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We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both…
This paper has been withdrawn by the authors. Measurements at many different angles spanning a broad range of electron densities indicate that the observed doubling of the period of Shubnikov-de Haas oscillations, which we had attributed to…
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…
Despite its non-Hermitian nature, the transverse optical beam shift exhibits both real eigenvalues and non-orthogonal eigenstates. To explore this unexpected similarity to typical PT (parity-time)-symmetric systems, we first categorize the…
Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states…
The non-linear $\Sigma$-Model minimally coupled with Maxwell theory in $3+1$ dimensions possesses a topologically non-trivial sector characterized by ``lasagna''-like configurations. We demonstrate that, when a specific quantization…
A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion…
Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…
In the context of hyperbolic systems of balance laws, the Shizuta-Kawashima coupling condition guarantees that all the variables of the system are dissipative even though the system is not totally dissipative. Hence it plays a crucial role…
This paper extends the model reduction method by the operator projection to the three-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order moment system is built on our careful study of infinite families of…
We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be…
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary…
We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and…
We analyze the possible types of ordering in a boson--fermion model. The Hamiltonian is inherently related to the Bose--Hubbard model for vector two-species bosons in optical lattices. We show that such model can be reduced to the…
A Backlund transformation between two hyperbolic Monge-Ampere systems may be described as a certain type of exterior differential system on a 6-dimensional manifold B. The transformation is homogeneous if the group of symmetries of the…