Current fluctuations for the second class particle: joint statistics

We study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe Ansatz approach, we derive the eigenvalues of the Gaudin operators and the corresponding Bethe Ansatz equations.

A method for inversion of periodic open boundary conditions in two-dimensional tidal models

Periodic boundary condition is commonly used in the FE homogenization method for predicting the thermo-mechanical properties of composites. However, its existing numerical algorithms are generally inefficient. Linear displacement boundary condition is much easier and more efficient to implement for the Representative Volume Elements (RVEs) with conformal and nonconformal surface meshes. Aiming at replacing the periodic boundary condition by the linear displacement boundary condition to easily and efficiently predict the thermo-mechanical properties of composites, this paper compares the implementation efficiency and prediction accuracy of the periodic and linear displacement boundary conditions. Regarding the prediction of the elastic properties of composites, the balance of micro-energy and macro-energy of the RVEs imposed the periodic and linear displacement boundary conditions is checked, and the results demonstrate that these two boundary conditions guarantee the Hill lemma (i.e. the balance of micro-energy and macro-energy of the RVEs). Moreover, comparing with the experimental test and the multi-step micro-mechanical method, the effectiveness of the periodic and linear displacement boundary conditions to predict the elastic properties of composites is validated.

Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems $\mathcal{PT}$ symmetry gives rise to stable and protected Dirac points. Here, we study a $\mathcal{PT}$-symmetric system which is both non-Hermitian and topological, namely a $\mathcal{PT}$-symmetric Dirac semimetal with non-Hermitian perturbations in three dimensions. We find that, in general, there are only two types of symmetry allowed non-Hermitian perturbations, namely non-Hermitian kinetic potentials, and non-Hermitian anti-commuting potentials. For both of these non-Hermitian potentials we investigate the band topology for open and periodic boundary conditions, determine the exceptional points, and compute the surface states. We find that with periodic boundary conditions, the non-Hermitian kinetic potential leads to exceptional rings, while the non-Hermitian anti-commuting potential generates exceptional spheres, which separate regions with broken $\mathcal{PT}$ symmetry from regions with unbroken $\mathcal{PT}$ symmetry. With open boundary conditions, the non-Hermitian kinetic potential induces a non-Hermitian skin effect which is localized on both sides of the sample due to symmetry, while the non-Hermitian anticommuting potential leads to Fermi ribbon surface states.

For the one-dimensional XXX model under the periodic boundary conditions, we\ndiscuss two types of eigenvectors, regular eigenvectors which have\nfinite-valued rapidities satisfying the Bethe ansatz equations, and non-regular\neigenvectors which are descendants of some regular eigenvectors under the\naction of the SU(2) spin-lowering operator. It was pointed out by many authors\nthat the non-regular eigenvectors should correspond to the Bethe ansatz\nwavefunctions which have multiple infinite rapidities. However, it has not been\nexplicitly shown whether such a delicate limiting procedure should be possible.\nIn this paper, we discuss it explicitly in the level of wavefunctions: we prove\nthat any non-regular eigenvector of the XXX model is derived from the Bethe\nansatz wavefunctions through some limit of infinite rapidities. We formulate\nthe regularization also in terms of the algebraic Bethe ansatz method. As an\napplication of infinite rapidity, we discuss the period of the spectral flow\nunder the twisted periodic boundary conditions.\n

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f ∞−A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.

A formal framework is established for the way in which cloud-resolving numerical models are used to investigate the role of precipitating cloud systems in climate and weather forecasting models. Emphasis is on models with periodic lateral boundary conditions that eliminate unrealistic numerically generated circulations caused by open boundary conditions in long-term simulations. Defined in this formalism is the concept of large-scale forcing and the cloud-environment interactions that are consistent with the periodic boundary conditions. Two-dimensional numerical simulations of the evolution of cloud systems during 1–7 September 1974 in Phase III of the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) are conducted. Based on the above formalism, a simple technique is used to force an anelastic cloud-resolving model with evolving large-scale horizontal wind field and large-scale forcing for the temperature and moisture obtained from the GATE data. The 7-day period selected i...

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

In this article, a new cellular automaton traffic flow model, in which randomisation effect is enhanced with the decrease of time gap and the long time stopped vehicle has large randomisation probability, is presented. Both periodic and open boundary conditions are considered. Under periodic boundary condition, the fundamental diagram and the properties of synchronised flow are studied in detail. Under open boundary condition, different congested patterns induced by an on-ramp are analysed. The results are consistent with the well-known results of Kerner's three-phase traffic theory published before.

We consider the Temperley–Lieb (TL) open quantum spin chain with “free” boundary conditions associated with the spin-s representation of quantum-deformed sl(2). We construct the transfer matrix, and determine its eigenvalues and the corresponding Bethe equations using analytical Bethe ansatz. We show that the transfer matrix has quantum group symmetry, and we propose explicit formulas for the number of solutions of the Bethe equations and the degeneracies of the transfer-matrix eigenvalues. We propose an algebraic Bethe ansatz construction of the off-shell Bethe states, and we conjecture that the on-shell Bethe states are highest-weight states of the quantum group. We also propose a determinant formula for the scalar product between an off-shell Bethe state and its on-shell dual, as well as for the square of the norm. We find that all of these results, except for the degeneracies and a constant factor in the scalar product, are universal in the sense that they do not depend on the value of the spin. In an appendix, we briefly consider the closed TL spin chain with periodic boundary conditions, and show how a previously-proposed solution can be improved so as to obtain the complete (albeit non-universal) spectrum.

Double-sided open periodic structures are analyzed using inhomogeneous plane wave scattering.The leaky and surface wave modes of several unit cells of different structures are computed using the poles of generalized reflection and transmission coefficients of inhomogeneous plane waves in the spectral domain.It is shown that the reflection and transmission coefficients of the zeroth order Floquet mode contain the poles of the Green's function of the complex stratified periodic structure.The properties of evanescent mode amplification as well as super resolution near field imaging in a wire medium are addressed.A balanced leaky wave antenna unit cell with double-sided radiation feature is introduced and it is shown that, in contrast to grounded structures, total absorption in lossless nonchiral double-sided open unit cells is not feasible as long as the behavior of the unit cell is well described by its fundamental mode.

Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straightforwardly implemented on top of an existing DMRG or MPS ground-state code. Although this approach is built on open-boundary MPS, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2-D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.

Abstract. Open boundary conditions were developed for atmospheric large-eddy simulation (LES) models and implemented into the Dutch Atmospheric Large-Eddy Simulation model. The implementation was tested in a “Big Brother”-like setup, in which the simulation with open boundary conditions was forced by an identical control simulation with periodic boundary conditions. The results show that the open boundary implementation has minimal influence on the solution. Both the mean state and the turbulent structures are close to the control simulation, and disturbances at the in- and outflow boundaries are negligible. To emulate a setup in which the LES is coupled to a coarser model, the influence of coarse boundary input was tested by smoothing the output of the periodic control simulation both temporally and spatially before feeding it as input to the simulation with open boundary conditions. When smoothing is applied over larger spatial and longer temporal scales, disturbances start to form at the inflow boundary and an area exists where turbulence needs to develop. Adding synthetic turbulence to the smoothed input reduces the size of this area and the magnitude of the disturbances.

Using the algebraic Bethe ansatz method, we obtain the eigenvalues of the transfer matrix of the supersymmetric model with Uq[osp(1|2)] symmetry under periodic boundary and twisted boundary conditions.

A solvable Anderson lattice model is formulated. The exact eigenstates of model Hamiltonian are constructed by using the Bethe ansatz. The Bethe ansatz equations are obtained from the periodic boundary conditions.