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Oscillons in gapless theories 无间隙理论中的振子
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-08 DOI: arxiv-2312.05308
P. Dorey, T. Romanczukiewicz, Y. Shnir, A. Wereszczynski
{"title":"Oscillons in gapless theories","authors":"P. Dorey, T. Romanczukiewicz, Y. Shnir, A. Wereszczynski","doi":"arxiv-2312.05308","DOIUrl":"https://doi.org/arxiv-2312.05308","url":null,"abstract":"We show that large scale oscillons, i.e., quasi-periodic, long living\u0000particle like solutions, may exist in massless theories, too. Their existence\u0000is explained using an effective (smeared) mass threshold which takes into\u0000account nonlinear (finite) perturbations.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574611","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
SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $mathbb{R}^{n+2}$ $mathbb{R}^{n+2}$中共形平坦的$n$维子漫游的SO$(2,n)$兼容嵌入
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-08 DOI: arxiv-2312.05049
E. Huguet, J. Queva, J. Renaud
{"title":"SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $mathbb{R}^{n+2}$","authors":"E. Huguet, J. Queva, J. Renaud","doi":"arxiv-2312.05049","DOIUrl":"https://doi.org/arxiv-2312.05049","url":null,"abstract":"We describe embeddings of $n$-dimensional Lorentzian manifolds, including\u0000Friedmann-Lema^itre-Robertson-Walker spaces, in $mathbb{R}^{n+2}$ such that\u0000the metrics of the submanifolds are inherited by a restriction from that of\u0000$mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of the\u0000ambient space reduces to conformal transformations on the submanifolds.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566881","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
Continuity of the critical value for long-range percolation 长程渗流临界值的连续性
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04099
Johannes Bäumler
{"title":"Continuity of the critical value for long-range percolation","authors":"Johannes Bäumler","doi":"arxiv-2312.04099","DOIUrl":"https://doi.org/arxiv-2312.04099","url":null,"abstract":"We show that for long-range percolation with polynomially decaying connection\u0000probabilities in dimension $dgeq 2$, the critical value depends continuously\u0000on the precise specifications of the model. Among other things, we use this\u0000result to show transience of the infinite supercritical long-range percolation\u0000cluster in dimension $dgeq 3$ and to prove a shape theorem for super-critical\u0000long-range percolation in the strong decay regime.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555425","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
Off-diagonal approach to the exact solution of quantum integrable systems 量子可积分系统精确解的非对角方法
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04153
Yi Qiao, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang
{"title":"Off-diagonal approach to the exact solution of quantum integrable systems","authors":"Yi Qiao, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang","doi":"arxiv-2312.04153","DOIUrl":"https://doi.org/arxiv-2312.04153","url":null,"abstract":"We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain\u0000under both periodic and open boundary conditions. We propose a new\u0000parametrization of the eigenvalues of transfer matrix. Based on it, we obtain\u0000the exact solution of the system. By analyzing the distribution of zero roots\u0000at the ground state, we obtain the explicit expressions of the eigenfunctions\u0000of the transfer matrix and the associated $mathbb{W}$ operator (see (2.8) and\u0000(3.20)) in the thermodynamic limit. We find that the ratio of the quantum\u0000determinant with the eigenvalue of $mathbb{W}$ operator for the ground state\u0000exhibits exponential decay behavior. Thus this fact ensures that the so-called\u0000inversion relation (the $t-W$ relation without the $W$-term) can be used to\u0000study the ground state properties of quantum integrable systems with/without\u0000$U(1)$-symmetry in the thermodynamic limit.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555549","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
One-dimensional hydrogenic ions with screened nuclear Coulomb field 具有屏蔽核库仑场的一维氢离子
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04033
Suchindram Dasgupta, Chirag Khurana, A. Shadi Tahvildar-Zadeh
