Fluctuation Induced Exotic Phases of Quantum Matter

通常情况下，波动会产生不稳定的影响。当端着一盘饮料穿过拥挤的房间时，人们希望避免人群的推搡。同样，走钢丝的人可能会避免在狂风大作的日子表演。然而，在许多情况下，波动可能会产生相反的效果，使系统稳定在原本可能不稳定的配置中。当噪声依赖于状态时，即当系统所经历的脉动力的频谱被系统的特定配置修改时，就会发生这种情况。例如，将扫帚放在指尖上保持平衡--练习使专家更接近Levy飞行中水平运动的分布。关键的一点是，扫帚所感受到的扭矩取决于它与垂直方向的角度。许多其他的例子可能也是这样看待的。例如，由于环境的波动，适应性强的物种、敏捷的商业和多样化的投资策略都是稳定的。这种现象也可能发生在量子系统中。在这种情况下，所涉及的涨落是由于海森堡测不准原理而发生的本征量子涨落。由于测不准原理，量子振荡器必须始终振动一点，因此总是携带一点能量，即所谓的零点能量。改变系统的状态可以改变这些本征量子振荡的频率，从而改变零点能量。当量子涨落很强时，零点能量的降低可能是决定系统采用何种状态的主要影响因素。将这一想法应用于具有非常强量子涨落的金属，已被证明对理解在实验中观察到的新状态非常有用。事实上，对新奇状态的观察推动了该理论各方面的发展，该理论提出的观点建议进行实验。这一提议将继续发展这种方法--这种方法已经被称为费米子量子无序有序。我们的目标是在四个主要方向上取得进展：-将理论方法扩展到新系统-扩展理论方法的精确度-通过实验探索新的量子顺序-实验和理论发现

Usually fluctuations have a destabilising effect. When carrying a tray of drinks through a crowded room one wishes to avoid the jostling of the crowd. Similarly, a tightrope walker would probably avoid performing on a blustery day. However, there are many instances where fluctuations can have the opposite effect, stabilising a system in a configuration that might otherwise be unstable. This occurs when the noise is state-dependent; that is, when the spectrum of the fluctuating forces experienced by the system is modified by the particular configuration of the system. Examples include the balancing of a broom on ones fingertip - practice leads the expert to approach ever more closely to a Levy flight distribution of horizontal movements. The crucial point is that the torque experienced by the broom depends upon its angle to the vertical. Many other examples may be viewed in this way. For example, adaptable species, agile businesses and diverse investment strategies are all stable because of fluctuations in the environment.This phenomenon can also occur in quantum systems. In this case, the fluctuations concerned are intrinsic quantum fluctuations occurring because of Heisenberg's uncertainty principle. A quantum oscillator must always oscillate a little because of the uncertainty principle and so always carries a little energy, known as the zero-point energy. Changing the state of the system can change the frequency of these intrinsic quantum oscillations and so change the zero point energy. When the quantum fluctuations are very strong, reducing the zero point energy can be the main influence deciding the state that the system adopts. Applying this idea to metals with very strong quantum fluctuations has proven very useful in understanding novel states observed in experiment. Indeed, the observation of novel states has driven developments of aspects of the theory and the perspective suggested by the theory has suggested experiments. This proposal will continue to develop this approach - which has become known as fermionic quantum order-by-disorder. We aim to make progress in four key directions: - Extend the theoretical approach to new systems - Extend the accuracy of the theoretical approach - Explore novel quantum order experimentally - Experimental and Theoretical discovery