Anyons Research Articles

Primary atomization of shear-thinning liquid jets: a direct numerical simulation study

Using direct numerical simulation, the primary atomization of shear-thinning liquid jets into stagnant gas is investigated. Starting from a Newtonian configuration with material properties approximately corresponding to a Diesel injection, two hypothetical shear-thinning cases using the power-law and the Carreau-Yasuda models for the calculation of the apparent viscosity are investigated. A recently developed tracking algorithm is used to identify droplets newly formed from the core jet, as well as all other droplets in the computational domain, and a number of relevant droplet characteristics, such as droplet volume, surface area and center of mass, is recorded at each time step. This allows a comparison of droplet characteristics on the basis of probability density functions. It is observed that the shear-thinning behavior of the liquid phase, which is particularly relevant at the interface, influences the droplet volumes and shapes. While the mean viscosity differs significantly for the different cases, the first- and second-order velocity and volume fraction statistics remain nearly unchanged.

Non-Abelian Anyon Statistics through ac Conductance of a Majorana Interferometer.

Demonstrating the non-Abelian Ising anyon statistics of Majorana zero modes in a physical platform still represents a major open challenge in physics. We here show that the linear low-frequency charge conductance of a Majorana interferometer containing a floating superconducting island can reveal the topological spin of quantum edge vortices. The latter are associated with chiral Majorana fermion edge modes and represent "flying" Ising anyons. We describe possible device implementations and outline how to detect non-Abelian anyon braiding through ac conductance measurements.

Gate tunable edge magnetoplasmon resonators

AbstractQuantum Hall systems are platforms of choice to study topological properties of condensed matter systems and anyonic exchange statistics. In this work we have developed a tunable radiofrequency edge magnetoplasmonic resonator controlled by both the magnetic field and a set of electrostatic gates, meant to serve as a versatile platform for future interferometric devices designed to evidence non-abelian anyons. In our device, gates allow us to change both the size of the resonant cavity and the electronic density of the two-dimensional electron gas. We show that we can continuously control the frequency response of our resonator, making it possible to develop an edge magnetoplasmon interferometer. As we reach smaller sizes of our resonator, finite size effects caused by the measurement probes manifest. In the future, such device will be a valuable tool to investigate the properties of non-abelian anyons in the fractional quantum Hall regime.

Aharonov-Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene.

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene Fabry-Pérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the Aharonov-Bohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the Aharonov-Bohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

Signature of anyonic statistics in the integer quantum Hall regime

Anyons are exotic low-dimensional quasiparticles whose unconventional quantum statistics extend the binary particle division into fermions and bosons. The fractional quantum Hall regime provides a natural host, with the first convincing anyon signatures recently observed through interferometry and cross-correlations of colliding beams. However, the fractional regime is rife with experimental complications, such as an anomalous tunneling density of states, which impede the manipulation of anyons. Here we show experimentally that the canonical integer quantum Hall regime can provide a robust anyon platform. Exploiting the Coulomb interaction between two copropagating quantum Hall channels, an electron injected into one channel splits into two fractional charges behaving as abelian anyons. Their unconventional statistics is revealed by negative cross-correlations between dilute quasiparticle beams. Similarly to fractional quantum Hall observations, we show that the negative signal stems from a time-domain braiding process, here involving the incident fractional quasiparticles and spontaneously generated electron-hole pairs. Beyond the dilute limit, a theoretical understanding is achieved via the edge magnetoplasmon description of interacting integer quantum Hall channels. Our findings establish that, counter-intuitively, the integer quantum Hall regime provides a platform of choice for exploring and manipulating quasiparticles with fractional quantum statistics.

Strongly coupled edge states in a graphene quantum Hall interferometer

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{2}}}{{\\boldsymbol{e}}}$$\\end{document} quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor ν<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, < \\, {{\\boldsymbol{2}}}$$\\end{document} to ν>7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}} \\, > \\, {{\\boldsymbol{7}}}$$\\end{document}, we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split ν=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\boldsymbol{\ u }}}={{\\boldsymbol{2}}}$$\\end{document} edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using density-tunable graphene.

