Open Boundary Conditions Research Articles

Mixing times and cutoffs in open quadratic fermionic systems

In classical probability theory, the term cutoff describes the property of some Markov chains to jump from (close to) their initial configuration to (close to) completely mixed in a very narrow window of time. We investigate how coherent quantum evolution affects the mixing properties in two fermionic quantum models (the ``gain/loss'' and ``topological'' models), whose time evolution is governed by a Lindblad equation quadratic in fermionic operators, allowing for a straightforward exact solution. We check that the cutoff phenomenon extends to the quantum case and examine how the mixing properties depend on the initial state. In the topological case, we further show how the mixing properties are affected by the presence of a long-lived edge zero mode when taking open boundary conditions.

Wave Simulation by the SWAN Model and FVCOM Considering the Sea-Water Level around the Zhoushan Islands

In this study, the numerical wave model Simulating Waves Nearshore (SWAN), which resolves nearshore wave processes, and a hydrodynamic model, the Finite-Volume Community Ocean Model (FVCOM), were coupled to simulate waves and currents during Typhoon Fung-wong (2014) and Typhoon Chan-hom (2015) around the Zhoushan Islands. Both of these models employ the same unique unstructured grid. In particular, the influence of sea-surface currents, e.g., typhoon-induced and tidal currents, as well as the sea-water level, on wave simulation was studied. The composite wind field, which is derived from the parametric Holland model and European Centre for Medium-Range Weather Forecasts (ECMWF) winds (H-E winds), was taken as the forcing field. TPXO.5 tide data, sea-surface temperatures from the HYbrid Coordinate Ocean Model (HYCOM), HYCOM sea-surface salinity, and HYCOM sea-surface current were treated as open-boundary conditions. The comparison of sea-surface-current speed between the FVCOM simulation and the National Centers for Environmental Prediction (NCEP) Climate Forecast System Version 2 (CFSv2) data revealed a root-mean-square error (RMSE) of about 0.1206 m/s, with a correlation (Cor) more than 0.8, while the RMSE of the simulated sea-water level when compared with the HYCOM data was around 0.13 m, with a Cor of about 0.86. The validation indicated that the simulated results in this study were reliable. A sensitive experiment revealed that the sea-water level affected the typhoon-induced wave simulation. Validation against the measurements from the moored buoys showed an RMSE of <0.9 m for the sea-water level, which specifically reflected less overestimation during the high-sea state. Moreover, the significant-wave-height (SWH) difference (SWH without the sea-water level minus SWH with the sea-water level) was as great as −0.5 m around the Zhoushan Islands during the low-sea state. Furthermore, we studied the typhoon-induced waves when Typhoon Fung-wong passed the Zhoushan Islands, revealing that the reduction of SWH could be up to 1 m in the Yangtze Estuary and tidal flats when the maximum waves occurred.

Complete solution of the tight binding model on a Cayley tree: strongly localised versus extended states

The complete set of Eigenstates and Eigenvalues of the nearest neighbour tight binding model on a Cayley tree with branching number b = 2 and M branching generations with open boundary conditions is derived. We find that of the N = 1 + 3(2 M − 1) total states only 3M + 1 states are extended throughout the Cayley tree. The remaining N − (3M + 1) states are found to be strongly localised states with finite amplitudes on only a subset of sites. In particular, there are, for M > 1, 3 × 2 M−2 surface states which are each antisymmetric combinations of only two sites on the surface of the Cayley tree and have energy eactly at E = 0, the middle of the band. The ground state and the first two excited states of the Cayley tree are found to be extended states with amplitudes on all sites of the Cayley tree, for all M. We use the results on the complete set of Eigenstates and Eigenvalues to derive the total density of states and a local density of states.

Graded off-diagonal Bethe ansatz solution of the SU(2|2) spin chain model with generic integrable boundaries

The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T−Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.

Electronic structure calculations in electrolyte solutions: Methods for neutralization of extended charged interfaces.

Density functional theory (DFT) is often used for simulating extended materials such as infinite crystals or surfaces, under periodic boundary conditions (PBCs). In such calculations, when the simulation cell has non-zero charge, electrical neutrality has to be imposed, and this is often done via a uniform background charge of opposite sign ("jellium"). This artificial neutralization does not occur in reality, where a different mechanism is followed as in the example of a charged electrode in electrolyte solution, where the surrounding electrolyte screens the local charge at the interface. The neutralizing effect of the surrounding electrolyte can be incorporated within a hybrid quantum-continuum model based on a modified Poisson-Boltzmann equation, where the concentrations of electrolyte ions are modified to achieve electroneutrality. Among the infinite possible ways of modifying the electrolyte charge, we propose here a physically optimal solution, which minimizes the deviation of concentrations of electrolyte ions from those in open boundary conditions (OBCs). This principle of correspondence of PBCs with OBCs leads to the correct concentration profiles of electrolyte ions, and electroneutrality within the simulation cell and in the bulk electrolyte is maintained simultaneously, as observed in experiments. This approach, which we call the Neutralization by Electrolyte Concentration Shift (NECS), is implemented in our electrolyte model in the Order-N Electronic Total Energy Package (ONETEP) linear-scaling DFT code, which makes use of a bespoke highly parallel Poisson-Boltzmann solver, DL_MG. We further propose another neutralization scheme ("accessible jellium"), which is a simplification of NECS. We demonstrate and compare the different neutralization schemes on several examples.

