不对称的简单排除过程的光谱边界:自由费米子,贝特的替代物和随机矩阵理论
Goran Nakerst1,2, Tomaž Prosen3, Masudul Haque1,2,4
1Institut für Theoretische Physik, <a href="https://ror.org/042aqky30">Technische Universität Dresden</a>, D-01062 Dresden, Germany.
Physical review. E
|August 20, 2024
概括
非对称的简单排除过程 (ASEP) 发生器表现出带有L或L+1尖峰的光谱边界. 这些尖峰源于Bethe ansatz中的根集群,并且与随机矩阵和图形理论密切相关.
科学领域:
- 统计力学 统计力学
- 非平衡系统 非平衡系统
- 量子场理论 量子场理论
背景情况:
- 非对称的简单排除过程 (ASEP) 是不平衡统计力学的一个基本模型.
- 了解ASEP发电机的光谱特性对于描述其动态至关重要.
- 之前的研究已经探讨了ASEP的动态,但详细的光谱边界分析仍然是一个活跃的领域.
研究的目的:
- 调查ASEP发电机的光谱特征,特别是其光谱边界.
- 分析边界条件 (周期和开放) 对光谱边界的影响.
- 为了将ASEP发生器连接到非赫密特式费米离子模型和随机矩阵理论.
主要方法:
- 在周期边界条件 (PBC) 和开放边界条件 (OBC) 下分析长度为L的有限ASEP链.
- 将ASEP发电机作为一个相互作用的非赫密特式费米离子模型来处理.
- 在PBC下应用Bethe坐标替代用于在非相互作用和ASEP极限之间进行插值.
- 连接到带有痕迹相关性的随机矩阵和具有明显循环结构的随机图.
主要成果:
- ASEP生成器的光谱边界显示了PBC的L尖峰和OBC的L+1尖峰.
- 在非相互作用极限中,多体光谱显示了一个带有突出尖峰的光谱边界.
- 对于PBCs的光谱边界中的尖峰起源于Bethe根的聚类.
- 尖尖的光谱边界结构强大,并且在相关的随机矩阵和随机图模型中观察到.
结论:
- ASEP发电机的光谱边界具有独特的尖结构,取决于边界条件.
- 坐标Bethe ansatz提供了一个框架,通过根集群来理解这些尖的起源.
- 该ASEP生成器与随机矩阵和随机图共享光谱边界特征,突出更广泛的数学连接.
相关概念视频
The Pauli Exclusion Principle
35.8K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
35.8K
Electrostatic Boundary Conditions
443
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
443
Electrostatic Boundary Conditions in Dielectrics
1.1K
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's...
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's...
1.1K
Crystal Field Theory - Tetrahedral and Square Planar Complexes
41.8K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
41.8K
The de Broglie Wavelength
25.4K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
25.4K
The Quantum-Mechanical Model of an Atom
42.1K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.1K