Numerical demonstration of Abelian fractional statistics of composite fermion excitations in the spherical geometry

Numerical demonstration of Abelian fractional statistics of composite fermion excitations in the spherical geometry

Tunable even- and odd-denominator fractional quantum Hall states in trilayer graphene

Fractional quantum Hall (FQH) states are exotic quantum many-body phases whose elementary charged excitations are anyons obeying fractional braiding statistics. While most FQH states are believed to have Abelian anyons, the Moore–Read type states with even denominators – appearing at half filling of a Landau level (LL) – are predicted to possess non-Abelian excitations with appealing potential in topological quantum computation. These states, however, depend sensitively on the orbital contents of the single-particle LL wavefunctions and the LL mixing. Here we report magnetotransport measurements on Bernal-stacked trilayer graphene, whose multiband structure facilitates interlaced LL mixing, which can be controlled by external magnetic and displacement fields. We observe robust FQH states including even-denominator ones at filling factors ν = − 9/2, − 3/2, 3/2 and 9/2. In addition, we fine-tune the LL mixing and crossings to drive quantum phase transitions of these half-filling states and neighbouring odd-denominator ones, exhibiting related emerging and waning behaviour.

Observation of the scaling dimension of fractional quantum Hall anyons

Unconventional quasiparticles emerging in the fractional quantum Hall regime1,2 present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated for nearly three decades3–5, the first convincing evidence of their anyonic quantum statistics has only recently been obtained6,7 and, so far, the so-called scaling dimension that determines the propagation dynamics of the quasiparticles remains elusive. In particular, although the nonlinearity of the tunnelling quasiparticle current should reveal their scaling dimension, the measurements fail to match theory, arguably because this observable is not robust to non-universal complications8–12. Here we expose the scaling dimension from the thermal noise to shot noise crossover and observe an agreement with expectations. Measurements are fitted to the predicted finite-temperature expression involving both the scaling dimension of the quasiparticles and their charge12,13, in contrast to previous charge investigations focusing on the high-bias shot-noise regime14. A systematic analysis, repeated on several constrictions and experimental conditions, consistently matches the theoretical scaling dimensions for the fractional quasiparticles emerging at filling factors ν = 1/3, 2/5 and 2/3. This establishes a central property of fractional quantum Hall anyons and demonstrates a powerful and complementary window into exotic quasiparticles.

Fusion surface models: 2+1d lattice models from fusion 2-categories

We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the “symmetry TFTs” for fusion 2-category symmetries play an important role.

Incorporating non-local anyonic statistics into a graph decomposition

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

Baryons as vortexes on the η′ domain wall

We show that the recent construction of Nf = 1 baryons on the η′ domain wall can be understood as vortexes of the principal effective theory — the Chern-Simons-Higgs theory — on a 2+1-dimensional sheet. This theory has a series of vortex solutions, and the vortex with unit topological charge naturally spins Nc/2, which coincides with the spin of the one-flavor baryon in QCD. Since the Nc scaling of the vortexes is the same as that of baryons, the latter can be regarded as the former. By virtue of the particle-vortex symmetry, the dual Zhang-Hansson-Kivelson theory indicates that the quark carries topological charge 1/Nc and obeys fractional statistics. The generalization to arbitrary Nf is also discussed.

Levitons in correlated nano-scale systems.

In this short review (written to celebrate David Campbell's 80th birthday), we provide a theoretical description of quantum transport in nanoscale systems in the presence of single-electron excitations generated by Lorentzian voltage drives, termed Levitons. These excitations allow us to realize the analog of quantum optics experiments using electrons instead of photons. Importantly, electrons in condensed matter systems are strongly affected by the presence of different types of non-trivial correlations, with no counterpart in the domain of photonic quantum optics. After providing a short introduction about Levitons in non-interacting systems, we focus on how they operate in the presence of two types of strong electronic correlations in nanoscale systems, such as those arising in the fractional quantum Hall effect or in superconducting systems. Specifically, we consider Levitons in a quantum Hall bar of the fractional quantum Hall effect, pinched by a quantum point contact, where anyons with fractional charge and statistics tunnel between opposite edges. In this case, a Leviton-Leviton interaction can be induced by the strongly correlated background. Concerning the effect of superconducting correlations on Levitons, we show that, in a normal metal system coupled to BCS superconductors, half-integer Levitons minimize the excess noise in the Andreev regime. Interestingly, energy-entangled electron states can be realized on-demand in this type of hybrid setup by exploiting crossed Andreev reflection. The results exposed in this review have potential applications in the context of quantum information and computation with single-electron flying qubits.

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.

