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We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the…
Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local…
In earlier papers we showed unpredictability beyond quantum uncertainty in atomic clocks, ensuing from a proven gap between given evidence and explanations of that evidence. Here we reconceive a clock, not as an isolated entity, but as…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
The vast majority of dynamical systems in classical physics are chaotic and exhibit the butterfly effect: a minute change in initial conditions can soon have exponentially large effects elsewhere. But this phenomenon is difficult to…
A non-local toy-model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase. It is…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
Schroedinger's wave function shows many aspects of a state of incomplete knowledge or information ("bit"): (1) it is usually defined on a space of classical configurations, (2) its generic entanglement is, therefore, analogous to…
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not…
An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only…