Theory of Dense Hydrogen and Correlated Quantum and Classical Systems

9988576 Ashcroft该基金支持致密氢（扩展到某些轻元素）的理论研究，以及具有新秩序状态的相关量子和经典系统。 从某种意义上说，氢是最丰富的元素（与其他元素的结合也很普遍），在高压缩下可以被视为与无处不在的果冻最简单、最现实、最可量化的区别。 它是一个基本系统，由于其基本哈密顿量的简单性，它在凝聚相中的性质是非常复杂的。 最近，氢在动态和静态方面都受到了非常持续的实验攻击。 激光冲击实验现在将氢压缩到大约10倍的状态（超过一个大气压的固体），温度高达20，000 K。 然而，在这些条件下，即使是像物态方程这样基本的东西，在理论上也几乎没有共识，三大研究主题中的第一个主题是关于稠密氢的，这是由于在高温和低温下质子配对都有显著的持续性这一事实所促成的：对于接近基态的条件，这已经被证明伴随着电子秩序的不寻常状态，其程度和范围需要进一步的研究。 在非常高的温度下，可以合理地预期配对将让位于致密的单原子和金属态，但在途中，我们遇到了中间条件（部分简并电子，特别是质子中的强配对关联），这引起了相当复杂的问题。 在到达相图上游的过程中会有一系列的转变，其中一些转变是否连续已经是一个有争议的问题。 实验上已知氢（和氘）的低温/高密度相图是丰富的，但它只得到了四极有序的部分解释。 一个有趣的挑战是将与电子对称性破缺的实验观察相关的新物理学结合起来，从而导致具有很大偶极特征的自洽场，而四极问题现在可以与之耦合。第二个主要的努力是以多体理论为中心，在一个预言之后，在高密度下，P金属可能具有与它们的一个大气压对应物异常不同的电子结构。 这产生于库仑系统中配对的广义观点（但扩展到赝势的情况），并导致迄今为止被认为相对简单的系统中出现新的有序态的可能性。 广义配对视图本身现在也可以扩展到各向异性系统，那些最直接的兴趣是分层的。 在这样的系统中，有效相互作用的性质，特别是如果单电子结构承认的粒子-空穴字符，是相当大的兴趣。 因为这样一来，相互作用就可能在三个维度上显著偏离相应的结果。 在准二维电子气中，这个问题也与本征超导性的可能性有关（即准二维电子空穴系综的真实基态可能表现出非对角长程有序）。 当这样的系统被带到相当低的密度时，对称性破缺到晶态是可以预期的，尽管在三维中，现在看来标准的约束（到简单的布拉维晶格）不一定导致最低能量的状态。 第三个主题涉及密度泛函理论也有广泛的应用在经典的背景下，特别是有重大影响的理论经典的非均匀系统。 经典系统通常比它们的量子类似物具有更高的相关性，因此，这里提出的近似类（例如粗粒化和加权密度方法）现在很可能在电子系统中得到应用。 因此，新的研究可以被视为对普遍存在的局域密度或局域自旋密度近似的梯度校正方法的可能替代方案的探索。 该基金支持凝聚态系统的理论研究。 有三大主题：对最简单的元素氢及其在高压和高温下的行为的研究;对带电量子粒子相互作用的研究;以及对经典相互作用系统的研究。 研究范围从相互作用系统物理学基础的非常基本的研究到新的氢相的现实计算。

9988576AshcroftThe grant supports theoretical studies of dense hydrogen (extended to certain light elements), and of correlated quantum and classical systems with novel states of order. In one sense hydrogen, the most abundant of elements (and rife in its combination with others) can be regarded at high compression as the simplest realistic and quantifiable departure from the ubiquitous jellium. It is a fundamental system and, given the simplicity of its basic Hamiltonian, its properties in the condensed phase are intriguingly complex. Hydrogen has recently come under very sustained experimental attack both dynamically and statically. Laser shock experiments now take hydrogen into a regime of around ten-fold compression (over the one atmosphere solid) and temperatures as high as 20,000K. Yet there seems to be little in the way of theoretical consensus on accounting even for something so basic as the equation of state under these conditions.The first of three major research themes, on dense hydrogen, is prompted by the fact that both at high temperatures and at low there is a remarkable persistence of proton-pairing: for near the ground state conditions this has been shown to be accompanied by unusual states of electronic order, the extent and range of which invite further investigation. At very high temperatures it is reasonably expected that the pairing will give way to a dense monatomic and metallic state, but en route we are presented with intermediate conditions (partially degenerate electrons, and especially strong pairing correlations in the protons) that give rise to a problem of considerable complexity. There will be a range of transitions on the way to the upper reaches of the phase diagram, and whether some of these are continuous or not is already a matter of debate. It is known experimentally that the low temperature/high density phase diagram of hydrogen (and deuterium) is rich, and yet it has received only partial explanation in terms of the ordering of quadrupoles. One interesting challenge is to incorporate the new physics associated with the experimental observation of electronic broken symmetry leading to self-consistent fields of a largely dipolar character to which the quadrupolar problem can now couple.A second major effort is to be centered on many-body theory, following on the heels of a prediction that at high densities the light s-p metals may have electronic structures unusually different from their one atmosphere counterparts. This arises from a generalized view of pairing in Coulomb systems (but extended to the case of pseudopotentials) and leads to the possibility of new ordered states in systems hitherto regarded as relatively simple. The generalized pairing view itself can also now be extended to anisotropic systems, those of most immediate interest being layered. The nature of effective interactions in such systems, particularly if the one-electron structure admits of a particle-hole character, is of considerable interest. For then the interactions can depart significantly from the corresponding results in three dimensions. In the quasi-two-dimensional electron gas the issue is also of some interest with respect to the possibility of intrinsic superconductivity (i.e. that the true ground state of quasi-two-dimensional electron-hole ensembles might exhibit off-diagonal long range order). When such systems are taken to quite low densities, symmetry breaking to a crystalline state is anticipated, though as in three-dimensions it appears now that the standard constraint (to simple Bravais lattices) does not necessarily lead to states of lowest energy. The third theme deals with density functional theory which has also had wide applications in a classical context, and in particular has had a major impact on the theory of classical inhomogeneous systems. Classical systems are often more highly correlated than their quantum analogs, and for this reason the class of approximations developed here (coarse graining and weighted density methods, for example) might well find application now in electronic systems. The new studies may therefore be viewed as an exploration of a possible alternative to gradient correction approaches to the ubiquitous local density or local spin density approximation.%%% This grant supports theoretical research on condensed matter systems. There are three broad themes: the study of the simplest element, hydrogen, and its behavior at high pressures and temperature; the study of interacting charged quantum particles; and, the study of classical interacting systems. The research ranges from very basic investigations of the foundations of the physics of interacting systems to realistic calculations of novel new phases of hydrogen.***