Theory of Dense Hydrogen and Correlated Quantum and Classical Systems

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的理论研究。从某种意义上说，氢是最丰富的元素（它与其他元素的结合也很普遍），在高度压缩的情况下，它可以被视为与无处不在的凝胶最简单、最现实、最可量化的区别。它是一个基本系统，鉴于其基本哈密顿量的简单性，它在凝聚态的性质是有趣的复杂。最近，氢在动态和静态两方面都受到了持续不断的实验攻击。现在的激光冲击实验将氢压缩到大约10倍的状态（超过一个大气固体），温度高达20,000K。然而，在这些条件下，即使是像状态方程这样基本的东西，似乎也很难在理论上达成一致。三个主要研究主题中的第一个，关于致密氢，是由于在高温和低温下都有一个显著的质子配对持续存在的事实：在接近基态的条件下，这已经被证明伴随着不寻常的电子秩序状态，其程度和范围需要进一步的研究。在非常高的温度下，我们可以合理地预期，这种配对将让位给致密的单原子和金属态，但在此过程中，我们遇到了中间条件（部分简并的电子，尤其是质子中强烈的配对相关性），这就产生了一个相当复杂的问题。在到达相图上游的过程中会有一系列的过渡，其中一些过渡是否连续已经是一个有争议的问题。实验表明，氢（和氘）的低温/高密度相图是丰富的，但在四极序方面只得到了部分解释。一个有趣的挑战是将新的物理学与电子破缺对称的实验观察结合起来，从而导致大部分具有偶极特征的自洽场，而四极问题现在可以与之耦合。第二个主要的努力是集中在多体理论上，紧随其后的是一个预测，即在高密度下，轻s-p金属的电子结构可能与单一大气中的金属不同。这源于库仑系统中配对的广义观点（但扩展到伪势的情况），并导致在迄今为止被认为相对简单的系统中出现新有序状态的可能性。广义配对视图本身现在也可以扩展到各向异性系统，那些最直接感兴趣的是分层。这种系统中有效相互作用的性质，特别是如果单电子结构允许粒子空穴特征，是相当有趣的。因为在三维空间中，相互作用会与相应的结果有很大的不同。在准二维电子气体中，本征超导的可能性（即准二维电子-空穴系综的真实基态可能表现出非对角线的长距离有序）也引起了一些兴趣。当这样的系统被带到相当低的密度时，可以预期对称性破缺到晶体状态，尽管在三维空间中，现在看来标准约束（简单的Bravais晶格）不一定会导致最低能量的状态。第三个主题涉及密度泛函理论，它在经典背景下也有广泛的应用，特别是对经典非齐次系统的理论产生了重大影响。经典系统通常比它们的量子类似物具有更高的相关性，因此这里开发的一类近似（例如粗粒度和加权密度方法）现在可能会在电子系统中得到很好的应用。因此，新的研究可以看作是对梯度校正方法的一种可能的替代方法的探索，以达到普遍存在的局部密度或局部自旋密度近似。本基金支持凝聚态体系的理论研究。有三大主题：研究最简单的元素氢及其在高压和高温下的行为；相互作用带电量子粒子的研究；以及经典相互作用系统的研究。研究范围从相互作用系统的物理基础的非常基本的调查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.***