Effective Equations of Motion for Quantum Systems

By M. Bojowald, Aureliano Skirzewski. 2005

184 citations recorded by the source corpus.

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/67654bf25e87f1d06d5426a3a33c4c4284658308

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Physical and Theoretical Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

Loop quantum cosmology of k = 1 FRW models (2006, background): “In a certain sense this procedure encapsulates the more familiar ‘effective action’ calculations in the Hamiltonian framework [27].”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, background): “(This is part of a general procedure which also contains the usual effective action techniques [91, 92 , 52, 93].) Similarly, effective classical equations for inhomogeneous models, which then would be partial differential equations in space-time coordinates, would be much easier to deal with than ”
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity (2007, background): “It seems to us that in order to make progress on this kind of questions one should first try to define a Hamiltonian notion of effective action, see [33] for a possible direction.”
Loop Quantum Cosmology (2005, background): “In fact, the dynamics of quantum variables provides a means for the systematic derivation of effective equations that are analogous to effective actions but can be computed in a purely canonical way [105, 282, 106].”
Anomaly freedom in perturbative loop quantum gravity (2008, background): “39 29 v1 [ gr -q c] 2”
Loop quantum cosmology of Bianchi type IX models (2009, methodology): “In the isotropic models, effective equations have been introduced via two different approaches —the embedding [33, 34] and the moment expansion [35] methods— in order to study the first order quantum-corrected equations of motion.”