Table of contents

Using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, one can show that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs on an arbitrary large finite domain in dimension d are the same as in the one-dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.

We present three types of dark solitons in quasi–one-dimensional spin-orbit coupled repulsive Bose-Einstein condensates. Among these families, two are always stable, while the third one is only stable sufficiently close to the linear regime. The solitons' excitation spectra reveal the potential existence of a second anomalous mode. While the first such mode describes the soliton oscillatory motion in a parabolic trap, the second, when present, reflects the double-well structure of the underlying single-particle spectrum. This novel mode results in moving density stripes in the vicinity of the soliton core, or in an out-of-phase oscillation of the constituent components, with little effect on the nearly stationary striped total density of the composite soliton.

By using a quantum Hamiltonian system with classically chaotic dynamics, we demonstrate that it is possible to propagate waves, at a semiclassical level, for extremely long times of the order of the Heisenberg time. We achieve this unexpected result with a new formula that evaluates the autocorrelation function of a quantum state living in the neighborhood of a short periodic orbit, the so-called resonance, in terms of the set of homoclinic orbits; this set is given by the intersection of the stable and unstable manifolds of the periodic orbit. Here we study the manifolds of the shortest periodic orbit of the hyperbola billiard (a chaotic Hamiltonian system), finding a surprisingly simple tree structure. Then, we compute a complete set consisting of the first 18 146 homoclinic orbits, and by using this data we analyze the convergence of the new formula. Finally, we compare the quantum and semiclassical autocorrelation of resonances up to the Heisenberg time, obtaining a relative error O(ℏ) in correspondence with semiclassical predictions.

We study the quantum Goos-Hänchen (GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor $(E_F/\Delta)$, with E_F the Fermi energy and Δ the gap. Interestingly, the GH effect appears only as a time delay $\delta t$ without any lateral shift, and the corresponding delay length is about $(E_F/\Delta)\lambda_F$, with $\lambda_F$ the Fermi wavelength. This makes the NS interface "sticky" when $\Delta \ll E_F$, since typically GH effects are of wavelength order. This "sticky" behavior can be further enhanced by a resonance mode in the NSNS interface. Finally, for a large Δ, the resonance-mode effect makes a transition from the Andreev to the specular reflection as the width of the sandwiched superconductor is reduced.

We investigate the decoherence effect of a bosonic bath on the Berry phase of a spin-$\frac{1}{2}$ in a time-dependent magnetic field, without making the Markovian approximation. A two-cycle process resulting in a pure Berry phase is considered. The low-frequency quantum noise significantly affects the Berry phase. In the adiabatic limit, the high-frequency quantum noise only has a small effect. The result is also valid in some more general situations.

We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time-reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, the finite survival probability of the ground state limits the time asymmetry to be less than ln 2. We illustrate our results for a concrete system and discuss the fixed point of the time asymmetry in the limit of infinitely repeated projections.

We present analytical formulae for the neutrino mixing angles at the next-to-leading order in the quark-lepton complementarity, and show that higher-order corrections are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading–order corrections 1) lead to a deviation of $\theta_{23}$ from maximal mixing, 2) reduce the predicted value of $\sin^2 2\theta_{13}$ by $9.8\%$, 3) provide the same value of $\sin^2 \theta_{12}$ as that of the tri-bimaximal mixing.

We propose a new concept of entanglement for quantum systems: entanglement in theory space. This is defined by decomposing a theory into two by an un-gauging procedure. We provide two examples where this newly introduced entanglement is closely related to conventional geometric entropies: deconstruction and AGT-type correspondence.

In this paper we will construct and analyse the superloop space formulation of a $\mathcal {N} =1$ supergauge theory in three dimensions. We will obtain expressions for the connection and the curvature in this superloop space in terms of ordinary supergauge fields. This curvature will vanish, unless there is a monopole in the spacetime. We will also construct a quantity which will give the monopole charge in this formalism. Finally, we will show how these results even hold for a deformed superspace.

State-selective and total cross-sections for single-electron capture from H⁻ by H⁺ covering the incident energy range from 10 to 3000 keV are computed by means of the four-body boundary corrected first Born (CB1-4B) approximation. A crucial connection between the Coulomb-distorted asymptotic state in the entrance channel and the pertinent perturbation, which causes the transition in the H⁺ − H⁻ collisions, is consistently used in our computations of the "prior" version of cross-sections. The obtained results from the CB1-4B method clearly outperform the earlier findings by the close-coupling methods for the same problem. Comparisons with the available measurements are carried out and excellent agreement with the CB1 method is recorded down to impact energies as low as 10 keV.

We describe an opto-mechanical effect that introduces an additional phase into a coherent light field. This effect is accomplished via the motion of a cavity which contains an ultradispersive medium. We have theoretically shown that this change of the phase, due to the enhanced Fizeau effect, can be used to measure displacements as small as $10^{-17}\ \text{cm/Hz}^{1/2}$. This technique can be used to detect the Coriolis Force.

