长久以来,透过各类传播媒介的介绍,大多数人似乎已经认定我们的老祖先很早就能运用智慧与勇气在蛮荒世界生存,成为自然界的伟大猎人。但事实似乎没有那么简单。本文从英国普利兹奖得主Roger Lewin和剑桥大学教授Robert A.Foley合著的《...长久以来,透过各类传播媒介的介绍,大多数人似乎已经认定我们的老祖先很早就能运用智慧与勇气在蛮荒世界生存,成为自然界的伟大猎人。但事实似乎没有那么简单。本文从英国普利兹奖得主Roger Lewin和剑桥大学教授Robert A.Foley合著的《人类演化原理》(Principles of Human Evolution)一书的相关研究成果,介绍人类先祖(hominins)究竟是猎人、猎物,或腐食者的争论。此外,也高度评价了该书以科学的视野与优美的文笔,让读者清楚掌握学者应如何解读考古材料,并且以侦探小说的笔调,描绘了人类先祖的生计与社会活动的演化。展开更多
The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation （SE） by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition princi...The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation （SE） by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H（0）. Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H（t）. On the other hand, any physical experiment may bring errors so that the initial state （input state） may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution （GAAS） is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.展开更多
文摘长久以来,透过各类传播媒介的介绍,大多数人似乎已经认定我们的老祖先很早就能运用智慧与勇气在蛮荒世界生存,成为自然界的伟大猎人。但事实似乎没有那么简单。本文从英国普利兹奖得主Roger Lewin和剑桥大学教授Robert A.Foley合著的《人类演化原理》(Principles of Human Evolution)一书的相关研究成果,介绍人类先祖(hominins)究竟是猎人、猎物,或腐食者的争论。此外,也高度评价了该书以科学的视野与优美的文笔,让读者清楚掌握学者应如何解读考古材料,并且以侦探小说的笔调,描绘了人类先祖的生计与社会活动的演化。
基金supported by the National Natural Science Foundation of China(Grant Nos.11371012,11171197 and 11401359)the Innovation Fund Project for Graduate Program of Shaanxi Normal University(GrantNo.2013CXB012)+2 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.GK201301007 and GK201404001)the Science Foundation of Weinan Normal University(Grant No.14YKS006)the Foundation of Mathematics Subject of Shaanxi Province(Grant No.14SXZD009)
文摘The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation （SE） by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H（0）. Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H（t）. On the other hand, any physical experiment may bring errors so that the initial state （input state） may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution （GAAS） is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.
