Nontrivial Boundary Research Articles

Hierarchical entanglement shells of multichannel Kondo clouds

Impurities or boundaries often impose nontrivial boundary conditions on a gapless bulk, resulting in distinct boundary universality classes for a given bulk, phase transitions, and non-Fermi liquids in diverse systems. The underlying boundary states however remain largely unexplored. This is related with a fundamental issue how a Kondo cloud spatially forms to screen a magnetic impurity in a metal. Here we predict the quantum-coherent spatial and energy structure of multichannel Kondo clouds, representative boundary states involving competing non-Fermi liquids, by studying quantum entanglement between the impurity and the channels. Entanglement shells of distinct non-Fermi liquids coexist in the structure, depending on the channels. As temperature increases, the shells become suppressed one by one from the outside, and the remaining outermost shell determines the thermal phase of each channel. Detection of the entanglement shells is experimentally feasible. Our findings suggest a guide to studying other boundary states and boundary-bulk entanglement.

Observation of bulk quadrupole in topological heat transport

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states—in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics.

Trapping of an active Brownian particle at a partially absorbing wall

Active matter concerns the self-organization of energy consuming elements such as motile bacteria or self-propelled colloids. A canonical example is an active Brownian particle (ABP) that moves at a constant speed while its direction of motion undergoes rotational diffusion. When ABPs are confined within a channel, they tend to accumulate at the channel walls, even when inter-particle interactions are ignored. Each particle pushes on the boundary until a tumble event reverses its direction. The wall thus acts as a sticky boundary. In this article, we consider a natural extension of sticky boundaries that allow for a particle to be permanently absorbed (killed) whilst attached to a wall. In particular, we investigate the first passage time (FPT) problem for an ABP in a two-dimensional channel where one of the walls is partially permeable. Calculating the exact FPT statistics requires solving a non-trivial two-way diffusion boundary value problem. We follow a different approach by separating out the dynamics away from the absorbing wall from the dynamics of absorption and escape whilst attached to the wall. By using probabilistic methods, we derive an explicit expression for the mean first passage time of absorption, assuming that the arrival statistics of particles at the wall are known. Our method also allows us to incorporate a more general encounter-based model of absorption.

Nonreciprocal amplification transition in a topological photonic network

We studied the transport properties of a driven-dissipative photonic network, where multiple photonic cavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we show that the correspondence between the nonreciprocal amplification transition and the topological phase transition breaks down as the transition conditions deviate significantly from each other. We found the exact transition condition for nonreciprocal amplification, supported by analytical calculation and numerical simulation. We also investigated the stability, the crossover from short- to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential applications in signal transmission and amplification, and also paves the way to study other topological and non-Hermitian systems with long-range coupling and nontrivial boundary effects.

Non-Hermitian boundary spectral winding

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian boundary localization and non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is demonstrated in a non-Hermitian breathing Kagome model with a triangle geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic boundary conditions with nontrivial spectral winding. In a trapezoidal geometry, such a boundary spectral winding can even co-exist with corner accumulation of edge states, instead of extended ones along 1D boundary of a triangle geometry. An OBC type of hybrid skin-topological effect may also emerge in a trapezoidal geometry, provided the boundary spectral winding completely vanishes. By studying the Green's function, we unveil that the boundary spectral winding can be detected from a topological response of the system to a local driving field, offering a realistic method to extract the nontrivial boundary topology for experimental studies.

Dark Energy Is the Cosmological Quantum Vacuum Energy of Light Particles—The Axion and the Lightest Neutrino

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as loga(t), where a(t) is the scale factor, while the particle contributions dilute as 1/a3(t), as it must be for massive particles. We find the explicit dark energy equation of state of today to be P=w(z)H: it turns to be slightly w(z)<−1 with w(z) asymptotically reaching the value −1 from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of 10−3 eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that w(z=0) is slightly below −1 by an amount ranging from (−1.5×10−3) to (−8×10−3) and we predict the axion mass to be in the range between 4 and 5 meV. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions.

