P. Dorey, T. Romanczukiewicz, Y. Shnir, A. Wereszczynski
We show that large scale oscillons, i.e., quasi-periodic, long living particle like solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takes into account nonlinear (finite) perturbations.
{"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":"60 1","pages":""},"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}
We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lema^itre-Robertson-Walker spaces, in $mathbb{R}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of $mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of the ambient space reduces to conformal transformations on the submanifolds.
{"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":"25 1","pages":""},"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}
We show that for long-range percolation with polynomially decaying connection probabilities in dimension $dgeq 2$, the critical value depends continuously on the precise specifications of the model. Among other things, we use this result to show transience of the infinite supercritical long-range percolation cluster in dimension $dgeq 3$ and to prove a shape theorem for super-critical long-range percolation in the strong decay regime.
{"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":"6 1","pages":""},"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}
Yi Qiao, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang
We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated $mathbb{W}$ operator (see (2.8) and (3.20)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of $mathbb{W}$ operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the $t-W$ relation without the $W$-term) can be used to study the ground state properties of quantum integrable systems with/without $U(1)$-symmetry in the thermodynamic limit.
{"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":"68 1","pages":""},"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}
Suchindram Dasgupta, Chirag Khurana, A. Shadi Tahvildar-Zadeh
We study the spectrum of the Dirac Hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The potential is screened at large distances so that it goes to zero exponentially at spatial infinity. We show that the Hamiltonian is essentially self-adjoint, the essential spectrum has the usual gap $(-mc^2,mc^2)$ in it, and that there are only finitely many eigenvalues in that gap, corresponding to ground and excited states for the system. We find a one-to-one correspondence between the eigenfunctions of this Hamiltonian and the heteroclinic saddle-saddle connectors of a certain dynamical system on a finite cylinder. We use this correspondence to study how the number of bound states changes with the nuclear charge.
{"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":"68 1","pages":""},"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}
Extending the results of cite{Wu}, we study the double-scaling limit SYK (DSSYK) model with an additional diagonal matrix with a fixed number $c$ of nonzero constant entries $theta$. This constant diagonal term can be rewritten in terms of Majorana fermion products. Its specific formula depends on the value of $c$. We find exact expressions for the moments of this model. More importantly, by proposing a moment-cumulant relation, we reinterpret the effect of introducing a constant term in the context of non-commutative probability theory. This gives rise to a $tilde{q}$ dependent mixture of independences within the moment formula. The parameter $tilde{q}$, derived from the q-Ornstein-Uhlenbeck (q-OU) process, controls this transformation. It interpolates between classical independence ($tilde{q}=1$) and Boolean independence ($tilde{q}=0$). The underlying combinatorial structures of this model provide the non-commutative probability connections. Additionally, we explore the potential relation between these connections and their gravitational path integral counterparts.
{"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":"4 1","pages":""},"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}
We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose (PPT). Under these free transformations, we show that logarithmic negativity emerges as the pivotal entanglement measure for determining entangled states' transformations, analogous to the role of entropy in the second law of thermodynamics. Previous results have proven that entanglement is irreversible under quantum operations that completely preserve PPT and leave open the question of reversibility for quantum operations that do not generate entanglement asymptotically. However, we find that going beyond the complete positivity constraint imposed by standard quantum mechanics enables a reversible theory of exact entanglement manipulation, which may suggest a potential incompatibility between the reversibility of entanglement and the fundamental principles of quantum mechanics.
{"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":"4 1","pages":""},"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}
The Discrete Gaussian Chain is a model of interfaces $Psi : mathbf{Z} to mathbf{Z}$ governed by the Hamiltonian $$ H(Psi)= sum_{ineq j} J_alpha(|i-j|) |Psi_i -Psi_j|^2 $$ with long-range coupling constants $J_alpha(k)asymp k^{-alpha}$. For any $alphain [2,3)$ and at high enough temperature, we prove an invariance principle for such an $alpha$-Discrete Gaussian Chain towards a $H(alpha)$-fractional Gaussian process where the Hurst index $H$ satisfies $H=H(alpha)=frac {alpha-2} 2$. This result goes beyond a conjecture by Fr"ohlich and Zegarlinski cite{frohlich1991phase} which conjectured fluctuations of order $n^{tfrac 1 2 (alpha-2) wedge 1}$ for the Discrete Gaussian Chain. More surprisingly, as opposed to the case of $2D$ Discrete Gaussian $Psi : mathbf{Z}^2 to mathbf{Z}$, we prove that the integers do not affect the {em effective temperature} of the discrete Gaussian Chain at large scales. Such an {em invisibility of the integers} had been predicted by Slurink and Hilhorst in the special case $alpha_c=2$ in cite{slurink1983roughening}. Our proof relies on four main ingredients: (1) A Caffareli-Silvestre extension for the discrete fractional Laplacian (which may be of independent interest) (2) A localisation of the chain in a smoother sub-domain (3) A Coulomb gas-type expansion in the spirit of Fr"ohlich-Spencer cite{FS} (4) Controlling the amount of Dirichlet Energy supported by a $1D$ band for the Green functions of $mathbf{Z}^2$ Bessel type random walks Our results also have implications for the so-called {em Boundary Sine-Gordon field}. Finally, we analyse the (easier) regimes where $alphain(1,2) cup (3,infty)$ as well as the $2D$ Discrete Gaussian with long-range coupling constants (for any $alpha>alpha_c=4$).
{"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":"11 1","pages":""},"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}
We propose commuting set of matrix-valued difference operators in terms of trigonometric ${rm GL}(N|M)$-valued $R$-matrices providing quantum supersymmetric (and possibly anisotropic) spin Ruijsenaars-Macdonald operators. Two types of trigonometric supersymmetric $R$-matrices are used. The first is the one related to the affine quantized algebra ${hat{mathcal U}}_q({rm gl}(N|M))$. The second is a graded version of the standard $mathbb Z_n$-invariant $A_{n-1}$ type $R$-matrix. We show that being properly normalized the latter graded $R$-matrix satisfies the associative Yang-Baxter equation. Next, we proceed to construction of long-range spin chains using the Polychronakos freezing trick. As a result we obtain a new family of spin chains, which extend the ${rm gl}(N|M)$-invariant Haldane-Shastry spin chain to q-deformed case with possible presence of anisotropy.
{"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":"165 1","pages":""},"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}
In recent years, the theory of superstatistics, which aims to describe non-equilibrium steady state systems, has gained attention due to its different real world applications, highlighting its versatility and concise mathematical formulation in terms of a probability density for the inverse temperature $beta=1/k_{B}T$. When exploring the domain of application of the superstatistical theory, recent works have shown some necessary conditions for a superstatistical description of a given steady state, in terms of the fundamental and microcanonical inverse temperature. In this work, a new theorem that establishes a sufficient condition for the existence of a superstatistical description of a particular steady state is presented, using the language of moment-generating functions and connecting them with properties of the derivatives of the fundamental inverse temperature.
{"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":"60 1","pages":""},"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}
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