Related papers: Quantum spin chains and integrable many-body syste…
In this note, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two--dimensional case…
Quantum simulators are engineered devices controllably designed to emulate complex and classically intractable quantum systems. A key challenge is to certify whether the simulator truly mimics the Hamiltonian of interest. This certification…
We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory…
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
The integrability of a quantum many-body system, which is characterized by the presence or absence of local conserved quantities, drastically impacts the dynamics of isolated systems, including thermalization. Nevertheless, a rigorous and…
The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation . A central question in…
A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of…
A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several…
We conjecture the quantum analogue of the classical trace formulae for the integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This is done by departing from the classical construction where the corresponding model is…
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We establish the precise relation between the integral kernel of the scattering matrix and the resonance in the massless Spin-Boson model which describes the interaction of a two-level quantum system with a second-quantized scalar field.…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We…
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding…
The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…