Related papers: Monitoring continuous spectrum observables: the st…
The classical sequential growth model for causal sets provides a template for the dynamics in the deep quantum regime. This growth dynamics is intrinsically temporal and causal, with each new element being added to the existing causal set…
A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…
We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\cal H}_0$ of the system, and targeting a unique dark state in ${\cal…
We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
The quantum dynamics of a damped and forced harmonic oscillator is investigated in terms of a Lindblad master equation. Elementary algebraic techniques are employed allowing for example to analyze the long time behavior, i.e. the quantum…
We consider a dynamic protocol for quantum many-body systems, which enables to study the interplay between unitary Hamiltonian driving and random local projective measurements. While the unitary dynamics tends to increase entanglement,…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
Accurate control of quantum systems requires precise measurement of the parameters that govern the dynamics, including control fields and interactions with the environment. Parameters will drift in time and experiments interleave protocols…
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…
In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in…
The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed…
We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical…
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
For Hamiltonian systems, level statistics provide a faithful diagnostic of quantum chaos. By analogy, the statistics of the Lindbladian spectrum are often used in open quantum systems, and the Grobe-Haake-Sommers conjecture proposes that…
We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have…