Inhomogeneous Configurations Research Articles

Effectively flat potential in the Friedberg–Lee–Sirlin model

The Friedberg–Lee–Sirlin (FLS) model is a well-known renormalizable theory of scalar fields that provides for the existence of non-topological solitons. Since this model was proposed, numerous works have been dedicated to studying its classical configurations and its general suitability for various physical problems in cosmology, quantum chromodynamics, etc. In this paper, we study how Q-balls in effective field theory (EFT) reproduce non-topological solitons in the full FLS theory. We obtain an analytical description of the simplified model and compare the results with numerical calculations and perturbation theory. We also study the condensation of charged bosons on the domain wall. A full numerical solution allows us to check the EFT methods for this problem. The latter analysis is based on the application of EFT methods to significantly inhomogeneous configurations. We give an interpretation of the results in terms of the shifted boson mass and the vacuum rearrangement.

Improving the reliability of machine learned potentials for modeling inhomogeneous liquids.

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical, and biological processes. Classical molecular dynamics simulations have been applied extensively to simulate the response of fluids to inhomogeneities directly, but are limited by the accuracy of the underlying interatomic potentials. Here, we use neural network potentials (NNPs) trained to ab initio simulations to accurately predict the inhomogeneous responses of two distinct fluids: liquid water and molten NaCl. Although NNPs can be readily trained to model complex bulk systems across a range of state points, we show that to appropriately model a fluid's response at an interface, relevant inhomogeneous configurations must be included in the training data. In order to sufficiently sample appropriate configurations of such inhomogeneous fluids, we develop protocols based on molecular dynamics simulations in the presence of external potentials. We demonstrate that NNPs trained on inhomogeneous fluid configurations can more accurately predict several key properties of fluids-including the density response, surface tension and size-dependent cavitation free energies-for liquid water and molten NaCl, compared to both empirical interatomic potentials and NNPs that are not trained on such inhomogeneous configurations. This work therefore provides a first demonstration and framework to extract the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Anomalies and persistent order in the chiral Gross-Neveu model

We study the 2d chiral Gross-Neveu model at finite temperature T and chemical potential μ. The analysis is performed by relating the theory to a SU(N) × U(1) Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At μ = 0 we show that a certain ℤ2-valued ’t Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any N and any T > 0. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for T > 0 of the inhomogeneous chiral phase configuration found at T = 0 for any N and any μ. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for T > 0 and any μ for periodic fermions, as expected from anomaly considerations. A large N analysis confirms the above findings.

Near-Zero Energy Consumption Capacitors by Controlling Inhomogeneous Polarization Configuration.

Taking into account the need for energy conservation, achieving near-zero energy loss, namely ultrahigh efficiency (η), in energy storage capacitors with large recoverable energy storage density (Wrec) plays an important role in applications, which is one of the major challenges in dielectric energy storage field. Here, guided by phase-field simulation, inhomogeneous polarization configuration with multiple symmetries and polarization magnitudes is controlled through aliovalent strongly polar double ion design to establish a strongly disordered state. A record-high η of ≈97.4% is realized in lead-free relaxors with a large Wrec of ≈8.6 J cm-3, which also give a giant Wrec of ≈11.6 J cm-3 with an ultrahigh η of ≈96.1% through high-energy ball milling, showing a breakthrough progress in ceramic capacitors with a maximum figure of merit of 330. This work demonstrates that controlling inhomogeneous polarization configuration is an effective avenue to develop new high-performance near-zero energy loss energy storage capacitors.

Topological study of the rearrangement of the magnetic vector field using magneto-optical images

A certain aspect of the topological properties of the in plane components of the field of a system of two magnets have been experimentally studied. Vector plots of the inhomogeneous field were obtained using computer processing of magneto-optical images in the longitudinal and transverse sensitivity of the Kerr effect. The topological characteristics of the field were changed by applying a homogeneous bias field in the plane. It is shown that the transition from the initial inhomogeneous configuration to a homogeneous one occurs according to various scenarios. The application of the external field leads to the appearance of new singular points, the number of which is due to Poincaré's theorem on the rotation of the vector field. It is shown that the transition from the initial inhomogeneous configuration to the homogeneous one occurs according to various scenarios through topologically non-equivalent structures and depends on the orientation of the resulting magnetic moment of the system relative to the observation plane.

