Non-trivial Distribution Research Articles

Simultaneous improvement of multiple transportation performances on link-coupled networks by global dynamic routing

The interconnected networks are facing with critical congestion issue due to the rapid growth of the traffic and the information on the links with limited capacity. We show that the traditional routing strategies are generally confronted with a tradeoff between the network capacity and the link usage when applying to the link-coupled network. To take a step to the issue, we propose a global dynamic routing (GDR) strategy that can simultaneously achieve multiple improvement of the transport performance with acceptable computational complexity at the cost of the average arrival time. Further analysis indicates the improvement is related to the nontrivial load distribution resulting from GDR. More surprisingly, the simulation experiments suggest our strategy GDR can suppress the occurrence of Braess-like paradox, which is a long-standing problem in transportation.

Describing quantum metrology with erasure errors using weight distributions of classical codes

Quantum sensors are expected to be a prominent use-case of quantum technologies, but, in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance $d\ensuremath{\ge}t+1$. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field after at most $t$ qubits of the quantum probe state are erased. We show that the quantum Fisher information is proportional to the variances of the weight distributions of the corresponding ${2}^{t}$ shortened codes. If the shortened codes of a fixed code with $d\ensuremath{\ge}t+1$ have a nontrivial weight distribution, then the probe states obtained by concatenating this code with repetition codes of increasing length enable asymptotically optimal field sensing that passively tolerates up to $t$ erasure errors.

Investigation of eigenfunctions of perturbation of the radial component of flow velocity

The flow of a thermoviscous model fluid in an annular channel with a given temperature field is considered. The problem of the stability of the flow of a thermoviscous fluid is solved on the basis of a generalized equation by the spectral method of expansion in Chebyshev polynomials of the first kind. The influence of taking into account the exponential dependence of fluid viscosity on temperature and channel geometry on the spectral characteristics of the equation of hydrodynamic stability of incompressible fluid flow in an annular channel is investigated. The eigenvalue spectra were obtained numerically. The spectral characteristics determine the structure of the eigenfunctions and the critical parameters of the flow of a thermoviscous fluid. In this case, the eigenfunctions demonstrate the behavior of transverse velocity disturbances, their possible growth or decay over time. Graphs of the eigenfunctions of the generalized flow stability equation in an annular channel have been constructed. It is shown that the structure of the spectra largely depends on both the properties of the liquid, determined by the functional dependence of viscosity, and on the geometry of the channel. The stability of the flow of a thermoviscous fluid depends on the presence of an eigenvalue with a positive imaginary part among the entire set of found eigenvalues for fixed parameters of the Reynolds number and wave number. It has been established that at small values of the thermoviscosity parameter the spectrum is comparable to the spectrum for isothermal fluid flow in a flat channel, however, as it increases, the number of eigenvalues and their density increase, that is, there are a greater number of points at which the problem has non-zero amplitudes of transverse velocity disturbances. It is worth noting that the diversity of eigenvalue spectra corresponds to the diversity of eigenfunctions, which have a nontrivial distribution of the oscillation amplitude over the cross section in each case. Smooth curves are obtained for a narrow channel, as for the case of a flat channel. However, as the ratio of the channel radii increases, “jumps” appear. Also, note that the eigenfunctions do not have the property of symmetry; this follows from the fact that the velocity profile in the unperturbed state also does not have symmetry. The maximum values of the eigenfunctions are shifted to the right from the center of the channel, which corresponds to the fact that disturbances arise and grow intensively near the hot wall.

Absorbing boundary condition as limiting case of imaginary potentials

Imaginary potentials such as V(x) = −iσ1Ω(x) (with σ > 0 a constant, Ω a subset of 3-space, and 1Ω its characteristic function) have been used in quantum mechanics as models of a detector. They represent the effect of a ‘soft’ detector that takes a while to notice a particle in the detector volume Ω. In order to model a ‘hard’ detector (i.e. one that registers a particle as soon as it enters Ω), one may think of taking the limit σ → ∞ of increasing detector strength σ. However, as pointed out by Allcock, in this limit the particle never enters Ω; its wave function gets reflected at the boundary ∂Ω of Ω in the same way as by a Dirichlet boundary condition on ∂Ω. This phenomenon, a cousin of the ‘quantum Zeno effect,’ might suggest that a hard detector is mathematically impossible. Nevertheless, a mathematical description of a hard detector has recently been put forward in the form of the ‘absorbing boundary rule’ involving an absorbing boundary condition on the detecting surface ∂Ω. We show here that in a suitable (non-obvious) limit, the imaginary potential V yields a non-trivial distribution of detection time and place in agreement with the absorbing boundary rule. That is, a hard detector can be obtained as a limit, but it is a different limit than Allcock considered.

Proximity-enhanced magnetocaloric effect in ferromagnetic trilayers

The demagnetization and associated magnetocaloric effect (MCE) in strong-weak-strong ferromagnetic trilayers, upon a reorientation of the strong ferromagnets from parallel to antiparallel (AP) magnetization, is simulated using atomistic spin dynamics. The simulations yield non-trivial spin distributions in the AP state, which in turn allows entropy to be calculated directly. The influence of longer-range spin–spin interactions and of variable strength of the external switching field are investigated. Finally, we find that the MCE in the system can be significantly improved by allowing the local exchange to vary through the spacer, which in practice can be implemented by spatially tailoring the spacer’s magnetic dilution.

Z n symmetry in the vortex muon decay

Polarization of a vortex state fermion has a rich structure due to the nontrivial momentum distribution of wave function. This larger freedom provides an unique opportunity to prepare fermions in exotic polarized states, which do not exist for plane wave state fermions. Based on the so-called spin–orbit state which was studied both theoretically and experimentally, we put forward a peculiar vortex muon whose polarization exhibits Z n symmetry and study its decay. We investigate the azimuthal distribution of the emitted electrons and find that it exhibits the same symmetry (Z n ) as the initial state.

A stochastic spatial model for the sterile insect control strategy

In the system we study, 1’s and 0’s represent occupied and vacant sites in the contact process with births at rate λ and deaths at rate 1. −1’s are sterile individuals that do not reproduce but appear spontaneously on vacant sites at rate α and die at rate θα. We show that the system (which is attractive but has no dual) dies out at the critical value and has a nontrivial stationary distribution when it is supercritical. Our most interesting results concern the asymptotics when α→0. In this regime the process resembles the contact process in a random environment.

Nanoscale Electric Field Probing in a Single Nanowire with Raman Spectroscopy and Elastic Strain.

In this work we investigate the Raman response of extremely strained gallium phosphide nanowires. We analyze new strain-induced spectral phenomena such as 2-fold and 3-fold phonon peak splitting which arise due to nontrivial internal electric field distribution coupled with inhomogeneous strain. We show that high bending strain acts as a probe allowing us to define the electric field distribution with deep subwavelength resolution using the corresponding changes of the Raman spectra. We investigate the nature of the localization with respect to nanowire diameter, excitation spot position, and light polarization, supporting the experiment with 3D numerical modeling. Based on our findings we propose a research tool allowing to precisely localize the electric field in a certain subwavelength region of the nanophotonic resonator.

Geodesic motion and phase-space evolution of massive neutrinos

The non-trivial phase-space distribution of relic neutrinos is responsible for the erasure of primordial density perturbations on small scales, which is one of the main cosmological signatures of neutrino mass. In this paper, we present a new code, fastdf, for generating 1%-accurate particle realisations of the neutrino phase-space distribution using relativistic perturbation theory. We use the geodesic equation to derive equations of motion for massive particles moving in a weakly perturbed spacetime and integrate particles accordingly. We demonstrate how to combine geodesic-based initial conditions with the δf method to minimise shot noise and clarify the definition of the neutrino momentum, finding that large errors result if the wrong parametrisation is used. Compared to standard Lagrangian methods with ad-hoc thermal motions, fastdf achieves substantial improvements in accuracy. We outline the approximation schemes used to speed up the code and to ensure symplectic integration that preserves phase-space density. Finally, we discuss implications for neutrino particles in cosmological N-body simulations. In particular, we argue that particle methods can accurately describe the neutrino distribution from z = 109, when neutrinos are linear and ultra-relativistic, down to z = 0, when they are nonlinear and non-relativistic. fastdf can be used to set up accurate initial conditions (ICs) for N-body simulations and has been integrated into the higher-order IC code monofonic.

Shear induced diffusion of platelets revisited.

The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation with a diffusion constant given by the so-called Zydney-Colton theory. Here we reconsider this hypothesis based on experimental observations and numerical simulations including a fully resolved suspension of red blood cells and platelets subject to a shear. We observe that the transport of platelets perpendicular to the flow can be characterized by a non-trivial distribution of velocities with and exponential decreasing bulk, followed by a power law tail. We conclude that such distribution of velocities leads to diffusion of platelets about two orders of magnitude higher than predicted by Zydney-Colton theory. We tested this distribution with a minimal stochastic model of platelets deposition to cover space and time scales similar to our experimental results, and confirm that the exponential-powerlaw distribution of velocities results in a coefficient of diffusion significantly larger than predicted by the Zydney-Colton theory.

