Details
| Original language | English |
|---|---|
| Pages (from-to) | 578-590 |
| Number of pages | 13 |
| Journal | Annalen der Physik (Leipzig) |
| Volume | 14 |
| Issue number | 9-10 |
| Publication status | Published - 1 Sept 2005 |
| Externally published | Yes |
Abstract
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between "particle" and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.
Keywords
- Coordinate-dependent mass, Effective quantum theories, Operator ordering
ASJC Scopus subject areas
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Annalen der Physik (Leipzig), Vol. 14, No. 9-10, 01.09.2005, p. 578-590.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Effective descriptions of complex quantum systems
T2 - Path integrals and operator ordering problems
AU - Eckern, Ulrich
AU - Gruber, Michael J.
AU - Schwab, Peter
PY - 2005/9/1
Y1 - 2005/9/1
N2 - We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between "particle" and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.
AB - We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between "particle" and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.
KW - Coordinate-dependent mass
KW - Effective quantum theories
KW - Operator ordering
UR - http://www.scopus.com/inward/record.url?scp=25844518382&partnerID=8YFLogxK
U2 - 10.1002/andp.200510150
DO - 10.1002/andp.200510150
M3 - Article
AN - SCOPUS:25844518382
VL - 14
SP - 578
EP - 590
JO - Annalen der Physik (Leipzig)
JF - Annalen der Physik (Leipzig)
SN - 0003-3804
IS - 9-10
ER -