Macroscopic limit of a solvable dynamical model

Hiromichi Nakazato, Saverio Pascazio

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (AgBr molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules are properly taken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N) limit, the system remains solvable and leads to interesting connections with the Jaynes-Cummings model, which describes the interaction of a particle with a maser. The visibility of the interference pattern produced by the two branch waves of the particle is computed, and the conditions under which the spin array behaves as a detector are investigated. The behavior of the visibility yields good insights into the issue of quantum measurements: It is found that, in the Nlimit, a superselection-rule space appears in the description of the (macroscopic) apparatus. In general, an initial thermal state of the detector provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses coherence as the temperature of the detector increases. The problem of imperfect measurements is also briefly discussed.

Original languageEnglish
Pages (from-to)1066-1081
Number of pages16
JournalPhysical Review A
Volume48
Issue number2
DOIs
Publication statusPublished - 1993
Externally publishedYes

Fingerprint

visibility
detectors
ground state
linear arrays
masers
molecules
energy transfer
interactions
interference
temperature

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

Cite this

Macroscopic limit of a solvable dynamical model. / Nakazato, Hiromichi; Pascazio, Saverio.

In: Physical Review A, Vol. 48, No. 2, 1993, p. 1066-1081.

Research output: Contribution to journalArticle

Nakazato, Hiromichi ; Pascazio, Saverio. / Macroscopic limit of a solvable dynamical model. In: Physical Review A. 1993 ; Vol. 48, No. 2. pp. 1066-1081.
@article{537c639026054136a7ea0c4a782159f8,
title = "Macroscopic limit of a solvable dynamical model",
abstract = "The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (AgBr molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules are properly taken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N) limit, the system remains solvable and leads to interesting connections with the Jaynes-Cummings model, which describes the interaction of a particle with a maser. The visibility of the interference pattern produced by the two branch waves of the particle is computed, and the conditions under which the spin array behaves as a detector are investigated. The behavior of the visibility yields good insights into the issue of quantum measurements: It is found that, in the Nlimit, a superselection-rule space appears in the description of the (macroscopic) apparatus. In general, an initial thermal state of the detector provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses coherence as the temperature of the detector increases. The problem of imperfect measurements is also briefly discussed.",
author = "Hiromichi Nakazato and Saverio Pascazio",
year = "1993",
doi = "10.1103/PhysRevA.48.1066",
language = "English",
volume = "48",
pages = "1066--1081",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "2",

}

TY - JOUR

T1 - Macroscopic limit of a solvable dynamical model

AU - Nakazato, Hiromichi

AU - Pascazio, Saverio

PY - 1993

Y1 - 1993

N2 - The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (AgBr molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules are properly taken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N) limit, the system remains solvable and leads to interesting connections with the Jaynes-Cummings model, which describes the interaction of a particle with a maser. The visibility of the interference pattern produced by the two branch waves of the particle is computed, and the conditions under which the spin array behaves as a detector are investigated. The behavior of the visibility yields good insights into the issue of quantum measurements: It is found that, in the Nlimit, a superselection-rule space appears in the description of the (macroscopic) apparatus. In general, an initial thermal state of the detector provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses coherence as the temperature of the detector increases. The problem of imperfect measurements is also briefly discussed.

AB - The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (AgBr molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules are properly taken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N) limit, the system remains solvable and leads to interesting connections with the Jaynes-Cummings model, which describes the interaction of a particle with a maser. The visibility of the interference pattern produced by the two branch waves of the particle is computed, and the conditions under which the spin array behaves as a detector are investigated. The behavior of the visibility yields good insights into the issue of quantum measurements: It is found that, in the Nlimit, a superselection-rule space appears in the description of the (macroscopic) apparatus. In general, an initial thermal state of the detector provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses coherence as the temperature of the detector increases. The problem of imperfect measurements is also briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=33750873854&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750873854&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.48.1066

DO - 10.1103/PhysRevA.48.1066

M3 - Article

AN - SCOPUS:33750873854

VL - 48

SP - 1066

EP - 1081

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -