Quantum Aspects of Condensed Matter

9971138 Chakravarty材料的量子力学性质不断产生新的和意想不到的现象。 在过去的十多年中，氧化物超导体、铼酸盐、锰酸盐、富勒烯和重电子材料引起了人们的注意。 最基本的兴趣是那些在宏观尺度上反映量子力学的性质。 这些发现不断地挑战着我们去扩展我们对物质性质的理解。 新的，固有的量子相的物质，如量子霍尔态被发现，因为是新的概念，如量子相变在绝对零度之间的根本不同的状态的物质完全由量子力学驱动。 控制物质量子态的性质仍然是一项引人入胜的智力事业。 我们开始意识到，在材料科学的基础上，必须有一套物理原理，很可能是简单的;然而，要发现这些原理，需要真正的思维转变。 那些长期以来为我们服务的传统材料的想法必须放弃。 人们再也不能在单一的长度和能量尺度上思考物理学，因为效应完全是集体的。 与高能物理相反，微观哈密顿量是确定的，但物质的状态包括深不可测的丰富性和复杂性。 因此，所有这些现象，顾名思义，必须是集体的。 看来，即使是电子作为嵌入物质中的粒子的基本概念也必须修改，因为这样的粒子可能不会保持其完整性，而是分裂成许多，这就是电荷和自旋的分数化概念。 这项研究的主旨是这种前瞻性的观点。 所选的研究课题直接涉及反映量子力学不寻常性质的现象。 讨论了物质从金属到绝缘体或从超导体到绝缘体的量子相变。 尽管历史悠久，但这些问题在任何深层意义上都没有得到解决;可以从意外发现的定期出现中找到证据。 理论上的困难在于，我们没有数学工具来处理物质中强相互作用的自由度。 该补助金的一个方面包括从场论的角度开发这些工具，适用于物质理论。 在另一个方向上，该补助金涉及超导概念的发展，其中配对的结果来自正常状态的电子动能的节省。 这是毫不掩饰的非常规，因为没有交换激发量子来调解电子之间的吸引力从而导致超导性的概念。 材料的量子力学性质不断产生新的和意想不到的现象。 在过去的十多年中，氧化物超导体、铼酸盐、锰酸盐、富勒烯和重电子材料引起了人们的注意。 最基本的兴趣是那些在宏观尺度上反映量子力学的性质。 这些发现不断地挑战着我们去扩展我们对物质性质的理解。 新的，固有的量子相的物质，如量子霍尔态被发现，因为是新的概念，如量子相变在绝对零度之间的根本不同的状态的物质完全由量子力学驱动。 控制物质量子态的性质仍然是一项引人入胜的智力事业。 我们开始意识到，在材料科学的基础上，必须有一套物理原理，很可能是简单的;然而，要发现这些原理，需要真正的思维转变。 我们长久以来对传统材料很感兴趣的想法必须放弃。 人们再也不能在单一的长度和能量尺度上思考物理学，因为效应完全是集体的。 与高能物理相反，微观哈密顿量是确定的，但物质的状态包括深不可测的丰富性和复杂性。 因此，所有这些现象，顾名思义，必须是集体的。 看来，即使是电子作为嵌入物质中的粒子的基本概念也必须修改，因为这样的粒子可能不会保持其完整性，而是分裂成许多，这就是电荷和自旋的分数化概念。 这项研究的主旨是这种前瞻性的观点。 所选的研究课题直接涉及反映量子力学不寻常性质的现象。 讨论了物质从金属到绝缘体或从超导体到绝缘体的量子相变。 尽管历史悠久，但这些问题在任何深层意义上都没有得到解决;可以从意外发现的定期出现中找到证据。 理论上的困难在于，我们没有数学工具来处理物质中强相互作用的自由度。 该补助金的一个方面包括从场论的角度开发这些工具，适用于物质理论。 在另一个方向上，该补助金涉及超导概念的发展，其中配对的结果来自正常状态的电子动能的节省。 ***

9971138ChakravartyQuantum mechanical properties of materials continue to produce novel and unexpected phenomena. Within the past decade or so, the oxide superconductors, ruthenates, manganates, fullerenes and heavy electron materials have attracted attention. Of fundamental interest are those properties that reflect quantum mechanics on a macroscopic scale. Such discoveries are challenging us continuously to extend our understanding of properties of matter. New, inherently quantum phases of matter, such as quantum Hall states are discovered, as are new concepts, such as quantum phase transitions at the absolute zero of temperature between fundamentally distinct states of matter driven entirely by quantum mechanics. Control over properties of quantum states of matter remains an engaging intellectual enterprise. We are beginning to realize that underlying the materials science, there must be a set of physical principles, most likely simple in character; however, to discover these principles a genuine shift in thinking is needed. The long-cherished ideas that have served us well for conventional materials have to be abandoned. One can no longer think in terms of physics on single length and energy scales, because the effects are entirely collective. In contrast to high energy physics, the microscopic Hamiltonian is known with certainty, but the states of matter comprise unfathomable richness and complexity. Thus, all such phenomena, by defintion, must be collective. It appears that even the basic notion of an electron as a particle embedded in matter has to be revised because such a particle may not retain its integrity but break up into many, which is the notion of fractionalization of charge and spin. The thrust of this research is this forward-looking view. The chosen research topics relate directly to the phenomena reflecting the unusual nature of quantum mechanics. Quantum phase transitions where matter is transformed from a metal to an insulator, or