Extracting dark-matter velocities from halo masses: A reconstruction conjecture

Increasing attention has recently focused on nontraditional dark-matter production mechanisms which result in primordial dark-matter velocity distributions with highly nonthermal shapes. In this paper, we undertake an assessment of how the detailed shape of a general dark-matter velocity distribution impacts structure formation in the nonlinear regime. In particular, we investigate the impact on the halo-mass and subhalo-mass functions, as well as on astrophysical observables such as satellite and cluster-number counts. We find that many of the standard expectations no longer hold in situations in which this velocity distribution takes a highly nontrivial, even multimodal shape. For example, we find that the nominal free-streaming scale alone becomes insufficient to characterize the effect of free-streaming on structure formation. In addition, we propose a simple one-line conjecture which can be used to ``reconstruct'' the primordial dark-matter velocity distribution directly from the shape of the halo-mass function. Although our conjecture is completely heuristic, we show that it successfully reproduces the salient features of the underlying dark-matter velocity distribution even for nontrivial distributions which are highly nonthermal and/or multimodal, such as might occur for nonminimal dark sectors. Moreover, since our approach relies only on the halo-mass function, our conjecture provides a method of probing dark-matter properties even for scenarios in which the dark and visible sectors interact only gravitationally.

Two decades of X-ray observations of the isolated neutron star RX J1856.5 − 3754: detection of thermal and non-thermal hard X-rays and refined spin-down measurement

ABSTRACT The soft X-ray pulsar RX J1856.5 − 3754 is the brightest member of a small class of thermally emitting, radio-silent, isolated neutron stars. Its X-ray spectrum is almost indistinguishable from a blackbody with $kT^\infty \approx {60}\, {\rm eV}$, but evidence of harder emission above $\sim {1}\, {\rm keV}$ has been recently found. We report on a spectral and timing analysis of RX J1856.5 − 3754 based on the large amount of data collected by XMM-Newton in 2002–2022, complemented by a dense monitoring campaign carried out by NICER in 2019. Through a phase-coherent timing analysis we obtained an improved value of the spin-down rate $\dot{\nu }=-6.042(4)\times 10^{-16}\, {\rm Hz\, s}^{-1}$, reducing by more than one order magnitude the uncertainty of the previous measurement, and yielding a characteristic spin-down field of $1.47\times 10^{13}\, {\rm G}$. We also detect two spectral components above $\sim 1\, {\rm keV}$: a blackbody-like one with $kT^\infty =138\pm 13\,$eV and emitting radius $31_{-16}^{+8}\,$m, and a power law with photon index $\Gamma =1.4_{-0.4}^{+0.5}$. The power-law 2–8 keV flux, $(2.5_{-0.6}^{+0.7})\times 10^{-15}\, {\rm erg}\, {\rm cm}^{-2}\, {\rm s}^{-1}$, corresponds to an efficiency of 10−3, in line with that seen in other pulsars. We also reveal a small difference between the 0.1–0.3 keV and 0.3–1.2 keV pulse profiles, as well as some evidence for a modulation above 1.2 keV. These results show that, notwithstanding its simple spectrum, RX J1856.5 − 3754 still has a non-trivial thermal surface distribution and features non-thermal emission as seen in other pulsars with higher spin-down power.

Two-dimensional quantitative near-field phase imaging using square and hexagonal interference devices

Abstract We demonstrate the formation of the near field with non-trivial phase distribution using surface plasmon interference devices, and experimental quantitative imaging of that phase with near-field phase microscopy. The phase distribution formed with a single device can be controlled by the polarization of the external illumination and the area of the device assigned to the object wave. A comparison of the experimental data to a numerical electromagnetic model and an analytical model assigns the origin of the near-field phase to the out-of-plane electric component of surface plasmon polaritons, and also verifies the predictive power of the models. We demonstrate a formation of near-field plane waves with different propagation directions on a single device, or even simultaneously at distinct areas of a single device. Our findings open the way to the imaging and tomography of phase objects in the near field.

Optimal Purification of a Spin Ensemble by Quantum-Algorithmic Feedback

Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state. This alternative, if realized, offers additional control capabilities for the design of quantum states. Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations. Our algorithmic approach maximizes the rate of state purification given the system’s physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder. We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates. Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations. Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability. This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.9 MoreReceived 29 October 2021Revised 7 March 2022Accepted 10 June 2022DOI:https://doi.org/10.1103/PhysRevX.12.031014Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum controlQuantum feedbackQuantum master equationQuantum thermodynamicsSpin coherencePhysical SystemsQuantum dotsTechniquesCoherent Raman electron spin resonance spectroscopyMaster equationSpin noise spectroscopyQuantum InformationCondensed Matter, Materials & Applied Physics

Spatial patterns in ecological systems: from microbial colonies to landscapes.