We investigate the dependence of the thermal Casimir force and the Casimir friction force between two graphene sheets on the drift velocity of the electrons in one graphene sheet. We show that the drift motion produces a measurable change of the thermal Casimir force due to the Doppler effect. The thermal Casimir force as well as the Casimir friction are strongly enhanced in the case of resonant photon tunneling when the energy of the emitted photon coincides with the energy of electron-hole pair excitations. In the case of resonant photon tunneling, even for temperatures above room temperature the Casimir friction is dominated by quantum friction due to quantum fluctuations. Quantum friction can be detected in frictional drag experiment between graphene sheets for high electric field.

We present a simple and general approach to formulate the lattice BGK model for high-speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) f^eq and a discrete velocity model with flexible velocity size. The DEDF is obtained by f^eq = C⁻¹M, where M is a set of moments of the Maxwellian distribution function, and C is the matrix connecting the DEDF and the moments. The numerical components of C are determined by the discrete velocity model. The calculation of C⁻¹ is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choice of the discrete velocity model has a high flexibility. The specific-heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of the system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities, the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to the deviation from thermodynamic equilibrium around the shock wave interfaces are shown.

The problem of gas rotation in a positive column of electric discharge with immobile striations in a longitudinal magnetic field is considered. This rotation around the axis of discharge is caused by the action of Ampère forces due to an eddy electric current that arises under conditions of noncollinear gradients of the electron concentration and temperature. In a stratified discharge, the plasma density and temperature are periodic functions of the longitudinal coordinate. The plasma density profile is described by the well-known Schottky model for a regime of ambipolar diffusion. In immobile striations, the velocity of rotation is limited by the two-dimensional gas viscosity. Formulas for the average velocity of gas rotation as a function of plasma parameters in striations are obtained and compared to formulas for the velocity of rotation of dusty plasma structures under the action of ion drag forces. The problem of gas rotation in moving striations in a longitudinal magnetic field requires special consideration, since the acceleration of gas rotation in this case has to be taken into account.

We investigate the branching of positive streamers in air and present the first systematic investigation of splitting into more than two branches. We study discharges in 100 mbar artificial air that is exposed to voltage pulses of 10 kV applied to a needle electrode 160 mm above a grounded plate. By imaging the discharge with two cameras from three angles, we establish that about every 200th branching event is a branching into three. Branching into three occurs more frequently for the relatively thicker streamers. In fact, we find that the surface of the total streamer cross-sections before and after a branching event is roughly the same.

Percolation and non-equilibrium front propagation in a two-dimensional network modeling wildfire spread is studied. The model includes a deterministic long-range interaction induced by flame radiation. It includes also a time weighting process due to the flame residence time and the activation (ignition) energy of the exposed combustible. For the square power decreasing radiation interaction, three weight-dependent regimes were previously found; a dynamical, a static, and a non-propagative regime (Zekri N. et al.Phys. Lett. A, 376 (2012) 2522). The weight effect on the percolation threshold is found here independent of the deterministic interaction. Using the Family-Vicsek scaling ansatz, the front dynamical exponents belong to the Edwards-Wilkinson model universality class at the saturation of the dynamical regime. They are weight dependent beyond saturation.

We study the behavior under rotating magnetic field of a nematic liquid crystal sandwiched between two parallel glass plates treated for partly sliding planar degenerate anchoring. This behavior is explained within a mean-field model taking into account the volume elasticity and the random planar anchoring of the molecules on the surfaces.

While the Θ-collapse of single long polymers in bad solvents is usually a continuous (tri-critical) phase transition, there are exceptions where it is preempted by a discontinuous crystallization (liquid $\leftrightarrow$ solid) transition. For a version of the bond fluctuation model (a model where monomers are represented as 2 × 2 × 2 cubes, and bonds can have lengths between 2 and $\sqrt {10}$) it was recently shown by Rampf et al. that there exist distinct collapse and crystallization transitions for long but finite chains. But as the chain length goes to infinity, both transition temperatures converge to the same T*, i.e. infinitely long polymers collapse immediately into a solid state. We explain this by the observation that polymers crystallize in Rampf et al.'s model into a non-trivial cubic crystal structure (the "A15" or "Cr₃Si" Frank-Kasper structure) which has many degenerate ground states and, as a consequence, Bloch walls. If one controls the polymer growth such that only one ground state is populated and Bloch walls are completely avoided, the liquid-solid transition is a smooth cross-over without any sharp transition at all.

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with probability δ, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying δ and the critical point δ_c = 0.5149(1) is determined from the power-law behavior of the order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the δ_c. Using the finite-size scaling analysis, we get $\beta /\bar {\nu }=0.20(1)$ and $1/\bar {\nu }=0.40(1)$, which implies β ≈ 1/2 and $\bar {\nu } \approx 5/2$. The Fisher exponent τ = 2.24(1) for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.