Robust multimodulus blind equalization algorithm for multilevel QAM signals in impulsive noise

As a blind equalization algorithm, the fractional lower-order statistics based multimodulus algorithm (FLOS-MMA) is suitable for equalizing multilevel quadrature amplitude modulation (QAM) signals in impulsive noise. However, the equalization performance of FLOS-MMA is severely degraded in strong impulsive noise because the first-order gradient of the cost function constrains the ability of FLOS to suppress large outliers in the equalizer output signal and is sensitive to large outliers in the equalizer input signal. To enhance the robustness of multimodulus blind equalization algorithm against impulsive noise, a FLOS based momentum fractional-order multimodulus algorithm (FLOS-MFOMMA) is proposed in this paper. The proposed algorithm mitigates the adverse effects of impulsive noise on the updating of equalizer coefficients by utilizing the fractional-order gradient and accelerates the convergence speed by incorporating a momentum term. Then, the steady-state excess mean square error and the computational complexity of FLOS-MFOMMA are analyzed theoretically. Finally, numerical simulations, for equalizing 16-QAM signals under impulsive noise environments, show that the proposed algorithm is superior to FLOS-MMA in terms of robustness and convergence speed.

Signatures of Fractional Statistics in Nonlinear Pump-Probe Spectroscopy.

We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two light pulses with an adjustable time delay between them. The relevant response coefficient exhibits a universal form that originates from the statistical phase acquired when anyons created by the first pulse braid around those created by the second. This behavior is shown to be qualitatively unchanged by nonuniversal physics including nonstatistical interactions and small nonzero temperatures. In magnetic systems, the signal of interest can be measured using currently available terahertz-domain probes, highlighting the potential usefulness of nonlinear spectroscopic techniques in the search for quantum spin liquids.

A hydrodynamical description of Bose liquid with fractional exclusion statistics

Hydrodynamical systems are usually taken as chaotic systems with fast relaxations. It is counter intuitive for ‘ideal’ gas to have a hydrodynamical description. We find that a hydrodynamical model of one-dimensional |Φ|6 theory shares the same ground state density profile, density-wave excitation, as well as the similar dynamical and statistical properties with the Calogero–Sutherland model in thermodynamic limit when their interaction strengths matches each other. The interaction strength g 0 in |Φ|6 theory is then the index of fractional statistics. Although the model is interacting in Bose liquid sense, but it shows integrability with periodical coherent evolution. We also discussed the fractional statistics emerges from the |Φ|6 theory.

Preface

The International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) is an interdisciplinary scientific event which aims to promote the knowledge and the development of high-quality research in mathematical fields that have to do with the applications of other scientific fields and the modern technological trends that appear in them, these fields being those of Physics, Chemistry, Biology, Medicine, Economics, Sociology, Environmental sciences etc.The 12th IC-MSQUARE took place in Belgrade, Serbia between August 28 and 31, 2023. In addition, (because in previous years the conference, due to the pandemic, took place only with online presentations), the possibility of participation via the internet was also adopted this time. Thus, apart from the talks and workshops held on site, we also had a large collection of pre-recorded presentations that were available to the participants through the conference website.The Conference was attended by more than 350 participants and hosted about 320 oral and virtual presentations while counted more than 1000 pre-registered authors. The 12th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical and Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics, Social Modeling etc.The scientific program was rather heavy, however, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time.All papers submitted to the Conference have been reviewed using a single-blind peer-review process. The review process adopted a scoring system (0-5 points) who rated the Relevance, Scientific quality, Contribution, Title and paper presentation, Tables and figures, Language and the References of each paper. The threshold for an article to be accepted was a score above 4 for the majority of the evaluated papers. Additionally, each paper was tested for similarity with already published content using the Turnitin software. All sources of similarities were checked and only original content was accepted. In this way, out of 308 papers that were evaluated for this volume, only 167 were accepted for publication.We would like to thank the Reviewers, the Members of the International Scientific Committees as well as the Members of the Organizing Committee.The Conference ChairmanDimitrios VlachosUniversity of PeloponneseList of International Scientific Committee, Organizing Committee are available in this pdf.

Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

Many-particle quantum systems with intermediate anyonic exchange statistics are supported in one spatial dimension. In this context, the anyon-anyon mapping is recast as a continuous transformation that generates shifts of the statistical parameter &amp;#x03BA;. We characterize the geometry of quantum states associated with different values of &amp;#x03BA;, i.e., different quantum statistics. While states in the bosonic and fermionic subspaces are always orthogonal, overlaps between anyonic states are generally finite and exhibit a universal form of the orthogonality catastrophe governed by a fundamental statistical factor, independent of the microscopic Hamiltonian. We characterize this decay using quantum speed limits on the flow of &amp;#x03BA;, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.

Modular transformation and anyonic statistics of multicomponent fractional quantum Hall states

Modular transformation and anyonic statistics of multicomponent fractional quantum Hall states