Related papers: Classical Integrability of the Zigzag Model

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like…

It is shown, that by means of a special projection operator, the Liouville equation for an N-particle distribution function of classical particles, driven from an equilibrium state by an external field, can be exactly converted into a…

In the standard model of particle physics, all fermions are fundamentally massless and only acquire their effective bare mass when the Higgs field condenses. Therefore, in a fundamental de Broglie-Bohm pilot-wave quantum field theory (valid…

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $\sigma$-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by…

The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which…

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has been a successful alternative approach to…

Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…

We obtain nonperturbative results in the framework of continuous Liouville theory. In particular, we express the specific heat ${\cal Z}$ of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres.…

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…

We give a short summary of our recent works on the classical integrable structure of two-dimensional non-linear sigma models defined on squashed three-dimensional spheres. There are two descriptions to describe the classical dynamics, 1)…

We consider the integrability of a two-parameter deformation of the Wess-Zumino-Witten model, previously introduced in relation with Poisson-Lie T-duality. The resulting family of Poisson-Lie dual models is shown to be integrable by using…

The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The…

We prove nonintegrability of a model Hamiltonian system defined on the Lie algebra $\mathfrak{su}_3$ suitable for investigation of connections between classical and quantum characteristics of chaos.

Completely integrable Hamiltonians defining classical mechanical systems of $N$ coupled oscillators are obtained from Poisson realizations of Heisenberg--Weyl, harmonic oscillator and $sl(2,\R)$ coalgebras. Various completely integrable…

For one 3-body and two 5-body planar choreographies on the same algebraic Lemniscate by Bernoulli we found explicitly a maximal possible set of (particular) Liouville integrals, 7 and 15, respectively, (including the total angular…

We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…

Time-dependent Ginzburg-Landau model with noise for neutral s-wave superconductor is derived from real-time finite-temperature quantum field theory by integrating over fermions in the density matrix propagator. Quantum decoherence due to…

Using the general method presented by Mohammedi \cite{NM} for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex…

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity…

In this paper we show that all supergravity billiards corresponding to sigma-models on any U/H non compact-symmetric space and obtained by compactifying supergravity to D=3 are fully integrable. The key point in establishing the integration…