Related papers: Quantization of formal classical dynamical r-matri…
Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the…
The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in…
We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, like evolutions that do not preserve the positivity of quantum states…
We study the relationship between general dynamical Poisson groupoids and Lie quasi-bialgebras. For a class of Lie quasi-bialgebras naturally compatible with a reductive decomposition, we extend the description of the moduli space of…
An explicit isomorphism between the $R$-matrix and Drinfeld presentations of the quantum affine algebra in type $A$ was given by Ding and I. Frenkel (1993). We show that this result can be extended to types $B$, $C$ and $D$ and give a…
Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of $ad L$. For generic $L$ a…
The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar…
A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used…
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277-300] for type $A$, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the…
The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…