It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

We consider Jordanian deformations of the AdS_5xS^5 superstring action. The deformations correspond to non-standard q-deformation. In particular, it is possible to perform partial deformations, for example, only for the S^5 part. Then the classical action and the Lax pair are constructed with a linear, twisted and extended R operator. It is shown that the action preserves the kappa-symmetry.

/pdf/jordanian-deformations-of-the-ads-5xs-5-superstring-rr2agi3qus.pdf

Jordanian deformations of the AdS_5xS^5 superstring

In this thesis we consider certain supersymmetric string theories on curved backgrounds containing the three-dimensional anti-de Sitter space, AdS3. On the one hand, these are gravity theories in three dimensions, which makes them simpler than real-world gravity but still rich in interesting phenomena. On the other hand, according to the holographic duality, each of these gravitational theories should be equivalent to a suitable quantum field theory with conformal symmetry in two dimensions, a CFT2. In that low dimension, such conformal field theories enjoy an infinite-dimensional Virasoro symmetry which strongly constrains them, but remain non-trivial. Our study is confined to a particular regime, the 't Hooft limit, in which the strings propagate freely. Free string theory can be described as a non-linear sigma model from the string worldsheet (geometrically, a two-dimensional cylinder) into a target space of the form AdS3xM, where M is a manifold without boundary. For us, M is a product of circles and three-dimensional spheres, namely M=S3xT4 or M=S3xS3xS1, both of which enjoy 16 supersymmetries. For the sake of brevity, our presentation is mostly focused on the massive sector of the former geometry, while more general cases are discussed in the concluding chapter. Our main result is to describe how these theories are integrable at the quantum level, i.e. how their worldsheet scattering matrix factorises and their spectrum can be efficiently computed by Bethe ansatz techniques. This is done both from the point of view of the worldsheet theory and of a dual spin chain picture. We also discuss how this procedure is supported by overwhelming evidence from independent (perturbative or semiclassical) calculations, up to two loops in the worldsheet theory expansion.

/pdf/towards-integrability-for-ads3-cft2-nz9zwp7qsu.pdf

Towards integrability for AdS3/CFT2

Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations

/pdf/the-hidden-symmetries-of-the-ads-5-s-5-superstring-3em9ueqbo4.pdf

The Hidden Symmetries of the ADS 5 × S 5 Superstring

Abelian Yang–Baxter deformations and TsT transformations

Interesting deformations of AdS5 × S5 such as the gravity dual of noncommutative SYM and Schodinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the associated construction based on R matrices that solve the classical Yang-Baxter equation, and present an overview of manifestly real R matrices associated to the various deformations. We also discuss when these R matrices should correspond to TsT transformations, which not all do, and briefly analyze the symmetries preserved by these deformations, for example finding Schrodinger superalgebras that were previously obtained as subalgebras of $$ \mathfrak{p}\mathfrak{s}\mathfrak{u} $$
 (2, 2|4). Our results contain a (singular) generalization of an apparently non-TsT deformation of AdS5 × S5, whose status as a string background is an interesting open question.

/pdf/on-classical-yang-baxter-based-deformations-of-the-ads-5-s-5-fzbs8pa66q.pdf

On classical Yang-Baxter based deformations of the AdS 5 × S 5 superstring

Interesting deformations of AdS_5 x S^5 such as the gravity dual of noncommutative SYM and Schodinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the associated construction based on R matrices that solve the classical Yang-Baxter equation, and present an overview of manifestly real R matrices associated to the various deformations. We also discuss when these R matrices should correspond to TsT transformations, which not all do, and briefly analyze the symmetries preserved by these deformations, for example finding Schrodinger superalgebras that were previously obtained as subalgebras of psu(2,2|4). Our results contain a (singular) generalization of an apparently non-TsT deformation of AdS_5 x S^5, whose status as a string background is an interesting open question.

On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring

We discuss the spectrum of a string propagating on eta-deformed AdS_5 x S^5 by treating its world-sheet theory as an integrable quantum field theory. The exact S-matrix of this field theory is given by a q-deformation of the AdS_5 x S^5 world-sheet S-matrix with real deformation parameter. By considering mirror (double Wick-rotated) versions of these world-sheet theories we give the Thermodynamic Bethe Ansatz description of their exact finite size spectra. Interestingly, this class of models maps onto itself under the mirror transformation. At the level of the string this appears to say that the light-cone worldsheet theories of strings on particular pairs of backgrounds are related by a double Wick rotation, a feature we call 'mirror duality'. We provide a partial check of these statements at the level of the sigma model by considering reduced actions and their corresponding (mirror) giant magnon solutions.

Stijn J. van Tongeren

Papers

Abelian Yang–Baxter deformations and TsT transformations

On classical Yang-Baxter based deformations of the AdS 5 × S 5 superstring

On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring

On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring

Almost abelian twists and AdS/CFT