Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws

Details Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws

2004-08-16

arxiv.org/abs/cond-mat/0408352v2

Phys. Rev. B 71, 165104 (2005)

Physics

Condensed Matter

Statistical Mechanics

14 pages, RevTeX4. Final version, typos in Eqs.(77), (A1) and (A2), which are present in the published version, corrected

Scientific paper

10.1103/PhysRevB.71.165104

We formulate equations of motion and conservation laws for a quantum many-body system in a co-moving Lagrangian reference frame. It is shown that generalized inertia forces in the co-moving frame are described by Green's deformation tensor $g_{\mu\nu}(\bm\xi,t)$ and a skew-symmetric vorticity tensor $\widetilde{F}_{\mu\nu}(\bm\xi,t)$, where $\bm\xi$ in the Lagrangian coordinate. Equations of motion are equivalent to those for a quantum many-body system in a space with time-dependent metric $g_{\mu\nu}(\bm\xi,t)$ in the presence of an effective magnetic field $\widetilde{F}_{\mu\nu}(\bm\xi,t)$. To illustrate the general formalism we apply it to the proof of the harmonic potential theorem. As another example of application we consider a fast long wavelength dynamics of a Fermi system in the dynamic Hartree approximation. In this case the kinetic equation in the Lagrangian frame can be solved explicitly. This allows us to formulate the description of a Fermi gas in terms of an effective nonlinear elasticity theory. We also discuss a relation of our results to time-dependent density functional theory.

Affiliated with

Also associated with

No associations

Rating

Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-579584