Aspects of quantum phase transitions

Quantum Noise and its Importance to the Quantum Classical Transition Problem: Energy Measurement Aspects

In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we consider the experimental limitations ruled by uncertainty principle. We have shown that the discrete nature of energy levels of integrable systems can be accessed by classical measurements. We have defined a precise limit for this procedure. It may be used as a tool to define the classical limit as far as the discrete spectra of integrable systems are concerned.

从复化到自相似性：量子临界性的新视角

From Complexification to Self-Similarity: New Aspects of Quantum Criticality

本文是量子临界性相关的小型综述，梳理复化方法在量子相变研究的最新进展，探讨复配分函数关联的自相似现象，并对该领域未来方向提出展望。

广义几何相位：数学方面

Generalised Geometric Phase: Mathematical Aspects

该研究为基于物理提出的广义几何相位提供数学基础，揭示量子系统中不同的射线空间与纤维丛结构，并将其理解为联络的（非）和乐，底层空间为伪凯勒流形。

探索共振腔中暗物质轴子与暗光子转化为光子的量子特性

Exploring Quantum Aspects of Dark Matter Axions and Dark Photons Transitioning to Photons in a Resonant Cavity

本研究从量子层面探究共振腔中暗物质轴子、暗光子向光子的转化机制，证实单跃迁受腔品质因数Q放大且无需暗物质波相干性，原理类似Purcell效应，为优化轴子探测提供量子视角的依据。

Universal aspects in the behavior of the entanglement spectrum in one dimension: scaling transition at the factorization point and ordered entangled structures

We investigate the scaling of the entanglement spectrum and of the Rényi block entropies and determine its universal aspects in the ground state of critical and noncritical one-dimensional quantum spin models. In all cases, the scaling exhibits an oscillatory behavior that terminates at the factorization point and whose frequency is universal. Parity effects in the scaling of the Rényi entropies for gapless models at zero field are thus shown to be a particular case of such universal behavior. Likewise, the absence of oscillations for the Ising chain in transverse field is due to the vanishing…

Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice

Recently the creation of novel topological states of matter by a periodic driving field has attracted great attention. To motivate further experimental and theoretical studies, we investigate interesting aspects of Floquet bands and topological phase transitions in a continuously driven Harper model. In such a continuously driven system with an odd number of Floquet bands, the bands are found to have nonzero Chern numbers in general and topological phase transitions take place as we tune various system parameters, such as the amplitude or the period of the driving field. The nontrivial Floquet…

New Aspects of Geometric Phases in Experiments with polarized Neutrons

Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron an…

Nonlocal Aspects of a Quantum Wave

Various aspects of nonlocality of a quantum wave are discussed. In particular, the question of the possibility of extracting information about the relative phase in a quantum wave is analyzed. It is argued that there is a profound difference in the nonlocal properties of the quantum wave between fermion and boson particles. The phase of the boson quantum state can be found from correlations between results of measurements in separate regions. These correlations are identical to the Einstein-Podolsky-Rosen (EPR) correlations between two entangled systems. An ensemble of results of measurements …

非谐 Lipkin-Meshkov-Glick 模型中的激发态量子相变：动力学方面

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects

本文研究了非谐 LMG 模型中新产生的激发态量子相变(ESQPT)的动力学影响，通过量子淬火协议分析存活概率、局部态密度、Loschmidt 回波和 OTOC 的演化，发现其动力学后果与标准模型中的 ESQPT 相似。

Geometrical aspects of weak measurements and quantum erasers

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak me…

Phase Estimation with Non-Unitary Interferometers: Information as a Metric

Determining the phase in one arm of a quantum interferometer is discussed taking into account the three non-ideal aspects in real experiments: non-deterministic state preparation, non-unitary state evolution due to losses during state propagation, and imperfect state detection. A general expression is written for the probability of a measurement outcome taking into account these three non-ideal aspects. As an example of applying the formalism, the classical Fisher information and fidelity (Shannon mutual information between phase and measurements) are computed for few-photon Fock and N00N stat…

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we desc…

周期性驱动非厄米特Su-Schrieffer-Heeger模型的拓扑特性

Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

研究周期性驱动非厄米特Su-Schrieffer-Heeger模型的拓扑特性，发现双正交几何相位作为拓扑指数，揭示了不同相变和零模行为。

Geometric Phases

The differential geometric aspects of Geometric Phases are reviewed.