相关论文: Ray space Riccati evolution and geometric phases f…

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…

The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\sigma equal…

The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…

We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional 3-body system with periodic boundary conditions. We demonstrate that such a 3-body system may be reduced…

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…

This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…

This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…

We present two examples of reductions from the evolution equations describing discrete Schlesinger transformations of Fuchsian systems to difference Painlev\'e equations: difference Painlev\'e equation d-$P\left({A}_{2}^{(1)*}\right)$ with…

In this paper we establish important relations between Hamiltonian dynamics and Riemannian structures on phase spaces for unitarily evolving finite level quantum systems in mixed states. We show that the energy dispersion (i.e. $1/\hbar$…

Using the Magri method one defines an involutive family of Hamiltonians on Banach Lie-Poisson space iR+UL_res^1 (which contains the restricted Grassmannian as a symplectic leaf) and on its complexification C+L_res^1. The hierarchy of…

We briefly report our application of a version of noncommutative geometry to the quantum Euclidean space $R^N_q$, for any $N \ge 3$; this space is covariant under the action of the quantum group $SO_q(N)$, and two covariant differential…

We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic…

We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the…

The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…

Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

As physical systems, qubits must evolve from input to output state. We describe a simple scheme in which the effect of a quantum gate is described by the action of an effective Hamiltonian acting for some characteristic time. This model…