{"title":"One-dimensional hydrogenic ions with screened nuclear Coulomb field","authors":"Suchindram Dasgupta, Chirag Khurana, A. Shadi Tahvildar-Zadeh","doi":"arxiv-2312.04033","DOIUrl":"https://doi.org/arxiv-2312.04033","url":null,"abstract":"We study the spectrum of the Dirac Hamiltonian in one space dimension for a\u0000single electron in the electrostatic potential of a point nucleus, in the\u0000Born-Oppenheimer approximation where the nucleus is assumed fixed at the\u0000origin. The potential is screened at large distances so that it goes to zero\u0000exponentially at spatial infinity. We show that the Hamiltonian is essentially\u0000self-adjoint, the essential spectrum has the usual gap $(-mc^2,mc^2)$ in it,\u0000and that there are only finitely many eigenvalues in that gap, corresponding to\u0000ground and excited states for the system. We find a one-to-one correspondence\u0000between the eigenfunctions of this Hamiltonian and the heteroclinic\u0000saddle-saddle connectors of a certain dynamical system on a finite cylinder. We\u0000use this correspondence to study how the number of bound states changes with\u0000the nuclear charge.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555546","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
Non-commutative probability insights into the double-scaling limit SYK Model with constant perturbations: moments, cumulants, and $q$-independence 对具有恒定扰动的双缩放极限 SYK 模型的非交换概率洞察：矩、累积量和 $q$-independence
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04297
Shuang Wu
{"title":"Non-commutative probability insights into the double-scaling limit SYK Model with constant perturbations: moments, cumulants, and $q$-independence","authors":"Shuang Wu","doi":"arxiv-2312.04297","DOIUrl":"https://doi.org/arxiv-2312.04297","url":null,"abstract":"Extending the results of cite{Wu}, we study the double-scaling limit SYK\u0000(DSSYK) model with an additional diagonal matrix with a fixed number $c$ of\u0000nonzero constant entries $theta$. This constant diagonal term can be rewritten\u0000in terms of Majorana fermion products. Its specific formula depends on the\u0000value of $c$. We find exact expressions for the moments of this model. More\u0000importantly, by proposing a moment-cumulant relation, we reinterpret the effect\u0000of introducing a constant term in the context of non-commutative probability\u0000theory. This gives rise to a $tilde{q}$ dependent mixture of independences\u0000within the moment formula. The parameter $tilde{q}$, derived from the\u0000q-Ornstein-Uhlenbeck (q-OU) process, controls this transformation. It\u0000interpolates between classical independence ($tilde{q}=1$) and Boolean\u0000independence ($tilde{q}=0$). The underlying combinatorial structures of this\u0000model provide the non-commutative probability connections. Additionally, we\u0000explore the potential relation between these connections and their\u0000gravitational path integral counterparts.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555597","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
Reversible Entanglement Beyond Quantum Operations 超越量子操作的可逆纠缠
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04456
Xin Wang, Yu-Ao Chen, Lei Zhang, Chenghong Zhu
{"title":"Reversible Entanglement Beyond Quantum Operations","authors":"Xin Wang, Yu-Ao Chen, Lei Zhang, Chenghong Zhu","doi":"arxiv-2312.04456","DOIUrl":"https://doi.org/arxiv-2312.04456","url":null,"abstract":"We introduce a reversible theory of exact entanglement manipulation by\u0000establishing a necessary and sufficient condition for state transfer under\u0000trace-preserving transformations that completely preserve the positivity of\u0000partial transpose (PPT). Under these free transformations, we show that\u0000logarithmic negativity emerges as the pivotal entanglement measure for\u0000determining entangled states' transformations, analogous to the role of entropy\u0000in the second law of thermodynamics. Previous results have proven that\u0000entanglement is irreversible under quantum operations that completely preserve\u0000PPT and leave open the question of reversibility for quantum operations that do\u0000not generate entanglement asymptotically. However, we find that going beyond\u0000the complete positivity constraint imposed by standard quantum mechanics\u0000enables a reversible theory of exact entanglement manipulation, which may\u0000suggest a potential incompatibility between the reversibility of entanglement\u0000and the fundamental principles of quantum mechanics.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138557151","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
Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian 通过离散分数拉普拉奇的卡法雷利-西尔维斯特雷扩展实现离散高斯链的整数不可见性
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04536
Christophe Garban
