Related papers: Chaotic string motion in a near pp-wave limit

We consider a chain of $n$ coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential $V_n = r^2/2 + \sigma_nU(r)$, where $U$…

We investigate the question of possible integrability of classical string motion in curved p-brane backgrounds. For example, the D3-brane metric interpolates between the flat and the AdS_5 x S^5 regions in which string propagation is…

We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations…

In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle…

We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various…

We elaborate on integrable dynamical systems from scalar-gravity Lagrangians that include the leading dilaton tadpole potentials of broken supersymmetry. In the static Dudas-Mourad compactifications from ten to nine dimensions, which rest…

We consider a pulsating string near a non-extremal black p-brane (p=5 and p=6) and investigate the chaos in the corresponding string dynamics by examining the Fast Lyapunov indicator(FLI) and Poincare section. In our system, the energy and…

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical…

Hamilton's principle is used to extend for the Toda lattice ODEs to systems of PDEs called the Toda lattice strand equations (T-Strands). The T-Strands in the $n$-particle Toda case comprise $4n-2$ quadratically nonlinear PDEs in one space…

A thermodynamic argument is presented suggesting that near-extremal spinning D1-D5-P black strings become unstable when their angular momentum exceeds $J_{crit} = {3Q_1Q_5}/2\sqrt{2}$. In contrast, the dimensionally reduced black holes are…

The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the asymptotic data of the trajectories define…

In this paper, we make a systematical and in-depth study on the chaotic dynamics of the string around the conformal black hole. Depending on the characteristic parameter of the conformal black hole and the initial position of the string,…

The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum operators of the corresponding quantum integrable models.…

We observe that the pp wave limit of $AdS_5\times M^5$ compactifications of type IIB string theory is universal, and maximally supersymmetric, as long as $M^5$ is smooth and preserves some supersymmetry. We investigate a specific case,…

Classical world-sheet string theory has recently been shown to be nonintegrable and chaotic in various confining string theory backgrounds -- the AdS soliton background in particular. In this paper we study a minisuperspace quantization of…

We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…

In this paper we consider the Toda lattice $(\mathbf{p}(t);\mathbf{q}(t))$ at thermal equilibrium, meaning that its variables $(p_j)$ and $(e^{q_j-q_{j+1}})$ are independent Gaussian and Gamma random variables, respectively. We show under…

We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality…

We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap…