Related papers: Unitary evolution as a uniqueness criterion
The Darwinian paradigm of biological evolution is based on the separability of the variation and selection processes. As a result, the population thinking had always been an integral part of the Darwinian approach. I propose an alternative…
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they…
We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques.
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
Observations suggest, that there may be periods in the history of the universe, including the present one, in which its evolution is driven by scalar fields. This paper is concerned with the solution of the evolution equations for a…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
We perform a detailed analysis of the non stationary solutions of the evolution (Fokker-Planck) equations associated to either stationary or non stationary quantum states by the stochastic mechanics. For the excited stationary states of…
We analyse when and why unitarity violations might occur in quantum cosmology restricted to minisuperspace. To this end we discuss in detail backscattering transitions between expanding and contracting solutions of the Wheeler-DeWitt…
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if…
The cosmology of flat FLRW universes dominated by a single scalar field is discussed. General features of the evolution of the universe and the scalar field are illustrated by specific examples. In particular the role of critical points,…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical…
We propose a condition, called convex quasi-linearity, for deterministic nonlinear quantum evolutions. Evolutions satisfying this condition do not allow for arbitrary fast signaling, therefore, they cannot be ruled out by a standard…