Related papers: New classical integrable systems from generalized …
This review explores recent advances in the theory of $T\bar{T}$ deformation, an irrelevant yet solvable deformation of quantum field theories defined via the quadratic form of the energy-momentum tensor. It addresses classical and quantum…
The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks…
We derive the TBA system of equations from the S-matrix describing integrable massive perturbation of the coset $G_l \times G_m / G_{l+m}$ by the field $(1,1,adj)$ for all the infinite series of the simple Lie algebras $G=A,B,C,D$. In the…
The classical and quantum representations of thermal equilibrium are strikingly different, even for free, non-interacting particles. While the first involves particles with well-defined positions and momenta, the second usually involves…
Recent advances in molecular cooling have enabled the realization of strongly dipolar Bose-Einstein condensates (BECs) of molecules, and BECs of many different molecular species may become experimentally accessible in the near future. Here,…
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two…
We discuss the description of generic excited states in the quantum deformed AdS_5 x S^5 mirror thermodynamic Bethe ansatz and derive the associated Y-system. This Y-system shows an interesting new feature; it depends explicitly on the…
We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in…
We study the formation of large-scale coherent structures (a condensate) for a system of two weakly interacting classical waves. Using the coupled defocusing nonlinear Schr\"odinger (NLS) equations as a representative model, we focus on…
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…
The classical spin system consisting of three spins with Heisenberg interaction is an example of a completely integrable mechanical system. In this paper we explicitly calculate thermodynamic quantities as density of states, specific heat,…
We present steps towards an ab initio derivation of generalised hydrodynamics in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb-Liniger model. This includes an…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S.…
We show that classical many-particle systems interacting with certain soft pair interactions in two dimensions exhibit novel low-temperature behaviors. Ground states span from disordered to crystalline. At some densities, a large fraction…
The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double…