Expansions about Free-Fermion Models
Saibal Mitra
本文介绍了一种简单的方法来展开一般六顶点模型关于自由费米子点的自由能。这种技术被用来验证库仑气体预测的行为的领先的奇异性的自由能交错F模型在零交错场。
A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction about the behavior of the leading singularity in the free energy of the staggered F-model at zero staggered field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients
Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit
我们推导出一个渐近展开的Wiener-Hopf行列式所产生的问题中的一维自由费米子计数线段在零温度。这个扩展是Toeplitz和Wiener-Hopf行列式理论中的结果的推广，称为广义Fisher-Hartwig猜想。该展开式的系数必须服从一定的周期性关系，这使得该展开式在“计数参数”中具有明显的周期性。我们提出了两种方法来计算这些系数，并验证周期性关系的顺序顺序：矩阵Riemann-Hilbert问题和Painleve V方程。我们表明，展开系数是多项式的计数参数，并列出明确的前几个系数。
Fisher-Hartwig expansion for Toeplitz determinants and the spectrum of a single-particle reduced density matrix for one-dimensional free fermions
本文研究了一维格点上自由费米子的单粒子约化密度矩阵所对应的具有正弦核的Toeplitz矩阵的谱。对于这个矩阵的谱行列式，最近已经证明了逆矩阵大小的Fisher-Hartwig展开。这种扩展可以通过使用离散Painleve方程理论中已知的递归关系，远离零点积累线，逐阶验证。我们执行这样的验证到第十阶，并计算相应的系数在Fisher-Hartwig展开。在假定Fisher-Hartwig展开式在整个谱参数范围内都是有效的情况下，我们进一步导出了一个方程关于该矩阵的本征值的展开式以及相应费米子问题中的von Neumann纠缠熵的展开式.这些分析结果得到了数值例子的支持。
White noise distribution theory for the Fermion system
本文给出了费米子系统的白噪声演算，并证明了Fock展开式。每个费米子白噪声泛函上的连续线性算子都由积分核算子序列唯一表示。这个级数称为Fock展开。
Solving models with generalized free fermions II: Path-product expansion and conserved charges
本文针对量子自旋系统中的自由费米子可解性，通过定义哈密顿量受挫图的图Clifford代数，推导出路径积展开以显式表达自由费米子模和局域守恒荷，并计算了无限温度动力学关联函数。
2D Fermions and Statistical Mechanics: Critical Dimers and Dirac Fermions in a background gauge field
本文研究了等径图上扭曲二聚物配分函数与背景规范场中2D Dirac配分函数的团簇展开，证明两者逐项匹配，并推广了Dubédat的相关计算。
This paper is the first of a series aiming at proving rigorously the analyticity and the Borel summability of generic quartic bosonic and fermionic vector models (generalizing the O(N) vector model) in diverse dimensions. Both non-relativistic (Schrödinger) and relativistic (Klein-Gordon and Dirac) kinetic terms are considered. The 4-tensor defining the interactions is constant but otherwise arbitrary, up to the symmetries imposed by the statistics of the field. In this paper, we focus on models of low dimensions: bosons and fermions for d = 0, 1, and relativistic bosons for d = 2. Moreover, w…
We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\sum_{n \ge 1} a_n q^n$, with $a_n \in \mathbb{Z}$. Such integrals arise in physics as the partition functions of free four-dimensional gauge theories on $S^3$ and, in particular, as the superconformal index of super Yang-Mills theory. We show that any such model can be expressed in terms of a system of free fermions in an ensemble parameterized by the infinite set of couplings. Integrating out the fermions in a given quantum state leads to a convergent expans…
Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
研究证明在量子系统中，自由膨胀过程导致宏观密度分布趋于均匀，揭示了量子力学中不可逆行为的出现，无需引入随机性。
We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the \textit{long time large deviation function}, found to agree with previous works using completely different t…
On The Weak-Coupling Limit for Bosons and Fermions
本文考虑一个大的玻色子或费米子系统。我们从与玻色-爱因斯坦统计和费米-狄拉克统计相容的初始数据开始。我们让相互作用的粒子系统在弱耦合状态下演化。我们表明，在极限，并高达二阶的潜力，微扰的扩展表示的值的单粒子维格纳函数在时间$t$，同意类似的扩展的解决方案的Uehling-Uhlenbeck方程。本文遵循的精神同伴工作[ \rcite{BCEP} ]，其中作者研究了弱耦合的限制粒子服从麦克斯韦-玻尔兹曼统计：在这里，他们证明了一个（更强）收敛的结果对玻尔兹曼方程的解决方案。
The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the re-summation of scalars at strong coupling. Then, we disentangle the form of the fermion contribution and show its strong coupling expansion. In particular, we derive the leading order with the appearance of a fermion-anti-fermion bound state first and then effective multiple bound states thereof. This reproduces the string minimal area result and also applies to the Nekrasov instanton partition function $\mathcal{Z}$…
Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions
本文提出了一种基于树确定性展开的随机算法，用于计算弱相互作用费米子的对数分区函数，实现了多项式时间复杂度。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。