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Electronic properties of carbon sheets and nanoribbons based on acepentalene-like building blocks

Two-dimensional allotropes of carbon are the subject of intense research in an effort to fine tune nanocarbon’s physical properties for their insertion into operational nanoscale devices. C57 and C65 lattices are examples of such proposed networks. They are hypothetically formed by the concatenation of acepentalene blocks and are shown to display a metallic behavior. Here, we use density functional theory to investigate the electronic properties of ribbons whose lattices are composed of these two 2D nanocarbons. These systems share the common feature with their parent structures of displaying a metallic behavior. However, they are also found to host spin-polarized states, thereby offering opportunities for their applications in spintronics. Furthermore, one of the 2D parent structures is found to also allow a non-trivial spin distribution, as well as corrugated phases, which was not previously reported for this system. Finally, the structural and electronic properties calculated for the C57 and C65 systems are rationalized in terms of a resonance model.

Transitioning to confined spaces impacts bacterial swimming and escape response

Symbiotic bacteria often navigate complex environments before colonizing privileged sites in their host organism. Chemical gradients are known to facilitate directional taxis of these bacteria, guiding them toward their eventual destination. However, less is known about the role of physical features in shaping the path the bacteria take and defining how they traverse a given space. The flagellated marine bacterium Vibrio fischeri, which forms a binary symbiosis with the Hawaiian bobtail squid, Euprymna scolopes, must navigate tight physical confinement during colonization, squeezing through a tissue bottleneck constricting to ∼2 μm in width on the way to its eventual home. Using microfluidic in vitro experiments, we discovered that V. fischeri cells alter their behavior upon entry into confined space, straightening their swimming paths and promoting escape from confinement. Using a computational model, we attributed this escape response to two factors: reduced directional fluctuation and a refractory period between reversals. Additional experiments in asymmetric capillary tubes confirmed that V. fischeri quickly escape from confined ends, even when drawn into the ends by chemoattraction. This avoidance was apparent down to a limit of confinement approaching the diameter of the cell itself, resulting in a balance between chemoattraction and evasion of physical confinement. Our findings demonstrate that nontrivial distributions of swimming bacteria can emerge from simple physical gradients in the level of confinement. Tight spaces may serve as an additional, crucial cue for bacteria while they navigate complex environments to enter specific habitats.

Phase retrieval and reconstruction of coherent synthesis by genetic algorithm

In the context of diffractive optics, phase retrieval is a heavily investigated process of recreating an entire complex electric field from partial amplitude-only information through iterative algorithms. However, existing methods can fall into local minima during reconstructions or struggle to recover unusual and novel electric field distributions. We present a numerical method based on a global-optimization genetic algorithm that reconstructs non-trivial electric field distributions from single diffracted intensity distributions. Diffraction and propagation of the optical fields over arbitrary distances is modeled through implementation of the angular spectrum technique. Additionally, a coherently-locked laser array system is used as an experimental case-study demonstrating 0.09π phase reconstruction accuracy of initial laser parameters from single intensity images.

Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V5S8

Introduction of spin–orbit coupling (SOC) in a Josephson junction (JJ) gives rise to unusual Josephson effects. We investigate JJs based on a newly discovered heterodimensional superlattice V5S8 with a special form of SOC. The unique homointerface of our JJs enables elimination of extrinsic effects due to interfaces and disorder. We observe asymmetric Fraunhofer patterns with respect to both the perpendicular magnetic field and the current. The asymmetry is influenced by an in-plane magnetic field. Analysis of the pattern points to a nontrivial spatial distribution of the Josephson current that is intrinsic to the SOC in V5S8.

Multipartitioning topological phases by vertex states and quantum entanglement

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)-dimensional conformal field theory -- these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states. This approach allows an explicit construction of the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix. For reflected entropy, we test the recent claim that states the difference between reflected entropy and mutual information is given, once short-range correlations are properly removed, by $(c/3)\ln 2$ where $c$ is the central charge of the topological liquid that measures ungappable edge degrees of freedom. As specific examples, we consider topological chiral $p$-wave superconductors and Chern insulators. We also study a specific lattice fermion model realizing Chern insulator phases and calculate the correlation measures numerically, both in its gapped phases and at critical points separating them.