arXiv: Mathematical Physics最新文献

The Non-isentropic Relativistic Euler System Written in a Symmetric Hyperbolic Form 对称双曲形式的非等熵相对论欧拉系统

arXiv: Mathematical Physics Pub Date : 2021-03-02 DOI: 10.1007/978-3-030-61346-4_3

U. Brauer, Lavi Karp

引用次数: 0

Thermodynamic formalism for generalized countable Markov shifts 广义可数马尔可夫位移的热力学形式

arXiv: Mathematical Physics Pub Date : 2020-12-17 DOI: 10.11606/T.45.2020.TDE-06012021-103444

T. Raszeja

{"title":"Thermodynamic formalism for generalized countable Markov shifts","authors":"T. Raszeja","doi":"10.11606/T.45.2020.TDE-06012021-103444","DOIUrl":"https://doi.org/10.11606/T.45.2020.TDE-06012021-103444","url":null,"abstract":"Countable Markov shifts, denoted by $Sigma_A$ for a 0-1 infinite matrix $A$, are central objects in symbolic dynamics and ergodic theory. R. Exel and M. Laca introduced the corresponding operator algebras, a generalization of the Cuntz-Krieger algebras for infinite countable alphabet, and the set $X_A$, a kind of Generalized Markov Shift (GMS) that coincides with $Sigma_A$ in the locally compact case. The set $Sigma_A$ is dense in $X_A$, and its complement, a set of finite allowed words, is dense in $X_A$ when non-empty. We develop the thermodynamic formalism for $X_A$, introducing the notion of conformal measure in it, and exploring its connections with the usual formalism for $Sigma_A$. New phenomena appear, as different types of phase transitions and new conformal measures undetected by the classical thermodynamic formalism for $A$ not row-finite. Given a potential $F$ and inverse of temperature $beta$, we study the existence of conformal measures $mu_{beta}$ associated to $beta F$. We present examples where there exists a critical $beta_c$ s. t. we have existence of conformal probabilities satisfying $mu_{beta}(Sigma_A)=0$ for every $beta > beta_c$ and, on the weak$^*$ topology, the set of conformal probabilities for $beta >beta_c$ collapses to the standard conformal probability $mu_{beta_c}$, $mu_{beta_c}(Sigma_A)=1$, for the limit $betatobeta_c$. We study in detail the generalized renewal shift and modifications of it. We highlight the bijection between infinite emitters of the alphabet and extremal conformal probabilities for this class of renewal type shifts. We prove the existence and uniqueness of the eigenmeasure probability of the Ruelle's transformation at low enough temperature for a particular potential on the generalized renewal shift; such measures are not detected on the standard renewal shift since for low temperatures, $beta F$ is transient.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81925549","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: 3

Chaos and Turing machines on bidimensional models at zero temperature 零温度下二维模型上的混沌和图灵机

arXiv: Mathematical Physics Pub Date : 2020-12-15 DOI: 10.11606/T.45.2020.TDE-04012021-102503

Gregorio Luis Dalle Vedove Nosaki

{"title":"Chaos and Turing machines on bidimensional models at zero temperature","authors":"Gregorio Luis Dalle Vedove Nosaki","doi":"10.11606/T.45.2020.TDE-04012021-102503","DOIUrl":"https://doi.org/10.11606/T.45.2020.TDE-04012021-102503","url":null,"abstract":"In equilibrium statistical mechanics or thermodynamics formalism one of the main objectives is to describe the behavior of families of equilibrium measures for a potential parametrized by the inverse temperature $beta$. Here we consider equilibrium measures as the shift invariant measures that maximizes the pressure. Other constructions already prove the chaotic behavior of these measures when the system freezes, that is, when $betarightarrow+infty$. One of the most important examples was given by Chazottes and Hochman where they prove the non-convergence of the equilibrium measures for a locally constant potential when the dimension is bigger then 3. In this work we present a construction of a bidimensional example described by a finite alphabet and a locally constant potential in which there exists a subsequence $(beta_k)_{kgeq 0}$ where the non-convergence occurs for any sequence of equilibrium measures at inverse of temperature $beta_k$ when $beta_krightarrow+infty$. In order to describe such an example, we use the construction described by Aubrun and Sablik which improves the result of Hochman used in the construction of Chazottes and Hochman.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85815397","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

The first order expansion of a ground state energy of the ϕ4 model with cutoffs 带截止点的ϕ4模型的基态能量的一阶展开

arXiv: Mathematical Physics Pub Date : 2020-12-09 DOI: 10.1063/5.0040022

Toshimitsu Takaesu

引用次数: 0

The classical limit of mean-field quantum spin systems 平均场量子自旋系统的经典极限

arXiv: Mathematical Physics Pub Date : 2020-12-01 DOI: 10.1063/5.0021120

Christiaan J. F. van de Ven

{"title":"The classical limit of mean-field quantum spin systems","authors":"Christiaan J. F. van de Ven","doi":"10.1063/5.0021120","DOIUrl":"https://doi.org/10.1063/5.0021120","url":null,"abstract":"The theory of strict deformation quantization of the two sphere $S^2subsetmathbb{R}^3$ is used to prove the existence of the classical limit of mean-field quantum spin chains, whose ensuing Hamiltonians are denoted by $H_N$ and where $N$ indicates the number of sites. Indeed, since the fibers $A_{1/N}=M_{N+1}(mathbb{C})$ and $A_0=C(S^2)$ form a continuous bundle of $C^*$-algebras over the base space $I={0}cup 1/mathbb{N}^*subset[0,1]$, one can define a strict deformation quantization of $A_0$ where quantization is specified by certain quantization maps $Q_{1/N}: tilde{A}_0 rightarrow A_{1/N}$, with $tilde{A}_0$ a dense Poisson subalgebra of $A_0$. Given now a sequence of such $H_N$, we show that under some assumptions a sequence of eigenvectors $psi_N$ of $H_N$ has a classical limit in the sense that $omega_0(f):=lim_{Ntoinfty}langlepsi_N,Q_{1/N}(f)psi_Nrangle$ exists as a state on $A_0$ given by $omega_0(f)=frac{1}{n}sum_{i=1}^nf(Omega_i)$, where $n$ is some natural number. We give an application regarding spontaneous symmetry breaking (SSB) and moreover we show that the spectrum of such a mean-field quantum spin system converges to the range of some polynomial in three real variables restricted to the sphere $S^2$.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":"2673 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85906811","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: 5

Heat kernel estimates for two-dimensional relativistic Hamiltonians with magnetic field 带磁场的二维相对论哈密顿量的热核估计

arXiv: Mathematical Physics Pub Date : 2020-11-27 DOI: 10.4171/ecr/18-1/16

H. Kovařík

引用次数: 0

Symmetry transformations of extremals and higher conserved quantities: Invariant Yang–Mills connections 极值和高守恒量的对称变换:不变Yang-Mills联系

arXiv: Mathematical Physics Pub Date : 2020-11-23 DOI: 10.1063/5.0038533

Luca Accornero, M. Palese

引用次数: 3

Heun operator of Lie type and the modified algebraic Bethe ansatz 李型的Heun算子与修正的代数Bethe ansatz

arXiv: Mathematical Physics Pub Date : 2020-11-23 DOI: 10.1063/5.0041097

Pierre-Antoine Bernard, N. Crampé, Dounia Shaaban Kabakibo, L. Vinet