Abstract
We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such a limit and a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of "reservoir"). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's "λ2T" limits are emphasized.
| Original language | English |
|---|---|
| Pages (from-to) | 189-221 |
| Number of pages | 33 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 245 |
| Issue number | 1-2 |
| Publication status | Published - 1997 Oct 15 |
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Keywords
- Quantum statistical mechanics
- Theory of quantum measurement
- Wiener process
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Emergence of a Wiener process as a result of the quantum mechanical interaction with a macroscopic medium. / Blasi, Raffaella; Nakazato, Hiromichi; Namiki, Mikio; Pascazio, Saverio.
In: Physica A: Statistical Mechanics and its Applications, Vol. 245, No. 1-2, 15.10.1997, p. 189-221.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Emergence of a Wiener process as a result of the quantum mechanical interaction with a macroscopic medium
AU - Blasi, Raffaella
AU - Nakazato, Hiromichi
AU - Namiki, Mikio
AU - Pascazio, Saverio
PY - 1997/10/15
Y1 - 1997/10/15
N2 - We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such a limit and a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of "reservoir"). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's "λ2T" limits are emphasized.
AB - We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such a limit and a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of "reservoir"). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's "λ2T" limits are emphasized.
KW - Quantum statistical mechanics
KW - Theory of quantum measurement
KW - Wiener process
UR - http://www.scopus.com/inward/record.url?scp=0031244743&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031244743&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0031244743
VL - 245
SP - 189
EP - 221
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 1-2
ER -