Related papers: Quantum Poincar\'e Recurrences
Classical and quantum correlation functions are derived for a system of non-interacting particles moving on a circle. It is shown that the decaying behaviour of the classical expression for the correlation function can be recovered from the…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying…
After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the…
One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the…
$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete…
The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have…
The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
The area entropy $A/4$ and the related Hawking temperature in the presence of event horizons are rederived, for de Sitter and black hole topologies, as a consequence of a tunneling of the wave functional associated to the classical coupled…
The quantum average energy decay and the purity decay are studied for a system particle as a function of the number of constituents of a discrete bath model. The system particle is subjected to two distinct physical situations: the harmonic…
We investigate the quantum fluctuation effects in the vicinity of the critical point of a $p$-orbital bosonic system in a square optical lattice using Wilsonian renormalization group, where the $p$-orbital bosons condense at nonzero momenta…
In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as…
Quantum phase transitions have been the subject of intense investigations in the last two decades [1]. Among other problems, these phase transitions are relevant in the study of heavy fermion systems, high temperature superconductors and…
We study the influence of particle interaction on a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding non-interacting (linear) system has been shown to have a topological transition…
We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
We consider canonically conjugated generalized space and linear momentum operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a generalized translation operator which produces infinitesimal deformed displacements…
Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than $\hbar$ [W.H. Zurek, Nature {\bf 412}, 712 (2001)]. We investigate the influence of…