studied by nonequilibrium molecular-dynamics simulation with Nóse-Hoover heat baths. Due to the nonlinear interaction in graphene and the topological asymmetry of the Möbius strip, the TR phenomenon emerges and the value of TR can be as large as 120%. This topology-induced TR is not very sensitive to the temperature and size of the system; while the position of heat bath is important, since it can induce additional asymmetry.

We calculate the spectral function of a one-dimensional strongly interacting chain of fermions, where the response can be well understood in terms of spinon and holon excitations. Upon increasing the spin imbalance between the spin species, we observe the single-electron response of the fully polarised system to emanate from the holon peak while the spinon response vanishes. For experimental setups that probe one-dimensional properties, we propose this method as an additional generic tool to aid the identification of spectral structures, e.g. in ARPES measurements. We show that this applies even to trapped systems having cold atomic gas experiments in mind. Calculations of the spectral function in a magnetic field are presented in the full momentum range for the first time.

By means of four-point transport measurements on bulk, high-T_c superconducting samples of composition (Sm_0.33Eu_0.33Gd_0.33)Ba₂Cu₃O_y exhibiting self-organized nanostripes formed by nanoclusters of the light-rare-earth–rich phase, we find that at temperatures close to the transition temperature the currents flowing parallel to the nanostripes are clearly larger than in the perpendicular direction. Constructing a pinning force diagram from the j_c(H_a)-data obtained, we find strong evidence for a dominating δT_c-pinning when the currents are flowing parallel to the nanostripes.

Electronic transport calculations for metallic interfaces based on density functional theory and a scattering theory on the Landauer-Büttiker level are presented. We study the modifications of the transport through Au due to prototypical impurities and interlayers. Our results show that the influence of S and Si impurities is well described in terms of simple vacancies. Metallic impurities and interlayers, on the other hand, have even more drastic effects, in particular when the Au s-d hybrid states at the Fermi energy are perturbed. The effects of a possible interface alloy formation are discussed in detail.

Recently there has been a renewed interest in the charge density wave transition of TiSe₂, fuelled by the possibility that this transition may be driven by the formation of an excitonic insulator or even an excitonic condensate. We show here that the recent ARPES measurements on TiSe₂ can also be interpreted in terms of an alternative scenario, in which the transition is due to a combination of Jahn-Teller effects and exciton formation. The hybrid exciton-phonons which cause the CDW formation interpolate between a purely structural and a purely electronic type of transition. Above the transition temperature, the electron-phonon coupling becomes ineffective but a finite mean-field density of excitons remains and gives rise to the observed diffuse ARPES signals.

The electronic structure and magnetic properties of In₂O₃ with four kinds of intrinsic point defects (O vacancy, In interstitial, O interstitial, and In vacancy) have been theoretically studied using the density functional theory. The defect energy states of the O vacancy and In interstitial are close to the bottom of conduction band and act as shallow donors, while the defect energy states of the In vacancy and O interstitial are just above the top of the valence band and act as shallow acceptors. Without addition of any magnetic ions, all the hole states are completely spin polarized, while the electron states display no spin polarization. This implies that semiconducting In₂O₃ can display magnetic ordering, purely due to the intrinsic defects. However, the formation energies for neutral p-type defects are too high to be thermodynamically stable at reasonable temperatures. Nevertheless, it is shown that negative charging can greatly decrease the formation energies of p-type defects, simultaneously removing the local magnetic moments. We conlcude that and will be the dominant compensating defects as In₂O₃ is doped with TM ions, such as Sn, Mo, V and Cr. This result is consistent with the general view that the p-type defect is a key feature to mediate ferromagnetic coupling between transition metal ions of dilute concentration in metal oxides.

Multilayer structures of nanocrystalline (nc-) SiC/silicon nitride spacer/Ag island films were designed by varying the spacer thickness, and the spectral characteristics of surface-plasmons (SPs)–enhanced photoluminescence (PL) in nc-SiC films have been investigated. The optical transmission spectra show that there are two SPs resonant optical absorption bands in the out-of-plane and in-plane modes for the Ag island film on the sample surface. While PL quenching occurred for the sample with the thinnest spacer, the maximum PL enhancement for nc-SiC is achieved when the thickness of the spacer is suitable, suggesting that the SP enhancement can dominate over nonradiative energy dissipation by varying the spacer thickness. In the case of PL enhancement, the PL excitation spectrum shows an enhancement peak at the resonant wavelength of the out-of-plane mode of SPs, indicating that the excitation enhancement in nc-SiC films occurs due to the incident-light resonant coupling with out-of-plane SPs. Whereas, the increased PL decay rate is observed in the temporal PL spectrum, implying that the SPs scattering enhancement in the nc-SiC film is induced by in-plane SP resonant coupling. In the case of PL quenching, although an enhancement factor less than 1 is observed in the PL excitation spectrum, an increased light emission decay rate is also revealed in the temporal PL spectrum, which indicates that the nonradiative energy dissipation of light emission in the Ag island film is the main coupling mechanism when the spacer is too thin.

