Related papers: Chaotic Evolution in Quantum Mechanics
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly.…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
The complication of chaotic oscillation under its transformation by linear inertial process is discussed. It is shown that such complication is begun from large scales of attractor and is pure dynamical process.
A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A…
Wave guides for classical electromagnetic fields can realize the quantum evolution of the wave function for a system of qubits. Phase shifts, switches and beam splits allow for the construction of arbitrary quantum gates. They can act at…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus…
We discover numerically that a moving wave packet in a quantum chaotic billiard will always evolve into a quantum state, whose density probability distribution is exponential. This exponential distribution is found to be universal for…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
Manifestation of dynamical instability and Hamiltonian chaos in the fundamental near-resonant matter-radiation interaction has been found analitically and in a Monte Carlo simulation in the behavior of atoms moving in a rigid optical…
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
The most debated status of the wave function of Quantum Mechanics is discussed in the light of the epistemological vs ontological opposition.