Squaring the fermion: The threefold way and the fate of zero modes

We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension we establish three fundamental no-go theorems that prove the absence of: parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting non-interacting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of non-interacting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.

Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems.

We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary conditions in non-Hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the nonvanishing current through the system.

Graphene gets bent

Graphene gets bent

Spin–Orbit Coupling-Induced Effective Interactions in Superconducting Nanowires in the Strong Correlation Regime

In the second order of the operator form of the perturbation theory, the effective interactions in a superconducting nanowire have been obtained at the strong electron correlations, when the spin–orbit coupling parameter is comparable with the hopping integral. Using the exact diagonalization technique, in short nanowires with the open boundary conditions at the strong Coulomb repulsion, the excitations corresponding to the Majorana edge states with the energy below the value of a bulk superconducting gap have been demonstrated.

Study on fuel consumption in the Kerner–Klenov–Wolf three-phase cellular automaton traffic flow model

Based on the Kerner–Klenov–Wolf three-phase cellular automaton traffic model, we study fuel consumption of vehicles on one-way lanes under open boundary conditions. The difference in the appearance of the phase diagram is found to be related to the length of the vehicle. Phase diagram is divided into free flow, congested phase I, congested phase II and maximum current (MC) phase for the 15 cells of vehicle length and lacks the maximum current (MC) phase for 5 cells of vehicle length. By analysis of the cross-correlation between local density and flow and the spatial–temporal patterns, synchronized flow (SF) on the area upstream of the road is determined. The numerical computations for fuel consumption on free flow, congested phase I, synchronous flow (SF) and maximum current (MC) are carried out. The results indicate that the injection rate and the removal rate have great impacts on fuel consumption in the open boundary traffic system. The maximum current (MC) phase and congested phase I maximize fuel consumption. The fuel consumption of synchronized flow (SF) exceeds that of the free flow, but lower than that of the congested phase I and the maximum current (MC).

Dynamics after quenches in one-dimensional quantum Ising-like systems

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter $g$ driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of $g$ around the critical value $g_c$, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of $g$. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.

The spectrum of the abelian sandpile model

In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral parameters which govern the asymptotic spectral gap and asymptotic mixing time. This paper gives a general method of determining the spectral parameters either computationally or asymptotically, and determines the spectral parameters in specific examples.

Traffic flow cellular automaton model with bi-directional information in an open boundary condition

AbstractWith Connected Vehicle Technologies being popular, drivers not only perceive downstream traffic information but also get upstream information by routinely checking backward traffic conditions, and the backward-looking frequency or probability is usually affected by prevailing traffic conditions. Meanwhile, the bi-directional perception range of drivers is expected to significantly increase, which results in more informed and coordinated driving behaviours. So, we propose a traffic flow bi-directional CA model with two perception ranges, and perform the numerical simulations with the field data collected from a one-lane highway in Richmond, California, USA as the benchmark data. Numerical results show that the CA model can effectively reproduce the oscillation of relatively congested traffic and the traffic hysteresis phenomenon. When adjusting the backward-looking probability and the perception range, the CA model can well simulate the travel times of all vehicles, and the generation and dissolution of traffic jams under various scenarios.

Prediction of extreme convective rainfall intensities using a free-running 3-D sub-km-scale cloud model initialized from WRF km-scale NWP forecasts

Most of the heavy rainfall comes from the severe convective storms. Convective scale numerical weather prediction with grid-lengths of a few km or less, is capable for a more successful representation of convective scale processes and explicitly representing different types of convective storms. However, despite these high-non-hydrostatic models, in some specific atmospheric cases associated with very intense convection, the present mesoscale models show some uncertainties and limitations in more accurate quantitative estimation of the intensity of heavy convective rainfall. In a way to overcome this problem we propose a novel forecasting system, that employs three-dimensional (3-D) cloud resolving model at Large Eddy Simulations (LES) type with greatly refined resolution of 100-m over a small sub-domain with the initial representative averaged vertical profiles derived from WRF-NMM 1-km forecasts. LES model is configured to explicitly simulate small-scale, high-intensity convective rainfall at that time and location where convective criteria and threshold values defined in the system interface are previously met. The cloud-model then evolves independently, with open lateral boundary conditions. A set of numerical experiments have been conducted and the method has been extensively tested on both tropical and mid-latitude convective cases. Results show some potential benefits in simulation of convective elements, cell structure and intensity. In this preliminary study, we show that the proposed method gives quantitatively more accurate forecast of high-intensity convective precipitation in most of the eight case-studies presented, when compared to the WRF-NMM 1-km scale forecasts. The improved skill of the forecasts using this forecast system will probably provide useful value to forecasters, so that they would be able to enhance their operational flood prediction capabilities and warnings of severe convective weather risk.