This work addresses the macroscopic deformations of spin-crossover (SC) thin sheets upon their cooperative transformation between the low-spin (LS) and the high-spin (HS) states from the viewpoint of electro-elastic interactions among molecules. When the size of each molecule changes depending on its spin state, the elastic interaction among the lattice distortions provides the cooperative interactions between the spin states, resulting in a macroscopic volume change. In this prospective contribution, we study the elasto-electronic properties of SC sheets in which the atoms can move according to the three directions of space. We predict that when HS and LS domains coexist, the system undergoes tremendous strain by compressing and expanding to differing degrees along the sheet, and it becomes far more favourable energetically to the sheet to buckle out of the plane. According to the elastic interaction between the SC atoms, we found the existence of a phase transition between flat and highly crumpled surfaces. This phenomenon was also investigated on two elastically coupled SC membranes where we demonstrate the existence of specific features of electro-elastic HS:LS interface. To enhance the quality of the surface layers, we have implemented the radial basis functions (RBF) interpolation which allowed to study small systems in a very accurate way. This method gives rise to a functional representation of a solid model, where gradients can be determined analytically, thus promising better understanding of the macroscopic crystal deformations and morphologies during the phase transition.

Dedicated to Prof. François Varret on the occasion of his 72nd birthday.

The fractional quantum Hall effect (FQHE) of topological insulator surface state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. Haldane's pseudopotentials for the Coulomb interaction are analytically obtained. The results show that by increasing the in-plane component of the tilted magnetic field, the FQHE state at n = 0 Landau level (LL) becomes more stable, while the stabilities of n = ± 1 LLs become weaker. Moreover, we find that the excitation gaps of the ν = 1/3, 1/5 and 1/7 FQHE states increase with increasing the tilt angle.

Conductivity of current-biased La_0.82 Ca_0.18 MnO₃ low-doped manganite single crystals has been investigated in wide temperature and magnetic field ranges. Strong zero-bias anomalies in the form of conductance minima and maxima have been observed below the Curie temperature T_C. Applied magnetic field and temperature strongly affect the anomaly and cause its transition from the conductance minimum to the conductance maximum. The observed anomalies are ascribed to Anderson localisation and combined Kondo and Fano effects.

We describe a variational calculation for the problem of screening of a point charge in a layered correlated metal close to the Mott transition where the screening is non-linear due to the proximity to the incompressible insulating state. This analysis can robustly account for locally incompressible regions induced by external charge and gives further insights, such as overscreening in the nearest nearby metallic layers while preserving overall charge neutrality.

We theoretically investigate the quasiparticle interference (QPI) in the optimally electron-doped BiS₂-layered superconductors with a two-orbital model. We show that possible pairing symmetries can be identified from their unique features in the density of states and QPI maps from magnetic or nonmagnetic impurities. Additionally, the inter-orbital nonmagnetic impurity scattering breaks the C₄ symmetry and exhibits a clear C₂ patterns in the QPI maps, in contrast to its negligible effect in the superconducting state of iron pnictides. The unambiguous features indicated in the QPI patterns can be used to probe the pairing symmetry as well as to uncover the impurity nature in BiS₂-layered superconductors with the STM measurement.

Three quantum particles with on-site repulsion and nearest-neighbour attraction on a one-dimensional lattice are considered. The three-body Schrödinger equation is reduced to a set of single-variable integral equations. Energies of three-particle bound complexes (trions) are found from self-consistency of the approximating matrix equation. In the case of spin-$\frac{1}{2}$ fermions, the ground-state trion energy, the excited-state energies, the trion spectra and stability regions are obtained for total spins S = 1/2 and S = 3/2. In the S = 1/2 sector, a narrow but finite parameter region is identified where the ground state consists of a stable fermion pair and an unbound fermion. Also presented is the reference case of spin-0 bosons.

The electron-hole conversion at the normal-metal superconductor interface in inversion-symmetric Weyl semimetals is investigated with an effective two-band model. We find that the specular Andreev reflection of Weyl fermions has two unusual features. The Andreev conductance for s-wave BCS pairing states is anisotropic, depending on the angle between the line connecting a pair of Weyl points and the normal of the junction, due to opposite chirality carried by the paired electrons. For the Fulde-Ferrell-Larkin-Ovchinnikov pairing states, the Andreev reflection spectrum is isotropic and is independent of the finite momentum of the Cooper pairs.

We present comprehensive studies of strain effects on the spin reorientation transition (SRT), the so-called Morin transition, in α-Fe₂O₃(0001) films. The α-Fe₂O₃(0001) epitaxial films were grown with a Cr₂O₃ buffer layer on Al₂O₃(0001) substrates through an oxide molecular beam epitaxy. The antiferromagnetic spin axis was monitored by using the Fe L₂-edge X-ray magnetic linear dichroism. The buffer layer was found to introduce compressive strain into the α-Fe₂O₃(0001) film due to its 1.6% smaller in-plane lattice constant. The degree of strain is monotonically reduced with the increase of the α-Fe₂O₃ film thickness and becomes relaxed in the thick region (> 20 nm). The transition temperature T_M, which increases up to ≃360 K, well above the bulk T_M = 263 K, for the film thickness ≃3 nm, gradually decreases as the film thickness increases. We also examined the Néel temperature T_N in the ultra-thin region (< 3 nm), which rapidly drops with the decrease of the film thickness. The correlation between T_M and the strain in the α-Fe₂O₃(0001) epitaxial films was found to be well explained in terms of two competing energies of magnetic dipole anisotropy and single-ion magnetocrystalline anisotropy except for the ultra-thin region, in which T_N is dominated by the finite-size effects.

We present a combined experimental and theoretical study describing the dynamical regimes displayed by a paramagnetic colloidal particle externally driven above a stripe-patterned magnetic garnet film. A circularly polarized rotating magnetic field modulates the stray field of the garnet film and generates a translating periodic potential which induces particle motion. Increasing the driving frequency, we observe a transition from a phase-locked motion with constant speed to a sliding dynamics characterized by a lower speed due to the loss of synchronization with the traveling potential. We explain the experimental findings with an analytically tractable theoretical model and interpret the particle dynamics in the presence of thermal noise. The model is in good quantitative agreement with the experiments.

Physiologic systems generate complex fluctuations in their output signals that reflect the underlying dynamics. We employed the base-scale entropy method and the power spectral analysis to study the 24 hours heart rate variability (HRV) signals. The results show that such profound circadian-, age- and pathologic-dependent changes are accompanied by changes in base-scale entropy and power spectral distribution. Moreover, the base-scale entropy changes reflect the corresponding changes in the autonomic nerve outflow. With the suppression of the vagal tone and dominance of the sympathetic tone in congestive heart failure (CHF) subjects, there is more variability in the date fluctuation mode. So the higher base-scale entropy belongs to CHF subjects. With the decrease of the sympathetic tone and the respiratory frequency (RSA) becoming more pronounced with slower breathing during sleeping, the base-scale entropy drops in CHF subjects. The HRV series of the two healthy groups have the same diurnal/nocturnal trend as the CHF series. The fluctuation dynamics trend of data in the three groups can be described as "HF effect".

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, which allows us to apply any of the many well-understood partitioning algorithms to the solution of community detection problems. We illustrate the approach by adapting the Laplacian spectral partitioning method to perform community inference, testing the resulting algorithm on a range of examples, including computer-generated and real-world networks. Both the quality of the results and the running time rival the best previous methods.

Conservation of energy and momentum in the classical theory of radiating electrons has been a challenging problem since its inception. We propose a formulation of classical electrodynamics in Hamiltonian form that satisfies the Maxwell equations and the Lorentz force. The radiated field is represented with eigenfunctions using the Gel'fand β-transform. The electron Hamiltonian is the standard one coupling the particles with the propagating fields. The dynamics conserves energy and excludes self-acceleration. A complete Hamiltonian formulation results from adding electrostatic action-at-a-distance coupling between electrons.

A recently proposed device, dubbed half-Josephson laser, provides a phase-lock between the optical phase and the superconducting phase difference between the leads of the device. In this paper we propose to utilize this phase-lock for the stabilization of voltage fluctuations, by two optical feedback schemes. The first scheme involves a single half-Josephson laser and allows to significantly decrease the diffusion coefficient of the superconducting phase difference. The second scheme involves a stable optical source and a fluctuating half-Josephson laser and permits quenching of the diffusion of the relative phase of the lasers. This opens up perspectives of the optical control of the superconducting phase and voltage fluctuations.

k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed-form analytic formulas for the probability that a confined random network remains fully connected after the removal of k − 1 nodes. Our analysis reveals that k-connectivity is governed by microscopic details of the network domain such as sharp corners rather than the macroscopic total volume. Hence, our results can aid in the design of reliable networks, an important problem in, e.g., wireless ad hoc and sensor networks.

Based on the first-principles density functional theory, we have studied the stability, electronic structure and ammonia storage capacity of metal-decorated graphene oxide (GO). Metal atoms (Mg and Li) are bonded strongly to the epoxy oxygen atoms on the surface of the GO sheet, which can act as high-surface-area adsorbent for the ammonia uptake and release. Each metal atom can bind several ammonia molecules around itself with a reasonable binding energy. We find metal-decorated GO can store up to tens of moles of ammonia per kilogram, which is far better than the recently reported excellent ammonia adsorption by GO.

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.