Observation of Square‐Root Higher‐Order Topological States in Photonic Waveguide Arrays

AbstractRecently, higher‐order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with a codimension larger than one, have been extensively explored because of unconventional bulk‐boundary correspondences. As a novel type of HOTIs, very recent works have explored the square‐root HOTIs, where the topologically nontrivial nature of bulk bands stems from the square of the Hamiltonian. In this paper, 2D square‐root HOTIs are experimentally demonstrated in photonic waveguide arrays written in glass using femtosecond laser direct‐write techniques. Edge and corner states are clearly observed at visible light spectra. The dynamical evolutions of topological boundary states are experimentally demonstrated, which verify the existence of photonic corner states in two band gaps. The symmetry‐protected corner states in the photonic square‐root HOTI may have potential applications in information processing and lasing.

Callan-Rubakov effect and higher charge monopoles

In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole’s magnetic field polarizes the fermions into purely in-going and out-going modes. Consistency requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric SU(N) monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the SU(5) Georgi-Glashow model and comment on the relation to baryon number violation.

Can machine learning accelerate soft material parameter identification from complex mechanical test data?

Identifying the constitutive parameters of soft materials often requires heterogeneous mechanical test modes, such as simple shear. In turn, interpreting the resulting complex deformations necessitates the use of inverse strategies that iteratively call forward finite element solutions. In the past, we have found that the cost of repeatedly solving non-trivial boundary value problems can be prohibitively expensive. In this current work, we leverage our prior experimentally derived mechanical test data to explore an alternative approach. Specifically, we investigate whether a machine learning-based approach can accelerate the process of identifying material parameters based on our mechanical test data. Toward this end, we pursue two different strategies. In the first strategy, we replace the forward finite element simulations within an iterative optimization framework with a machine learning-based metamodel. Here, we explore both Gaussian process regression and neural network metamodels. In the second strategy, we forgo the iterative optimization framework and use a stand alone neural network to predict the entire material parameter set directly from experimental results. We first evaluate both approaches with simple shear experiments on blood clot, an isotropic, homogeneous material. Next, we evaluate both approaches against simple shearand uniaxial loading experiments on right ventricular myocardium, an anisotropic, heterogeneous material. We find that replacing the forward finite element simulations with metamodels significantly accelerates the parameter identification process with excellent results in the case of blood clot, and with satisfying results in the case of right ventricular myocardium. On the other hand, we find that replacing the entire optimization framework with a neural network yielded unsatisfying results, especially for right ventricular myocardium. Overall, the importance of our work stems from providing a baseline example showing how machine learning can accelerate the process of material parameter identification for soft materials from complex mechanical data, and from providing an open access experimental and simulation dataset that may serve as a benchmark dataset for others interested in applying machine learning techniques to soft tissue biomechanics.

New constructions of nef classes on self-products of curves

We study the nef cone of self-products of a curve. When the curve is very general of genus \(g>2\), we construct a nontrivial class of self-intersection 0 on the boundary of the nef cone. Up to symmetry, this is the only known nontrivial boundary example that exists for all \(g > 2\). When the curve is general, we identify nef classes that improve on known examples for arbitrary curves. We also consider self-products of more than two copies of the curve.

Theory of superconductivity mediated by topological phonons

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the superconducting critical temperature has a non-monotonic behaviour with respect to the phononic frequency in the Kramers-like point. This remarkable behaviour is produced by a resonance, that occurs when electrons and phonons on the topological surfaces have the same energy: this effectively increases the electron-phonon interaction and hence the Cooper pair binding energy, thus establishing an optimal condition for the superconducting phase. With this mechanism, the $T_{c}$ can be increased by well over a factor two, and the maximum enhancement occurs in the degenerate phononic flat-band limit.

Resummation for quantum propagators in bounded spaces.

We outline an approach to calculating the quantum mechanical propagator in the presence of geometrically nontrivial Dirichlet boundary conditions. The method is based on a generalization of an integral transform of the propagator studied in previous work (the so-called "hit function") and a convergent sequence of Padé approximants that exposes the limit of perfectly reflecting boundaries. In this paper the generalized hit function is defined as a many-point propagator, and we describe its relation to the sum over trajectories in the Feynman path integral. We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in D=1 and D=3 dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, nonlocalized potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.

Interplay between quantum anomalous Hall effect and magnetic skyrmions

SignificanceQuantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK), as two typical topological states in momentum (K) and real (R) spaces, attract much interest in condensed matter physics. However, the interplay between these two states remains to be explored. We propose that the interplay between QAHE and SK may generate an RK joint topological skyrmion (RK-SK), characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Furthermore, the emerging external field-tunable CBS in RK-SK could create additional degrees of freedom for SK manipulations, beyond the traditional SK. Meanwhile, external field can realize a rare topological phase transition between K and R spaces. Our work opens avenues for exploring unconventional quantum states and topological phase transitions in different spaces.

