翻訳と辞書 Words near each other ・ Quantum pseudo-telepathy ・ Quantum Psychology ・ Quantum q-Krawtchouk polynomials ・ Quantum Quality Productions ・ Quantum radar ・ Quantum readout of PUFs ・ Quantum Reality ・ Quantum realm ・ Quantum Redshift ・ Quantum refereed game ・ Quantum reference frame ・ Quantum reflection ・ Quantum register ・ Quantum relative entropy ・ Quantum revival ・ Quantum rotor model ・ Quantum satis ・ Quantum sensor ・ Quantum Sheep ・ Quantum simulator ・ Quantum singularity ・ Quantum solid ・ Quantum solvent ・ Quantum sort ・ Quantum spacetime ・ Quantum spin Hall effect ・ Quantum spin liquid ・ Quantum spin model ・ Quantum spin tunneling ・ Quantum Sports Cars Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quantum rotor model ： ウィキペディア英語版 Quantum rotor model The quantum rotor model is a mathematical model for a quantum system. It can be visualized as an array of rotating electrons which behave as rigid rotors that interact through short-range dipole-dipole magnetic forces originating from their magnetic dipole moments (neglecting Coulomb forces). The model differs from similar spin-models such as the Ising model and the Heisenberg model in that it includes a term analogous to kinetic energy. Although elementary quantum rotors do not exist in nature, the model can describe effective degrees of freedom for a system of sufficiently small number of closely coupled electrons in low-energy states. Suppose the n-dimensional position (orientation) vector of the model at a given site $i$ is $\backslash mathbf$. Then, we can define rotor momentum $\backslash mathbf$ by the commutation relation of components $\backslash alpha,\backslash beta$ $()=i\backslash delta\_$ However, it is found convenient〔 to use rotor angular momentum operators $\backslash mathbf$ defined (in 3 dimensions) by components $L\_=\backslash varepsilon\_n\_p\_$ Then, the magnetic interactions between the quantum rotors, and thus their energy states, can be described by the following Hamiltonian: :$H\_R=\backslash frac\backslash sum\_i\backslash mathbf\_i^2-J\backslash sum\_\backslash mathbf\_i\backslash cdot\backslash mathbf\_j$ where $J,\backslash bar$ are constants.. The interaction sum is taken over nearest neighbors, as indicated by the angle brackets. For very small and very large $\backslash bar$, the Hamiltonian predicts two distinct configurations (ground states), namely "magnetically" ordered rotors and disordered or "paramagnetic" rotors, respectively.〔 The interactions between the quantum rotors can be described by another (equivalent) Hamiltonian, which treats the rotors not as magnetic moments but as local electric currents. ==Properties== One of the important features of the rotor model is the continuous O(N) symmetry, and hence the corresponding continuous symmetry breaking in the magnetically ordered state. In a system with two layers of Heisenberg spins $\backslash mathbf\_$ and $\backslash mathbf\_$, the rotor model approximates the low-energy states of a Heisenberg antiferromagnet, with the Hamiltonian :$H\_d=K\backslash sum\_i\backslash mathbf\_\backslash cdot\backslash mathbf\_+J\backslash sum\_\backslash left(\backslash mathbf\_\backslash cdot\backslash mathbf\_+\backslash mathbf\_\backslash cdot\backslash mathbf\_\backslash right)$ using the correspondence $\backslash mathbf\_i=\backslash mathbf\_+\backslash mathbf\_$〔 The particular case of quantum rotor model which has the O(2) symmetry can be used to describe a superconducting array of Josephson junctions or the behavior of bosons in optical lattices.〔 Another specific case of O(3) symmetry is equivalent to a system of two layers (bilayer) of a quantum Heisenberg antiferromagnet; it can also describe double-layer quantum Hall ferromagnets. It can also be shown that the phase transition for the two dimensional rotor model has the same universality class as that of antiferromagnetic Heisenberg spin models. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantum rotor model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.