arXiv - PHYS - Mathematical Physics最新文献_第10页

Failures of the Feynman-Dyson diagrammatic perturbation expansion of propagators 传播者的费曼-戴森图解扰动扩展的失败

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.03157

So Hirata, Ireneusz Grabowski, Rodney J. Bartlett

{"title":"Failures of the Feynman-Dyson diagrammatic perturbation expansion of propagators","authors":"So Hirata, Ireneusz Grabowski, Rodney J. Bartlett","doi":"arxiv-2312.03157","DOIUrl":"https://doi.org/arxiv-2312.03157","url":null,"abstract":"Using a general-order many-body Green's-function method for molecules, we\u0000illustrate numerically three pathological behaviors of the Feynman-Dyson\u0000diagrammatic perturbation expansion of one-particle many-body Green's functions\u0000as electron propagators. First, the perturbation expansion of the\u0000frequency-dependent self-energy is nonconvergent at the exact self-energy in\u0000wide domains of frequency. Second, the Dyson equation with an odd-order\u0000self-energy has a qualitatively wrong shape and, as a result, most of their\u0000satellite roots are complex and nonphysical. Third, the Dyson equation with an\u0000even-order self-energy has an exponentially increasing number of roots as the\u0000perturbation order is raised, which quickly exceeds the correct number of\u0000roots. Infinite partial summation of diagrams by vertex or edge modification\u0000exacerbates these problems. Not only does the nonconvergence render\u0000higher-order perturbation theories useless for satellite roots, but it also\u0000calls into question the validity of their combined use with the ans\"{a}tze\u0000requiring the knowledge of all poles and residues. Such ans\"{a}tze include the\u0000Galitskii-Migdal formula, self-consistent Green's-function methods,\u0000Luttinger-Ward functional, and some models of the algebraic diagrammatic\u0000construction.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimality of generalized Choi maps in $M_3$ 广义Choi映射在M_3中的最优性

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02814

Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński

引用次数: 0

Calculation of Relativistic Single-Particle States 相对论单粒子态的计算

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02500

D. Wingard, B. Kónya, Z. Papp

引用次数: 0

Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations 时变哈密顿量的量子模拟——应用于非自治常微分方程和偏微分方程

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02817

Yu Cao, Shi Jin, Nana Liu

{"title":"Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations","authors":"Yu Cao, Shi Jin, Nana Liu","doi":"arxiv-2312.02817","DOIUrl":"https://doi.org/arxiv-2312.02817","url":null,"abstract":"Non-autonomous dynamical systems appear in a very wide range of interesting\u0000applications, both in classical and quantum dynamics, where in the latter case\u0000it corresponds to having a time-dependent Hamiltonian. However, the quantum\u0000simulation of these systems often needs to appeal to rather complicated\u0000procedures involving the Dyson series, considerations of time-ordering,\u0000requirement of time steps to be discrete and/or requiring multiple measurements\u0000and postselection. These procedures are generally much more complicated than\u0000the quantum simulation of time-independent Hamiltonians. Here we propose an\u0000alternative formalism that turns any non-autonomous unitary dynamical system\u0000into an autonomous unitary system, i.e., quantum system with a time-independent\u0000Hamiltonian, in one higher dimension, while keeping time continuous. This makes\u0000the simulation with time-dependent Hamiltonians not much more difficult than\u0000that of time-independent Hamiltonians, and can also be framed in terms of an\u0000analogue quantum system evolving continuously in time. We show how our new\u0000quantum protocol for time-dependent Hamiltonians can be performed in a\u0000resource-efficient way and without measurements, and can be made possible on\u0000either continuous-variable, qubit or hybrid systems. Combined with a technique\u0000called Schrodingerisation, this dilation technique can be applied to the\u0000quantum simulation of any linear ODEs and PDEs, and nonlinear ODEs and certain\u0000nonlinear PDEs, with time-dependent coefficients.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rydberg atoms on a ladder 梯子上的里德伯原子

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02747

Tomislav Došlić, Mate Puljiz, Stjepan Šebek, Josip Žubrinić

引用次数: 0

Upper tail large deviation for the one-dimensional frog model 上尾偏差大，为一维青蛙模型

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02745

Van Hao Can, Naoki Kubota, Shuta Nakajima

{"title":"Upper tail large deviation for the one-dimensional frog model","authors":"Van Hao Can, Naoki Kubota, Shuta Nakajima","doi":"arxiv-2312.02745","DOIUrl":"https://doi.org/arxiv-2312.02745","url":null,"abstract":"In this paper, we study the upper tail large deviation for the\u0000one-dimensional frog model. In this model, sleeping and active frogs are\u0000assigned to vertices on $mathbb Z$. While sleeping frogs do not move, the\u0000active ones move as independent simple random walks and activate any sleeping\u0000frogs. The main object of interest in this model is the asymptotic behavior of\u0000the first passage time ${rm T}(0,n)$, which is the time needed to activate the\u0000frog at the vertex $n$, assuming there is only one active frog at $0$ at the\u0000beginning. While the law of large numbers and central limit theorems have been\u0000well established, the intricacies of large deviations remain elusive. Using\u0000renewal theory, B'erard and Ram'irez have pointed out a slowdown phenomenon\u0000where the probability that the first passage time ${rm T}(0,n)$ is\u0000significantly larger than its expectation decays sub-exponentially and lies\u0000between $exp(-n^{1/2+o(1)})$ and $exp(-n^{1/3+o(1)})$. In this article, using\u0000a novel covering process approach, we confirm that $1/2$ is the correct\u0000exponent, i.e., the rate of upper large deviations is given by $n^{1/2}$.\u0000Moreover, we obtain an explicit rate function that is characterized by\u0000properties of Brownian motion and is strictly concave.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138521805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mean square displacement of Brownian paths perturbed by bounded pair potentials 受有界对势扰动的布朗路径的均方位移

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02709

Volker Betz, Tobias Schmidt, Mark Sellke

引用次数: 0

A new class of distances on complex projective spaces 复射影空间上一类新的距离

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02583

Rafał Bistroń, Michał Eckstein, Shmuel Friedland, Tomasz Miller, Karol Życzkowski

引用次数: 0

A remark on certain restricted plane partitions and crystal melting model 关于某些受限平面分区和晶体熔化模型的评述

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-05 DOI: arxiv-2312.02749

Chenglang Yang

引用次数: 0

Integrable extensions of two-center Coulomb systems 双中心库仑系统的可积扩展

arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-04 DOI: arxiv-2312.02013

Francisco Correa, Octavio Quintana

引用次数: 0