Related papers: Conditions for the Quantum to Classical Transition…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We investigate the quantum-classical transition in the delta-kicked rotor and the attainment of the classical limit in terms of measurement-induced state-localization. It is possible to study the transition by fixing the environmentally…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hbar$ is increased. We show evidence to the contrary in the behavior of…
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 boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with…
We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase-diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between…
Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$…
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…