Linear stability analysis in inhomogeneous equilibrium configurations

Linear stability analysis in inhomogeneous equilibrium configurations

Lengthwise Fracture Analysis of Inhomogeneous Viscoelastic Cantilever Beam Subjected to Sinusoidal Strains

This paper describes a research of lengthwise fracture in a viscoelastic inhomogeneous cantilever beam under strain that is a sinusoidal function of time. The beam mechanical behavior is investigated by a model having two linear springs and a linear dashpot. The beam material is continuously inhomogeneous along thickness. Therefore, the modules of elasticity of the springs and the coefficient of viscosity of the dashpot vary smoothly in the thickness direction. The compliance method is applied to derive the strain energy release rate (SERR) for the lengthwise crack in the beam structure. The integral J is applied for verification. The stress-strain-time dependence of the viscoelastic model is used for describing the behavior of the beam when obtaining solutions of the SERR and the J-integral. Solutions are derived for both positive and negative rotation angle of the lower crack arm end (when the angle is positive, the upper crack arm is load free, while at negative angle both crack arms are loaded). The effects of various factors including the sign of the angle of rotation on the SERR are analyzed.

Asymmetry-driven reconfigurability of magnetic vortices in hemispherical shells

Inhomogeneous magnetic configurations like vortices attract tremendous appeal as an emerging candidate in understanding nanoscale spin behaviours and utilizing their spin configurations for advanced technological applications. For vortex-driven practical applications, independent control and manipulation of both the circularity and polarity of the magnetic vortex is a prerequisite. In this study, we have shown that both the circularity and polarity of the magnetic vortex in an asymmetric hemispherical shell can be controlled by changing a single parameter - the direction of the in-plane external magnetic field. Furthermore, our results demonstrate the influence of geometrical asymmetry on the characteristics of magnetic vortices in ferromagnetic permalloy shells. These findings are expected to be helpful while designing vortex-based advanced technologies.

Triple longitudinal fracture of inhomogeneous beam under four-point bending an analytical study by using a non-linear elastic material model

The present paper is devoted to fracture analysis of an inhomogeneous non-linear elastic beam configuration with three parallel longitudinal cracks. The material is continuously inhomogeneous along the beam height. The beam is subjected to four-point bending. The longitudinal fracture behavior is studied by applying the J-integral approach. Solutions to the J-integral are obtained for the three cracks. For this purpose, the curvature and the coordinates of neutral axes of the crack arms are determined by using the equations for equilibrium of the elementary forces in the cross-sections of different portions of the beam. The solutions to the J-integral are valid for arbitrary locations of the cracks along the beam height. Thus, the solutions are very useful for evaluating of the effects of locations of cracks on the fracture. The longitudinal fracture behavior is studied also in terms of the strain energy release rate in order to verify the solutions to the J-integral. Solutions to the strain energy release rate are derived for the three cracks by considering the complementary strain energy in the beam. The solutions to the J-integral are applied to evaluate the effects of locations of the cracks, the material inhomogeneity, the sizes of the beam cross-section, and the coordinates of the applications points of the external forces on the longitudinal fracture behavior of the beam.

Disorder-induced dynamical Griffiths singularities after certain quantum quenches

We demonstrate that in a class of disordered quantum systems the dynamical partition function is not an analytical function in a time window after certain quantum quenches. We related this behavior to rare and large regions with atypical inhomogeneity configurations. We also quantify the strength of the associated singularities and their signatures in experiments and numerical studies.

Rational design and structural engineering of heterogeneous single-atom nanozyme for biosensing

Nanozymes, an emerging family of heterogeneous nanomaterials with enzyme-like characteristics, offer significant advantages as alternatives to natural enzymes for diverse biocatalytic applications. Nevertheless, the inhomogeneous configuration of nanomaterials makes it extremely challenging to develop nanozymes of desired performance and reaction mechanism. Single-atom nanozymes (SAzymes) that are composed of single-atomic active sites may provide an answer to these challenges with remarkable enzyme-like activity and specificity. The well-defined coordination microenvironments of SAzymes offer a suitable model system to investigate the structure–activity relationship and thus bridge the gap between natural enzyme and nanozyme. In this review, we would first present an overview of discoveries, advantages, and classifications of SAzymes. Then, we would discuss the reaction mechanism, design principles, and biosensing applications of a series of typical SAzymes with a focus on the rational design strategies for targeted reaction and the effort to uncover the catalytic mechanism at the atomic scale. Finally, we would provide the challenges and future perspectives of SAzymes as the next-generation nanozymes.

Integer and fractionalized vortex lattices and off-diagonal long-range order

We analyze the implication of off-diagonal long-range order (ODLRO) for inhomogeneous periodic field configurations and multi-component order parameters. For single component order parameters we show that the only static, periodic field configuration consistent with ODLRO is a vortex lattice with integer flux in units of the flux quantum in each unit cell. For a superconductor with g degenerate components, fractional vortices are allowed. Depending on the precise order-parameter manifold, they tend to occur in units of 1/g of the flux quantum. These results are well known to emerge from the Ginzburg-Landau or BCS theories of superconductivity. Our results imply that they are valid even if these theories no-longer apply. Integer and fractional vortex lattices are transparently seen to emerge as a consequence of the macroscopic coherence and single valuedness of the condensate.

