Related papers: Time dynamics of Bethe ansatz solvable models
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…
A protocol for explicitly constructing the exact time-evolution operators generated by $2 \times 2$ time-dependent $PT$-symmetry Hamiltonians is reported. Its mathematical applicability is illustrated with the help of appropriate examples.…
Motivated by Heilmann and Lieb's work, we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence…
We study the universal non-stationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the…
In this paper, an inverse-free dynamical system with fixed-time convergence is presented to solve the system of absolute value equations (AVEs). Under a mild condition, it is proved that the solution of the proposed dynamical system…
We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of…
We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The…
We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of…
We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson…
We present a novel method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a…
A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum $sl_3$ Gaudin model is presented.
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…
We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up.…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution…
In this paper we formulate a general method for building completely integrable quantum systems. The method is based on the use of the so-called multi-parameter spectral equations, i.e. equations with several spectral parameters. We show…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…