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Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…

The evolution of a quantum system under observation becomes retarded or even impeded. We review this ``quantum Zeno effect'' in the light of the criticism that has been raised upon a previous attempt to demonstrate it, of later…

Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…

The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical…

A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stuckelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging,…

The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect…

We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…

We observe the quantum Zeno effect -- where the act of measurement slows the rate of quantum state transitions -- in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following…

We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for…

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…

Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…

The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…

Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…

A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…

We study the effect of frequent projective measurements on the dynamics of quantum self-sustaining systems, by considering the prototypical example of the quantum Van der Pol oscillator. Quantum fluctuations are responsible for phase…

$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations…

The implications of a deformed Heisenberg algebra on the Friedmann-Robertson-Walker cosmological models are investigated. We consider the Snyder non-commutative space in which the translation group is undeformed and the rotational…

Quantum Zeno and anti-Zeno effects in an asymmetric nonlinear optical coupler are studied. The asymmetric nonlinear optical coupler is composed of a linear waveguide ($\chi^{\left(1\right)}$) and a nonlinear waveguide…

In this note we investigate the stability of the classical ground state of the Quantum Hall Soliton proposed recently in hep-th/0010105 . We explore two possible perturbations which are not spherically symmetric and we find that the…

In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…