Semiclassical wavepackets emerging from interaction with an environment
We study the quantum evolution in dimension three of a system composed by a test 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 highly correlated continuous superposition of states with well localized position and momentum, and the oscillators are in the ground state. Furthermore, we assume that the positions of the oscillators are not collinear with the center of the spherical wave. Under suitable assumptions on the physical parameters characterizing the model, we give an asymptotic expression of the solution of the Schrödinger equation of the system with an explicit control of the error. The result shows that the approximate expression of the wave function is the sum of two terms, orthogonal in L{sup 2}(R{sup 3(N+1)}) and describing rather different situations. In the first one, all the oscillators remain in their ground state and the test particle is described by the free evolution of a slightly deformed spherical wave. The second one consists of a sum of N terms where in each term there is only one excited oscillator and the test particle is correspondingly described by the free evolution of a wave packet,more »
 Authors:

^{[1]};
^{[2]}
 D.I.S.I.M., Università di L’Aquila, Via Vetoio  Loc. Coppito  67010 L’Aquila (Italy)
 Dipartimento di Matematica, “Sapienza” Università di Roma, P.le A. Moro 5, 00185 Roma (Italy)
 Publication Date:
 OSTI Identifier:
 22251138
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; EQUATIONS; ERRORS; GROUND STATES; HARMONIC OSCILLATORS; SEMICLASSICAL APPROXIMATION; SPHERICAL CONFIGURATION; TEST PARTICLES; TRAJECTORIES; WAVE FUNCTIONS; WAVE PACKETS