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Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…

In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…

One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is…

Entanglement speeds up evolution of a pure bipartite spin state, in line with the time energy uncertainty. However if the state is mixed this is not necessarily the case. We provide a counter example and point to other factors affecting…

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…

The extension of thermodynamic principles to active matter remains a challenge due to the non-equilibrium nature inherent to active systems. In this study, we introduce a framework to assess entropy in our minimal macroscopic experiment…

Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary…

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators…

The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the…

We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…

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…

The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…

We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…

Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…

The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator…

The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…

In two previous papers, the author raised the possibility of a special relativistic Liouville equation. The conclusion then was yes, such an equation is possible in 8N phase space if a Lorentz-invariant Universal (LiU) time can be defined…

It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighbourhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states,…

When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of…