{"title":"Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian","authors":"Christophe Garban","doi":"arxiv-2312.04536","DOIUrl":"https://doi.org/arxiv-2312.04536","url":null,"abstract":"The Discrete Gaussian Chain is a model of interfaces $Psi : mathbf{Z} to\u0000mathbf{Z}$ governed by the Hamiltonian $$ H(Psi)= sum_{ineq j}\u0000J_alpha(|i-j|) |Psi_i -Psi_j|^2 $$ with long-range coupling constants\u0000$J_alpha(k)asymp k^{-alpha}$. For any $alphain [2,3)$ and at high enough\u0000temperature, we prove an invariance principle for such an $alpha$-Discrete\u0000Gaussian Chain towards a $H(alpha)$-fractional Gaussian process where the\u0000Hurst index $H$ satisfies $H=H(alpha)=frac {alpha-2} 2$. This result goes beyond a conjecture by Fr\"ohlich and Zegarlinski\u0000cite{frohlich1991phase} which conjectured fluctuations of order $n^{tfrac 1 2\u0000(alpha-2) wedge 1}$ for the Discrete Gaussian Chain. More surprisingly, as opposed to the case of $2D$ Discrete Gaussian $Psi :\u0000mathbf{Z}^2 to mathbf{Z}$, we prove that the integers do not affect the {em\u0000effective temperature} of the discrete Gaussian Chain at large scales. Such an\u0000{em invisibility of the integers} had been predicted by Slurink and Hilhorst\u0000in the special case $alpha_c=2$ in cite{slurink1983roughening}. Our proof relies on four main ingredients: (1) A Caffareli-Silvestre\u0000extension for the discrete fractional Laplacian (which may be of independent\u0000interest) (2) A localisation of the chain in a smoother sub-domain (3) A\u0000Coulomb gas-type expansion in the spirit of Fr\"ohlich-Spencer cite{FS} (4)\u0000Controlling the amount of Dirichlet Energy supported by a $1D$ band for the\u0000Green functions of $mathbf{Z}^2$ Bessel type random walks Our results also have implications for the so-called {em Boundary\u0000Sine-Gordon field}. Finally, we analyse the (easier) regimes where\u0000$alphain(1,2) cup (3,infty)$ as well as the $2D$ Discrete Gaussian with\u0000long-range coupling constants (for any $alpha>alpha_c=4$).","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555276","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
Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation 哈丹-沙斯特里型 q变形长程自旋链的超对称广义化和联立杨-巴克斯特方程的三角 GL(N|M) 解
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04525
M. Matushko, A. Zotov
{"title":"Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation","authors":"M. Matushko, A. Zotov","doi":"arxiv-2312.04525","DOIUrl":"https://doi.org/arxiv-2312.04525","url":null,"abstract":"We propose commuting set of matrix-valued difference operators in terms of\u0000trigonometric ${rm GL}(N|M)$-valued $R$-matrices providing quantum\u0000supersymmetric (and possibly anisotropic) spin Ruijsenaars-Macdonald operators.\u0000Two types of trigonometric supersymmetric $R$-matrices are used. The first is\u0000the one related to the affine quantized algebra ${hat{mathcal U}}_q({rm\u0000gl}(N|M))$. The second is a graded version of the standard $mathbb\u0000Z_n$-invariant $A_{n-1}$ type $R$-matrix. We show that being properly\u0000normalized the latter graded $R$-matrix satisfies the associative Yang-Baxter\u0000equation. Next, we proceed to construction of long-range spin chains using the\u0000Polychronakos freezing trick. As a result we obtain a new family of spin\u0000chains, which extend the ${rm gl}(N|M)$-invariant Haldane-Shastry spin chain\u0000to q-deformed case with possible presence of anisotropy.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555418","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
A sufficient condition for superstatistics in steady state ensembles 稳态集合中超统计的充分条件
arXiv - PHYS - Mathematical Physics Pub Date : 2023-12-07 DOI: arxiv-2312.04283
Constanza Farías, Sergio Davis
{"title":"A sufficient condition for superstatistics in steady state ensembles","authors":"Constanza Farías, Sergio Davis","doi":"arxiv-2312.04283","DOIUrl":"https://doi.org/arxiv-2312.04283","url":null,"abstract":"In recent years, the theory of superstatistics, which aims to describe\u0000non-equilibrium steady state systems, has gained attention due to its different\u0000real world applications, highlighting its versatility and concise mathematical\u0000formulation in terms of a probability density for the inverse temperature\u0000$beta=1/k_{B}T$. When exploring the domain of application of the\u0000superstatistical theory, recent works have shown some necessary conditions for\u0000a superstatistical description of a given steady state, in terms of the\u0000fundamental and microcanonical inverse temperature. In this work, a new theorem\u0000that establishes a sufficient condition for the existence of a superstatistical\u0000description of a particular steady state is presented, using the language of\u0000moment-generating functions and connecting them with properties of the\u0000derivatives of the fundamental inverse temperature.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555541","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
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