Related papers: Quantum vs Classical Integrability in Ruijsenaars-…

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…

In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general…

The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the…

Recently, Feh\'er and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider $n$-particle systems, with phase space symplectomorphic to the $(n-1)$-dimensional complex projective space.…

The classical quantization of a Lienard-type nonlinear oscillator is achieved by a quantization scheme (M.C. Nucci. Theor. Math. Phys., 168:997--1004, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order…

We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…

We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of…

Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…

Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…

These notes correspond to a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularity and expose recent research in…

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of…

From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars'). The corresponding r-matrix is shown to be the classical $Z_n$-symmetric elliptic r-matrix,…

In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems…

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the…

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to…

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat…

Decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to…

Quantum computing offers the potential for superior computational capabilities, particularly for data-intensive tasks. However, the current state of quantum hardware puts heavy restrictions on input size. To address this, hybrid transfer…