%0 Journal Article %1 Shreif2011 %A Shreif, Zeina %A Ortoleva, Peter %D 2011 %K graphene %T Scaling Behavior of Quantum Nanosystems: Emergence of Quasi-particles, Collective Modes, and Mixed Exchange Symmetry States %U http://arxiv.org/abs/1103.1862 %X Quantum nanosystems such as graphene nanoribbons or superconducting nanoparticles are studied via a multiscale approach. Long space-time dynamics is derived using a perturbation expansion in the ratio of the nearest-neighbor distance to a nanometer-scale characteristic length, and a theorem on the equivalence of long-time averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schr"odinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nano-assembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a Coarse-grained Mean-field (CGMF) approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested.

@article{Shreif2011, abstract = { Quantum nanosystems such as graphene nanoribbons or superconducting nanoparticles are studied via a multiscale approach. Long space-time dynamics is derived using a perturbation expansion in the ratio of the nearest-neighbor distance to a nanometer-scale characteristic length, and a theorem on the equivalence of long-time averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schr\"odinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nano-assembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a Coarse-grained Mean-field (CGMF) approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested. }, added-at = {2011-03-18T01:03:05.000+0100}, author = {Shreif, Zeina and Ortoleva, Peter}, biburl = {https://www.bibsonomy.org/bibtex/2b88c18187c3794cd5df79e44ec7e69d6/corneliu}, description = {Scaling Behavior of Quantum Nanosystems: Emergence of Quasi-particles, Collective Modes, and Mixed Exchange Symmetry States}, interhash = {0800d1e230eb51cd0839e3a06ca9e432}, intrahash = {b88c18187c3794cd5df79e44ec7e69d6}, keywords = {graphene}, note = {cite arxiv:1103.1862 Comment: Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics; Keywords: Quantum nanosystems, coarse-grained wave equation, mean field theory, multiscale analysis}, timestamp = {2011-03-18T01:03:05.000+0100}, title = {Scaling Behavior of Quantum Nanosystems: Emergence of Quasi-particles, Collective Modes, and Mixed Exchange Symmetry States}, url = {http://arxiv.org/abs/1103.1862}, year = 2011 }