from a superconductor to an insulator is addressed. Despite a long histroy these problems are unresolved in any deep sense of the word; proof of which can be found in the regular appearance of unexpected discoveries. The theoretical difficulty is that we do not have the mathematical tools to treat strongly interacting degrees of freedom in matter. An aspect of this grant consists of developing such tools from the perspective of field theory, as applied to the theory of matter. In yet another direction, the grant concerns the development of a notion of superconductivity in which pairing results from the saving of the electronic kinetic energy of the normal state. This is unabashedly unconventional because there is no notion of exchanging a quantum of excitation to mediate attraction between electrons resulting in superconductivity.%%% Quantum mechanical properties of materials continue to produce novel and unexpected phenomena. Within the past decade or so, the oxide superconductors, ruthenates, manganates, fullerenes and heavy electron materials have attracted attention. Of fundamental interest are those properties that reflect quantum mechanics on a macroscopic scale. Such discoveries are challenging us continuously to extend our understanding of properties of matter. New, inherently quantum phases of matter, such as quantum Hall states are discovered, as are new concepts, such as quantum phase transitions at the absolute zero of temperature between fundamentally distinct states of matter driven entirely by quantum mechanics. Control over properties of quantum states of matter remains an engaging intellectual enterprise. We are beginning to realize that underlying the materials science, there must be a set of physical principles, most likely simple in character; however, to discover these principles a genuine shift in thinking is needed. The long-cherished ideas that have served us well for conventional materials have to be abandoned. One can no longer think in terms of physics on single length and energy scales, because the effects are entirely collective. In contrast to high energy physics, the microscopic Hamiltonian is known with certainty, but the states of matter comprise unfathomable richness and complexity. Thus, all such phenomena, by defintion, must be collective. It appears that even the basic notion of an electron as a particle embedded in matter has to be revised because such a particle may not retain its integrity but break up into many, which is the notion of fractionalization of charge and spin. The thrust of this research is this forward-looking view. The chosen research topics relate directly to the phenomena reflecting the unusual nature of quantum mechanics. Quantum phase transitions where matter is transformed from a metal to an insulator, or from a superconductor to an insulator is addressed. Despite a long histroy these problems are unresolved in any deep sense of the word; proof of which can be found in the regular appearance of unexpected discoveries. The theoretical difficulty is that we do not have the mathematical tools to treat strongly interacting degrees of freedom in matter. An aspect of this grant consists of developing such tools from the perspective of field theory, as applied to the theory of matter. In yet another direction, the grant concerns the development of a notion of superconductivity in which pairing results from the saving of the electronic kinetic energy of the normal state. ***