Preparing exact eigenstates of the open XXZ chain on a quantum computer

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (L M) 2M M! terms, the algorithm requires L + M2+ 2M qubits.

Numerical constraints and non-spatial open boundary conditions for the Wigner equation

We discuss boundary value problems for the characteristic stationary von Neumann equation (stationary sigma equation) and the stationary Wigner equation in a single spatial dimension. The two equations are related by a Fourier transform in the non-spatial coordinate. In general, a solution to the characteristic equation does not produce a corresponding Wigner solution as the Fourier transform will not exist. Solution of the stationary Wigner equation on a shifted k-grid gives unphysical results. Results showing a negative differential resistance in IV-curves of resonant tunneling diodes using Frensley’s method are a numerical artefact from using upwinding on a coarse grid. We introduce the integro-differential sigma equation which avoids distributional parts at $$k=0$$ k = 0 in the Wigner transform. The Wigner equation for $$k=0$$ k = 0 represents an algebraic constraint needed to avoid poles in the solution at $$k=0$$ k = 0 . We impose the inverse Fourier transform of the integrability constraint in the integro-differential sigma equation. After a cutoff, we find that this gives fully homogeneous boundary conditions in the non-spatial coordinate which is overdetermined. Employing an absorbing potential layer double homogeneous boundary conditions are naturally fulfilled. Simulation results for resonant tunneling diodes from solving the constrained sigma equation in the least squares sense with an absorbing potential reproduce results from the quantum transmitting boundary with high accuracy. We discuss the zero bias case where also good agreement is found. In conclusion, we argue that properly formulated open boundary conditions have to be imposed on non-spatial boundaries in the sigma equation both in the stationary and the transient case. When solving the Wigner equation, an absorbing potential layer has to be employed.

Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions.

Modeling of the Turkish Strait System Using a High Resolution Unstructured Grid Ocean Circulation Model

The Turkish Strait System, which is the only connection between the Black Sea and the Mediterranean Sea, is a challenging region for ocean circulation models due to topographic constraints and water mass structure. We present a newly developed high resolution unstructured finite element grid model to simulate the Turkish Strait System using realistic atmospheric forcing and lateral open boundary conditions. We find that the jet flowing from the Bosphorus Strait into the Marmara creates an anticyclonic circulation. The eddy kinetic energy field is high around the jets exiting from the Bosphorus Strait, Dardanelles Strait, and also the leeward side of the islands in the Marmara Sea. The model successfully captures the two-layer structure of the Sea of Marmara. The volume transport at the Bosphorus is around 120 km3/year which is consistent with the recent observations. The largest bias in the model is at the interface depth due to the shallower mixed layer.

Open fishchain in N = 4 Supersymmetric Yang-Mills Theory

We consider a cusped Wilson line with J insertions of scalar fields in $$ \mathcal{N} $$ N = 4 SYM and prove that in a certain limit the Feynman graphs are integrable to all loop orders. We identify the integrable system as a quantum fishchain with open boundary conditions. The existence of the boundary degrees of freedom results in the boundary reflection operator acting non-trivially on the physical space. We derive the Baxter equation for Q-functions and provide the quantisation condition for the spectrum. This allows us to find the non-perturbative spectrum numerically.

Projected sea-level changes in the marginal seas near China based on dynamical downscaling

Projections of future sea-level changes are usually based on global climate models (GCMs). However, the changes in shallow coastal regions, like the marginal seas near China, cannot be fully resolved in GCMs. To improve regional sea-level simulations, a high-resolution (~8 km) regional ocean model is set up for the marginal seas near China for both the historical (1994-2015) and future (2079-2100) periods under representative concentration pathways (RCPs) 4.5 and 8.5. The historical ocean simulations are evaluated at different spatiotemporal scales, and the model is then integrated for the future period, driven by projected monthly climatological climate change signals from 8 GCMs individually via both surface and open boundary conditions. The downscaled ocean changes derived by comparing historical and future experiments reveal greater spatial details than those from GCMs, e.g., a low dynamic sea level (DSL) centre of -0.15 m in the middle of the South China Sea (SCS). As a novel test, the downscaled results driven by the ensemble mean forcings are almost identical with the ensemble average results from individually downscaled cases. Forcing of the DSL change and increased cyclonic circulation in the SCS are dominated by the climate change signals from the Pacific, while the DSL change in the East China marginal seas is caused by both local atmosphere forcing and signals from the Pacific. The method of downscaling developed in this study is a useful modelling protocol for adaptation and mitigation planning for future oceanic climate changes.

Floquet Second-Order Topological Phases in Momentum Space

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.

Tools and technologies for NEMO models: the case of the Generic Interfaces developed in the framework of IMMERSE

<p>Setting new model configurations based on NEMO requires the definition of initial/boundary condition and the validation of numerical solutions. In the framework of IMMERSE H2020 project, CMCC is developing new tools and technological capacities for handling in easy and reliable way external products, such CMEMS or coastal ocean data, for research-to-operations applications. Generic Interfaces for NEMO (InterNEMO) allow for 3 main scopes: 1) to access and discover the CMEMS catalogue, including both model and observational data; 2) to manipulate accessed datasets, including coastal ocean data, to extract relevant physical information to use for setting initial/boundary conditions for a new NEMO-based configurations; 3) to prepare NEMO set of upstream files and to validate NEMO solution by using CMEMS observational datasets. InterNEMO implements also technologies to connect a NEMO user to Wekeo DIAS (https://www.wekeo.eu/) for the interoperable accessing and processing of CMEMS data. In this contribution, we present the InterNEMO architecture developed in Python via Jupyter Notebooks, to support the user/researcher to easily discover, design and configure modeling components required by the new NEMO-based configuration. InterNEMO is tested for the Black Sea hydrodynamical model configuration, developed by CMCC in the framework of the Black Sea Monitoring and Forecasting Centre (BS-MFC) for CMEMS a) to show how to access CMEMS observations through Wekeo DIAS and use them to validate numerical solutions and b) to define open boundary conditions from an unstructured grid model configuration based on Shyfem, developed for the Marmara Sea.</p>