Radiative topological biphoton states in modulated qubit arrays

We study topological properties of bound pairs of photons in spatially-modulated qubit arrays (arrays of two-level atoms) coupled to a waveguide. While bound pairs behave like Bloch waves, they are topologically nontrivial in the parameter space formed by the center-of-mass momentum and the modulation phase, where the latter plays the role of a synthetic dimension. In a superlattice where each unit cell contains three two-level atoms (qubits), we calculate the Chern numbers for the bound-state photon bands, which are found to be $(1,-2,1)$. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. Unlike the conventional case of the bulk-edge correspondence, these novel edge modes not only exist in gaps separating the bound-pair bands, but they also may merge with and penetrate into the bands. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.

One-dimensional one-band topologically nontrivial non-Hermitian system simulated in optical cavities

We propose a scheme for simulating a momentum dependent non-Hermitian Hamiltonian term by adding loss in the hopping process in a one-dimensional array of optical cavities, which leads to a one-band topological nontrivial non-Hermitian model. We find that there is a kind of transition from all real energy spectrum to all imaginary one under open boundary conditions: the eigenvalues are all real or imaginary dependent on which amplitude of the Hermitian or non-Hermitian part is dominant even though the eigenvalues of the bulk system are complex under the periodic boundary condition. In addition, for such a non-Hermitian Hamiltonian, the left eigenvectors are the mirror symmetry of the right eigenvectors. Finally, by using the input-output formula, we show that the distribution of the boundary states can be directly observed by detecting the optical transmission in both cases.

The Effects of Strategic Openness on Short- Versus Long-term Firm Performance

Recent work points out that strategic openness is an important instrument of impression management to shape legitimacy while also with significant competitive pressure for losing control of resources. How are these effects of strategic openness reflected in firm performance? Answers to this question, we pointed a comprehensive framework examining the dynamic and contingent effects of strategic openness on firm performance. We show how nearly identical mechanisms driving the openness-performance relationship can yield both inverted U- and U-shaped effects due to differences in relative strength between legitimacy and competition. Consistent with our theoretical framework, results combining a text analysis of 29120 annual reports with the financial data from 3366 listed companies in China show an inverted U-shaped effect in the short run, flipping to U-shaped as the time window gets longer, and these relationships are moderated by firms’ strategy deviation and securities reports attention. This study offers new insights into optimal strategic open boundary conditions, supporting a more general yet more precise theory of open paradox.

Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices

We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has shares features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation.

Exactly Solvable Magnet of Conformal Spins in Four Dimensions.

We provide the eigenfunctions for a quantum chain of N conformal spins with nearest-neighbor interaction and open boundary conditions in the irreducible representation of SO(1,5) of scaling dimension Δ=2-iλ and spin numbers ℓ=ℓ[over ˙]=0. The spectrum of the model is separated into N equal contributions, each dependent on a quantum number Y_{a}=[ν_{a},n_{a}] which labels a representation of the principal series. The eigenfunctions are orthogonal and we computed the spectral measure by means of a new star-triangle identity. Any portion of a conformal Feynmann diagram with square lattice topology can be represented in terms of separated variables, and we reproduce the all-loop "fishnet" integrals computed by B. Basso and L. Dixon via bootstrap techniques. We conjecture that the proposed eigenfunctions form a complete set and provide a tool for the direct computation of conformal data in the fishnet limit of the supersymmetric N=4 Yang-Mills theory at finite order in the coupling, by means of a cutting-and-gluing procedure on the square lattice.

Bulk-boundary correspondence in non-Hermitian Hopf-link exceptional line semimetals

We consider a 3-dimensional (3D) non-Hermitian exceptional line semimetal model and take open boundary conditions in x, y, and z directions separately. In each case, we calculate the parameter regions where the bulk-boundary correspondence is broken. The breakdown of the bulk-boundary correspondence is manifested by the deviation from unit circles of generalized Brillouin zones (GBZ) and the discrepancy between spectra calculated with open boundary conditions (OBC) and periodic boundary conditions (PBC). The consistency between OBC and PBC spectra can be recovered if the PBC spectra are calculated with GBZs. We use both unit-circle Brillouin zones (BZ) and GBZs to plot the topological phase diagrams. The systematic analysis of the differences between the two phase diagrams suggests that it is necessary to use GBZ to characterize the bulk-boundary correspondence of non-Hermitian models.