Bootstrapping boundary-localized interactions II. Minimal models at the boundary

We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m’th unitary diagonal minimal model. For large m we can demonstrate the existence of the fixed point perturbatively, and for smaller values we use the numerical conformal bootstrap to obtain a sharp kink that smoothly matches onto the perturbative predictions. The wider numerical analysis also yields universal bounds for the spectrum of any other boundary condition for the free scalar field. A second kink in these bounds hints at a second class of non-standard boundary conditions, as yet unidentified.

A graphene inspired electromagnetic superlens

In this paper we propose a new paradigm to create superlenses inspired by n–p–n junctions of graphene. We show that by adjoining an n-type region and a p-type region with a crystal dislocation, it is possible to mimic the interaction of complementary Hamiltonians and achieve subwavelength imaging. We introduce an effective model of the system, and show that it predicts perfect lensing for both propagating and evanescent waves due to the excitation of a resonant mode at the interface between each region. This phenomenon is the consequence of a nontrivial boundary condition at the n–p interfaces due to a dislocation of the graphene ‘atoms’. We discuss practical realizations of such superlenses in electronic and photonic platforms. Using full wave simulations, we study in detail the performance of a photonic realization of the lens based on a honeycomb array of dielectric cylinders embedded in a metal.

A review on the Cahn–Hilliard equation: classical results and recent advances in dynamic boundary conditions

<abstract><p>The Cahn–Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to different contexts in various scientific fields. In this survey article, we briefly review the derivation, structure as well as some analytical issues for the Cahn–Hilliard equation and its variants. Our focus will be placed on the well-posedness as well as long-time behavior of global solutions for the Cahn–Hilliard equation in the classical setting and recent progresses on the dynamic boundary conditions that describe non-trivial boundary effects.</p></abstract>

On the Geometric Approach to the Boundary Problem in Supergravity

We review the geometric superspace approach to the boundary problem in supergravity, retracing the geometric construction of four-dimensional supergravity Lagrangians in the presence of a non-trivial boundary of spacetime. We first focus on pure N=1 and N=2 theories with negative cosmological constant. Here, the supersymmetry invariance of the action requires the addition of topological (boundary) contributions which generalize at the supersymmetric level the Euler-Gauss-Bonnet term. Moreover, one finds that the boundary values of the super field-strengths are dynamically fixed to constant values, corresponding to the vanishing of the OSp(N|4)-covariant supercurvatures at the boundary. We then consider the case of vanishing cosmological constant where, in the presence of a non-trivial boundary, the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. In all the cases listed above, the full, supersymmetric Lagrangian can be recast in a MacDowell-Mansouri(-like) form. We then report on the application of the results to specific problems regarding cases where the boundary is located asymptotically, relevant for a holographic analysis.

Persistently foliar composite knots

A knot $\kappa$ in $S^3$ is persistently foliar if, for each non-trivial boundary slope, there is a co-oriented taut foliation meeting the boundary of the knot complement transversely in a foliation by curves of that slope. For rational slopes, these foliations may be capped off by disks to obtain a co-oriented taut foliation in every manifold obtained by non-trivial Dehn surgery on that knot. We show that any composite knot with a persistently foliar summand is persistently foliar and that any nontrivial connected sum of fibered knots is persistently foliar. As an application, it follows that any composite knot in which each of two summands is fibered or at least one summand is nontorus alternating or Montesinos is persistently foliar. We note that, in constructing foliations in the complements of fibered summands, we build branched surfaces whose complementary regions agree with those of Gabai's product disk decompositions, except for the one containing the boundary of the knot complement. It is this boundary region which provides for persistence.

Hexagon bootstrap in the double scaling limit

We study the six-particle amplitude in planar mathcal{N} = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

Cosmic voids and filaments from quantum gravity

Using computer simulations, we study the geometry of a typical quantum universe, i.e., the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with nontrivial boundary conditions. They are a close analogue of the harmonic coordinate condition used in the context of GR (Kuchar and Torre in Phys Rev D 43:419–441, 1991). It is highly nontrivial that these ideas can be applied to understand the structures which appear in very irregular and fluctuating geometries. The field configurations reveal cosmic web structures surprisingly similar to the ones observed in the present-day universe.