English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the quantum evolution in dimension three of a system composed by atest particle interacting with an environment made of $N$ harmonic oscillators.At time zero the test particle is described by a spherical wave, i.e. a highlycorrelated continuous superposition of states with well localized position andmomentum, and the oscillators are in the ground state. Under suitableassumptions on the physical parameters characterizing the model, we give anasymptotic expression of the solution of the Schr\"odinger equation of thesystem with an explicit control of the error. The result shows that theapproximate expression of the wave function is the sum of two terms, orthogonalin $L^2(\erre^{3(N+1)})$ and describing rather different situations. In thefirst one all the oscillators remain in their ground state and the testparticle is described by the free evolution of a slightly deformed sphericalwave. The second one consists of a sum of $N$ terms where in each term there isonly one excited oscillator and the test particle is correspondingly describedby the free evolution of a wave packet, well concentrated in position andmomentum. Moreover the wave packet emerges from the excited oscillator with anaverage momentum parallel to the line joining the oscillator with the center ofthe initial spherical wave. Such wave packet represents a semiclassical statefor the test particle, propagating along the corresponding classicaltrajectory. The main result of our analysis is to show how such a semiclassicalstate can be produced, starting from the original spherical wave, as a resultof the interaction with the environment.

Semiclassical wave-packets emerging from interaction with an environment