A transfer matrix approach to study ballistic charge transport in few-layer graphene with chiral-symmetric stacking configurations is developed. We demonstrate that the chiral symmetry justifies a non-Abelian gauge transformation at the spectral degeneracy point (zero energy). This transformation proves the equivalence of zero-energy transport properties of the multilayer to those of the system of uncoupled monolayers. Similar transformation can be applied in order to gauge away an arbitrary magnetic field, weak strain, and hopping disorder in the bulk of the sample. Finally, we calculate the full-counting statistics at arbitrary energy for different stacking configurations. The predicted gate-voltage dependence of conductance and noise can be measured in clean multilayer samples with generic metallic leads.

We study the effects of Parkinson's disease (PD) on phase synchronisation and cross-modulation of instantaneous amplitudes and frequencies for brain waves during sleep. Analysing data from 40 full-night EEGs (electro-encephalograms) of ten patients with PD and ten age-matched healthy controls we find that phase synchronisation between the left and right hemisphere of the brain is characteristically reduced in patients with PD. Since there is no such difference in phase synchronisation for EEGs from the same hemisphere, our results suggest the possibility of a relation with problems in coordinated motion of left and right limbs in some patients with PD. Using the novel technique of amplitude and frequency cross-modulation analysis, relating oscillations in different EEG bands and distinguishing both positive and negative modulation, we observe an even more significant decrease in patients for several band combinations.

Equations, based on Rayleigh's drag law valid for high Reynolds number, are derived for two-dimensional motion through a compressible atmosphere in isentropic equilibrium, such as characterizes the Earth's troposphere. Solutions yield horizontal and vertical displacement, velocity, and acceleration as a function of altitude and ground-level temperature. An exact analytical solution to the equations linearized in the aero-thermodynamic parameter is given; in general the equations must be solved numerically. The theory, applied to the unpowered fall of a large aircraft stabilized to flat descent by symmetrical, sequential deployment of horizontal and vertical decelerators, shows that such an aircraft can be brought down with mean peak deployment and impact decelerations below 10g.

The elastic properties of double-stranded DNA (ds-DNA) molecules are believed to play an important role in their biological functions. By using a mesoscale model, we construct a simple cylinder-DNA-surface system to explore the radial elastic property of a ds-DNA molecule through a Langevin-dynamics-based computer simulation. The numerical predictions of the radial elastic property are favorable with the recent experimental results. The analysis of the hydrogen bonds and base stacking interaction shows that local conformation transition occurs through the breaking of local hydrogen bonds, and this transition minimizes the inner strain aggregated during compression. This behavior provides an alternative method for studying the local property of ds-DNA, which is expected to be helpful in better understanding the local interaction between ds-DNA and protein, and the mechanics of the short-segment DNA molecule.

We performed a spatiotemporal analysis of a one-dimensional array of airborne geese. The one-dimensional structure of individuals exhibits large fluctuations with backward propagation. In field measurements, we measured properties such as the phase velocity, the dispersion relation, and effective interactions. We also proposed a simplified model for nonlinear wave propagation, which is identical to that for highway traffic flow. Our results strongly imply that fluctuations in the array originate from the excitation of collective modes in its intrinsic dynamics.

We study the continuous-partial-measurement–induced entanglement dynamics of two phase qubits in a superconducting loop coupled by capacity. It is shown that entanglement does not change monotonously during the measurement process, and is robust against small fluctuations of the tunneling probability. We find entanglement sudden birth induced by continuous partial measurement for an initially separable state. Furthermore, we show that with the help of continuous partial measurement an almost pure state can be generated from a totally mixed state.

In this article we reconsider the old mysterious relation, advocated by Dirac and Weinberg, between the mass of the pion, the fundamental physical constants, and the Hubble parameter. By introducing the cosmological density parameters, we show how the corresponding equation may be written in a form that is invariant with respect to the expansion of the Universe and without invoking a varying gravitational "constant", as was originally proposed by Dirac. It is suggested that, through this relation, Nature gives a hint that pions dominate the "content" of the quantum vacuum.