Related papers: The structures of state space concerning Quantum D…
We recast the Podle\`s spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the…
We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In…
It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…
Using Lindblad approach to study decoherence of quantum systems, we study the decoherence and decay of entangled states, formed by two basic states of a chain of thee qubits. We look on these states for a possible regular dependence on…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble…
The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time…
We present a detailed analysis of decoherence free subspaces and develop a rigorous theory that provides necessary and sufficient conditions for dynamically stable decoherence free subspaces. This allows us to identify a special class of…
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. Master equations such as the Lindblad equation preserve the trace of this matrix.…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We study the minimum time related to the quantum speed limit that characterizes the evolution of an open quantum system with the help of a simple model in the short and long time limits. We compare in particular the situation corresponding…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
I discuss the concept of quasi-state decompositions for ground states and equilibrium states of quantum spin systems. Some recent results on the ground states of a class of one-dimensional quantum spin models are summarized and new work in…