Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0408169 · Physics Letters A

Resonances and adiabatic invariance in classical and quantum scattering theory

Sudhir R. Jain

Published Dec 24, 2004• 8 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2004.12.014

Related papers

Adiabatic Theorems for Quantum Resonances

Walid K. Abou Salem, Jürg Martin Fröhlich

arXiv:math-ph/0607054•Communications in Mathematical Physics•Mar 16, 2007•35 citations

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Jeong Ryeol Choi

An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.

Advances in Mathematical Physics•Jan 1, 2015•4 citations

Classical and quantum adiabatic invariants

E. Gozzi

Physics Letters B•Dec 1, 1985•14 citations

Exact time-dependent decoherence factor and its adiabatic classical limit

Shen, J Q, Chen, P, Hong Mao

The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what obtained by other authors, and futhermore we obtain the more general results concerning the time-dependent non-adiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric phase factor.

•Feb 15, 2003•0 citations

Scattering and Resonances: Classical and Quantum Dynamics

Pierre Gaspard

Elsevier eBooks•Jan 1, 1993•12 citations

Resonances and scattering in the classical limit

J. M. Combes, Pierre Duclos, Ruedi Seiler

•Jan 1, 1984•1 citation
An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what obtained by other authors, and futhermore we obtain the more general results concerning the time-dependent non-adiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric phase factor.