Related papers: Quantum integrability in the multistate Landau-Zen…
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
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…
Three exactly solvable Hamiltonians of complex structure are studied in the framework of a semi-classical approach. The quantized trajectories for intrinsic coordinates correspond to energies which may be classified in collective bands. For…
We investigate the quantum integrability of the Landau-Lifshitz model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization,…
For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1…
A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant…
Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, $r$-matrices and integrals of motion in involution are explicitly proposed for…
The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…
Non-Hermitian quantum systems with explicit time dependence are of ever-increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a PT-symmetric non-Hermitian $N$-level Landau-Zener…
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…
The modular (or entanglement) Hamiltonian correspondent to the half-space-bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known…
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, $\gamma_n$…
We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such…
We show, in general, how to transform the nonautonomous nonlinear Schroedinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear…
We prove that linear degeneracy is a necessary conditions for systems in Jordan-block form to admit a compatible quasilinear differential constraint. Such condition is also sufficient for 2x2 systems and turns out to be equivalent to…
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…
This review work addresses the recent advances in solving more comprehensive Hamiltonians. The generalized tight-binding model is developed to investigate the feature-rich quantization phenomena in emergent 2D materials. The mutli-orbital…