Superfluid properties of bright solitons in a ring

We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.

To the Statistical Description of the Structure Formation in Coulomb-like Systems

A new solution to the problem of the calculation of the partition function for a Coulomb-like system is proposed. The quantum-field-theory approach is used to give a statistical description of a system of interacting particles with due regard to an arbitrary spatially inhomogeneous configuration. The formation of structures in a Coulomb-like system is analyzed and applied to thedusty plasma treatment. A necessary condition for the crystal formation in a three-dimensional system of dust particles is obtained. In the one-dimensional case, an exact solution for the spatial distribution of charged particles is presented.

Kibble mechanism for electroweak magnetic monopoles and magnetic fields

The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum Bλ ∝ λ−2, where λ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.

Spontaneous Symmetry Breaking via Inhomogeneities and the Differential Surface Tension.

We discuss spontaneously broken quantum field theories with a continuous global symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the path integral is dominated by inhomogeneous field configurations and that these are unambiguously related to the flatness of the effective potential in the broken phase. We determine characteristic features of these inhomogeneities, including their topology and the scaling of the associated excess energy with their size. Concerning the latter we introduce the differential surface tension-the generalization of the concept of a surface tension pertaining to discrete symmetries. Within our approach, spontaneous symmetry breaking is captured merely via the existence of inhomogeneities, i.e., without the inclusion of an explicit breaking parameter and a careful double limiting procedure to define the order parameter. While here we consider the three-dimensional O(2) model, we also elaborate on possible implications of our findings for the chiral limit of QCD.

Particle creation in the spin modes of a dynamically oscillating two-component Bose-Einstein condensate

We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, triggered by the dynamical evolution of the condensate density. We first make use of a Thomas-Fermi approximation to develop a tractable theoretical model of the quantum dynamics of the Bogoliubov excitations in a harmonically trapped condensate with a time-dependent trapping frequency. The predictions of this model are then compared to an ab-initio numerical study of the correlation functions of density and spin fluctuations for general spatially inhomogeneous configurations. Results are shown for the two cases of expanding and oscillating condensates: while the quantum excitation of spin modes remains weak and relatively featureless in the case of an expanding condensate, clear and experimentally promising signatures of particle creation are anticipated for the oscillating case under suitable resonance conditions between the density and the spin modes.

Observables in inhomogeneous ground states at large global charge

As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ1/ρ2, the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ1/ρ2 ≪ 1. We also compute, at fixed set of charges, ρ1, ρ2, the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ1 + ρ2)3/2, as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

Quantum scars and bulk coherence in a symmetry-protected topological phase

Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-$1/2$ chain with three-site "cluster" terms hosting a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase. Focusing on the weakly interacting regime, we find that eigenstates with volume-law entanglement coexist with area-law entangled eigenstates throughout the spectrum. We show that a subset of the latter can be constructed by virtue of repeated cluster excitations on the even or odd sublattice of the chain, resulting in an equidistant "tower" of states, analogous to the phenomenology of quantum many-body scars. We further demonstrate that these scarred eigenstates support nonthermal expectation values of local cluster operators in the bulk and exhibit signatures of topological order even at finite energy densities. Studying the dynamics for out-of-equilibrium states drawn from the noninteracting "cluster basis", we unveil that nonthermalizing bulk dynamics can be observed on long time scales if clusters on odd and even sites are energetically detuned. In this case, cluster excitations remain essentially confined to one of the two sublattices such that inhomogeneous cluster configurations cannot equilibrate and thermalization of the full system is impeded. Our work sheds light on the role of quantum many-body scars in preserving SPT order at finite temperature and the possibility of coherent bulk dynamics in models with SPT order beyond the existence of long-lived edge modes.

Pion crystals hosting topologically stable baryons

We construct analytic (3+1)-dimensional inhomogeneous and topologically non-trivial pion systems using chiral perturbation theory. We discuss the effect of isospin asymmetry with vanishing electromagnetic interactions as well as some particular configurations with non-vanishing electromagnetic interactions. The inhomogeneous configurations of the pion fields are characterized by a non-vanishing topological charge that can be identified with baryons surrounded by a cloud of pions. This system supports a topologically protected persistent superflow. When the electromagnetic field is turned on the superflow corresponds to an electromagnetic supercurrent.