Related papers: Continuous collapse models on finite dimensional H…
We deal with two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and…
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are…
The question of whether interactions can break dynamical localization in quantum kicked rotor systems has been the subject of a long--standing debate. Here, we introduce an extended mapping from the kicked Lieb--Liniger model to a…
Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on…
Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that…
It is shown that quantized dynamical system with second class constraints has infinite dimensional Hilbert space.
We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
We demonstrate the occurrence of permanent spikes using the Lemaitre-Tolman-Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated…
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…
This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small…
We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the…
In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…
Theories including a collapse mechanism have been presented various years ago. They are based on a modification of standard quantum mechanics in which nonlinear and stochastic terms are added to the evolution equation. Their principal…
For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the…
Long-range hoppings in quantum disordered systems are known to yield quantum multifractality, whose features can go beyond the characteristic properties associated with an Anderson transition. Indeed, critical dynamics of long-range quantum…
We present a quantum computational framework for SU(2) lattice gauge theory, leveraging continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as…
We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically…
Recent advances in quantum simulators permit unitary evolution interspersed with locally resolved mid-circuit measurements. This paves the way for the observation of large-scale space-time structures in quantum trajectories and opens a…
Penrose has suggested that large fluctuations of the gravitational energy of quantum systems, resulting from fluctuations of its density in space, may induce a quantum collapse mechanism \cite{Penrose-1996}, but he did not propose a precise…