Quantum Aspects of Condensed Matter

9971138 chakravarty材料的量子力学特性不断产生新奇和意想不到的现象。在过去的十年左右，氧化物超导体、钌酸盐、锰酸盐、富勒烯和重电子材料引起了人们的注意。最重要的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对物质性质的理解。新的、固有的物质量子相被发现，比如量子霍尔态，还有一些新概念被发现，比如完全由量子力学驱动的物质基本不同状态之间的绝对零度温度下的量子相变。控制物质量子态的特性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，一定有一套物理原理，很可能是简单的；然而，要发现这些原则，需要在思维上进行真正的转变。长期以来为传统材料服务的理念必须被抛弃。人们不能再从物理的角度考虑单一的长度和能量尺度，因为这些影响完全是集体的。与高能物理学相比，微观的哈密顿量是确定的，但物质的状态包含着深不可测的丰富性和复杂性。因此，所有这些现象，根据定义，必须是集体的。似乎连电子作为嵌入物质中的粒子的基本概念都必须修改，因为这样的粒子可能不会保持其完整性，而是分裂成许多个，这就是电荷和自旋分块化的概念。这项研究的主旨就是这种前瞻性的观点。所选择的研究课题与反映量子力学不寻常性质的现象直接相关。量子相变是指物质从金属转变为绝缘体，或从超导体转变为绝缘体。尽管历史悠久，但这些问题在任何深刻的意义上都没有得到解决；我们可以从经常出现的意想不到的发现中找到证据。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。这项拨款的一个方面包括从场论的角度开发这些工具，应用于物质理论。在另一个方向上，这项资助涉及超导概念的发展，在超导概念中，配对是由于正常状态下电子动能的节省而产生的。这是毫不掩饰的非常规，因为没有交换量子激发来调解电子之间的吸引力从而导致超导的概念。材料的量子力学特性不断产生新奇和意想不到的现象。在过去的十年左右，氧化物超导体、钌酸盐、锰酸盐、富勒烯和重电子材料引起了人们的注意。最重要的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对物质性质的理解。新的、固有的物质量子相被发现，比如量子霍尔态，还有一些新概念被发现，比如完全由量子力学驱动的物质基本不同状态之间的绝对零度温度下的量子相变。控制物质量子态的特性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，一定有一套物理原理，很可能是简单的；然而，要发现这些原则，需要在思维上进行真正的转变。长期以来为传统材料服务的理念必须被抛弃。人们不能再从物理的角度考虑单一的长度和能量尺度，因为这些影响完全是集体的。与高能物理学相比，微观的哈密顿量是确定的，但物质的状态包含着深不可测的丰富性和复杂性。因此，所有这些现象，根据定义，必须是集体的。似乎连电子作为嵌入物质中的粒子的基本概念都必须修改，因为这样的粒子可能不会保持其完整性，而是分裂成许多个，这就是电荷和自旋分块化的概念。这项研究的主旨就是这种前瞻性的观点。所选择的研究课题与反映量子力学不寻常性质的现象直接相关。量子相变是指物质从金属转变为绝缘体，或从超导体转变为绝缘体。尽管历史悠久，但这些问题在任何深刻的意义上都没有得到解决；我们可以从经常出现的意想不到的发现中找到证据。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。这项拨款的一个方面包括从场论的角度开发这些工具，应用于物质理论。在另一个方向上，这项资助涉及超导概念的发展，在超导概念中，配对是由于正常状态下电子动能的节省而产生的。* * *

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. ***