Saturation of dephasing time in mesoscopic devices produced by a ferromagnetic state

We consider an exchange model of itinerant electrons in a Heisenberg ferromagnet and we assume that the ferromagnet is in a fully polarized state. Using the Holstein-Primakoff transformation we are able to obtain a boson-fermion Hamiltonian that is well-known in the interaction between light and matter. This model describes the spontaneous emission in two-level atoms that is the proper decoherence mechanism when the number of modes of the radiation field is taken increasingly large, the vacuum acting as a reservoir. In the same way one can see that the interaction between the bosonic modes of spin waves and an itinerant electron produces decoherence by spin flipping with a rate proportional to the size of the system. In this way we are able to show that the experiments on quantum dots, described in D. K. Ferry et al. [Phys. Rev. Lett. {\bf 82}, 4687 (1999)], and nanowires, described in D. Natelson et al. [Phys. Rev. Lett. {\bf 86}, 1821 (2001)], can be understood as the interaction of itinerant electrons and an electron gas in a fully polarized state.Comment: 10 pages, no figure. Changed title. Revised version accepted for publication in Physical Review

Well-posedness of the Ericksen-Leslie system

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.Comment: 16 page

Symplectic reduction and topology for applications in classical molecular dynamics

This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate system to the center of mass coordinate system relevant to molecular collision dynamics. For the case of two-body molecular systems constrained to a plane, symplectic reduction is employed to demonstrate explicitly the separation of translational, rotational, and internal energies and the corresponding reductions of the phase space describing the dynamics for Hamiltonian systems with symmetry. Further, by examining the topology of the energy-momentum map, a unified treatment is presented of the reduction results for the description of (i) the classical dynamics of rotating and vibrating diatomic molecules, which correspond to bound trajectories and (ii) the classical dynamics of atom–atom collisions, which correspond to scattering trajectories. This provides a framework for the treatment of the dynamics of larger N-body systems, including the dynamics of larger rotating and vibrating polyatomic molecular systems and the dynamics of molecule–molecule collisions

Superradiance in spin-JJ particles: Effects of multiple levels

We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems, and compare the results based on a novel approach we have developed in {[}Yelin \textit{et al.}, arXiv:quant-ph/0509184{]}. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that the superradiance, which is well-known as a many-body phenomenon, can also be modified by multiple level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have multi-level structure which is partially harmonic.Comment: 11 pages, 7 figure

The Cardy-Verlinde Formula and Asymptotically Flat Charged Black Holes

We show that the modified Cardy-Verlinde formula without the Casimir effect term is satisfied by asymptotically flat charged black holes in arbitrary dimensions. Thermodynamic quantities of the charged black holes are shown to satisfy the energy-temperature relation of a two-dimensional CFT, which supports the claim in our previous work (Phys. Rev. D61, 044013, hep-th/9910244) that thermodynamics of charged black holes in higher dimensions can be effectively described by two-dimensional theories. We also check the Cardy formula for the two-dimensional black hole compactified from a dilatonic charged black hole in higher dimensions.Comment: 6 pages, LaTeX, references adde