相关论文: Quantum and Classical Integrable Systems

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…

The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of…

We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…

Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…

The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…

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…

In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…

Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…

We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…

We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…

We consider a hybrid quantum system consisting of a qubit system continuously evolving according to its fixed own Hamiltonian and a quantum computer. The qubit system couples to a quantum computer through a fixed interaction Hamiltonian,…

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…

We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum…

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…

A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras,…