Kick and fix: the roots of quantum control

When two operators $A$ and $B$ do not commute, the calculation of the exponential operator $e^{A+B}$ is a difficult and crucial problem. The applications are vast and diversified: to name but a few examples, quantum evolutions, product formulas, quantum control, Zeno effect. The latter are of great interest in quantum applications and quantum technologies. We present here a historical survey of results and techniques, and discuss differences and similarities. We also highlight the link with the strong coupling regime, via the adiabatic theorem, and contend that the "pulsed" and "continuous" formulations differ only in the order by which two limits are taken, and are but two faces of the same coin.Comment: 6 page

A Brief History of the GKLS Equation

We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.Comment: Based on a talk given by D.C. at the 48th Symposium on Mathematical Physics "Gorini-Kossakowski-Lindblad-Sudarshan Master Equation - 40 Years After" (Toru\'n, June 10-12, 2016). To be published in the special volume of OSI

SHORT-TIME BEHAVIOR OF THE CORRELATION FUNCTIONS FOR THE QUANTUM LANGEVIN EQUATION

We analyze the quantum Langevin equation obtained for the Ford-Kac-Mazur and related models. We study an explicit expression for the correlation function of the noise, obtained by making use of the normal-ordered product of operators. Such an expression is divergence-free, does not require any frequency cutoff, and yields the classical (Markoffian) case in the limit of vanishing \ensuremath{\Elzxh}. We also bring to light and discuss two different regimes for the momentum autocorrelation. The high-temperature and weak-coupling limits are considered, and the latter is shown to be related to van Hove's ``{\ensuremath{\lambda}}^{2}T'' limit. \textcopyright{} 1996 The American Physical Society

Decoherence in neutron interferometry at low transmission probability

Abstract We present a simplified and improved analysis of some recent experiments of neutron interferometry at low transmission probability. It is shown that both the density fluctuations of the elementary constituents of the absorber and the uncertainties in the sample thickness can be analyzed with the same formalism, and that they lead to a reduction of the visibility of the interference pattern. The effect is quantitatively estimated in the Gaussian case. In the context of quantum measurements, the process can be viewed as a partial dephasing characterized by the decoherence parameter. Possible experimental tests are proposed

Temporal behavior of quantum mechanical systems

The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system. Some attempts at extracting the exponential decay law from quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known ``$\lambda^2T$" limit. We clarify these general arguments by introducing and studying a solvable dynamical model. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.Comment: 48 pages, LaTeX, uuencoded file with 7 figures include

Long-time memory in non-Markovian evolutions

If the dynamics of an open quantum systems is non-Markovian, its {asymptotic} state strongly depends on the initial conditions, even if the dynamics possesses an {invariant} state. This is the very essence of memory effects. In particular, the {asymptotic} state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the non-invariance of equilibrium becomes a clear sign of non-Markovianity.Comment: 6 page

Decoherence in neutron interferometry

Abstract The coherence properties of a neutron are analyzed by making use of the Wigner quasi-distribution function. We discuss, in particular, highly non-classical, Schrodinger-cat-like neutron states that can be obtained in an interferometer or in a magnetic field. The dephasing and decoherence effects are quantitatively defined by introducing a "decoherence parameter", that enables one to emphasize some peculiar aspects of irreversibility and decoherence in neutron scattering

Quantum Typicality and Initial Conditions

If the state of a quantum system is sampled out of a suitable ensemble, the measurement of some observables will yield (almost) always the same result. This leads us to the notion of quantum typicality: for some quantities the initial conditions are immaterial. We discuss this problem in the framework of Bose-Einstein condensates.Comment: 8 page