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Journal of Mathematical Physics
Journal Prestige (SJR): 0.644  Citation Impact (citeScore): 1 Number of Followers: 25  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0022-2488 - ISSN (Online) 1089-7658 Published by AIP  [27 journals]
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- Fluctuations in the spectrum of non-Hermitian i.i.d. matrices
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Authors: Giorgio Cipolloni
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
We consider large non-Hermitian random matrices X with independent identically distributed real or complex entries. In this paper, we review recent results about the eigenvalues of X: (i) universality of local eigenvalue statistics close to the edge of the spectrum of X [Cipolloni et al., “Edge universality for non-Hermitian random matrices,” Probab. Theory Relat. Fields 179, 1–28 (2021)], which is the non-Hermitian analog of the celebrated Tracy–Widom universality; (ii) central limit theorem for linear eigenvalue statistics of macroscopic test functions having 2 + ϵ derivatives [Cipolloni et al., “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” Commun. Pure Appl. Math. (published online) (2021) and Cipolloni et al., “Fluctuation around the circular law for random matrices with real entries,” Electron. J. Probab. 26, 1–61 (2021)]. The main novel ingredients in the proof of these results are local laws for products of two resolvents of the Hermitization of X at two different spectral parameters, coupling of weakly dependent Dyson Brownian motions, and the lower tail estimate for the smallest singular value of X − z in the transitional regime z ≈ 1 [Cipolloni et al., “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probab. Math. Phys. 1, 101–146 (2020)].
Citation: Journal of Mathematical Physics
PubDate: 2022-05-12T10:11:05Z
DOI: 10.1063/5.0089089
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- The [math]-deformations of associative Rota–Baxter algebras and homotopy
Rota–Baxter operators-
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Authors: Apurba Das, Satyendra Kumar Mishra
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
A relative Rota–Baxter algebra is a triple (A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev, Sheng, and Tang, we construct an L∞[1]-algebra whose Maurer–Cartan elements are precisely relative Rota–Baxter algebras. By a standard twisting, we define a new L∞[1]-algebra that controls Maurer–Cartan deformations of a relative Rota–Baxter algebra (A, M, T). We introduce the cohomology of a relative Rota–Baxter algebra (A, M, T) and study infinitesimal deformations in terms of this cohomology (in low dimensions). As an application, we deduce cohomology of triangular skew-symmetric infinitesimal bialgebras and discuss their infinitesimal deformations. Finally, we define homotopy relative Rota–Baxter operators and find their relationship with homotopy dendriform algebras and homotopy pre-Lie algebras.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-12T10:11:04Z
DOI: 10.1063/5.0076566
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- Strong solutions to the 2D Cauchy problem of compressible non-isothermal
nematic liquid crystal flows with vacuum at infinity-
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Authors: Hong Chen, Ziqi Wan, Xin Zhong
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
We are concerned with the Cauchy problem of compressible non-isothermal nematic liquid crystal flows in [math] with zero density at infinity. By weighted energy estimates and a Hardy-type inequality, we derive the local existence and uniqueness of strong solutions, provided that the initial density and gradient of the orientation decay not too slowly at infinity. The novelty of this paper is that we allow vacuum at infinity.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-12T02:51:21Z
DOI: 10.1063/5.0092182
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- Skew-symmetric hom-algebroids and their representation theory
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Authors: Esmaeil Peyghan, Leila Nourmohammadifar
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
In this paper, we introduce skew-symmetric hom-algebroids and linear almost Poisson structures on dual hom-bundles. In addition, we show that these two geometric notions are related to each other and present several interesting examples of them. Moreover, we study the representation theory of skew-symmetric hom-algebroids and their dual spaces. Finally, we give the notion of phase spaces of skew-symmetric algebroids.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-10T09:46:32Z
DOI: 10.1063/5.0087960
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- New asymptotically flat static vacuum metrics with near Euclidean boundary
data-
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Authors: Zhongshan An, Lan-Hsuan Huang
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
In our prior work toward Bartnik’s static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm that large classes of boundary hypersurfaces are static regular. In this paper, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-09T10:32:24Z
DOI: 10.1063/5.0089527
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- Exponential decay of correlations in the one-dimensional Coulomb gas
ensembles-
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Authors: Tatyana S. Turova
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
We consider the Gibbs measure on the configurations of N particles on R+ with one fixed particle at one end at 0. The potential includes pair-wise Coulomb interactions between any particle and its 2K neighbors. Only when K = 1, the model is within the rank-one operators, and it was treated previously. Here, for the case K ≥ 2, exponentially fast convergence of density distribution for the spacings between particles is proved when N → ∞. In addition, we establish the exponential decay of correlations between the spacings when the number of particles between them is increasing. We treat in detail the case K = 2; when K> 2, the proof works in a similar manner.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-09T10:32:23Z
DOI: 10.1063/5.0089803
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- Classical dynamics from self-consistency equations in quantum mechanics
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Authors: J.-B. Bru, W. de Siqueira Pedra
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
During the last three decades, Pavel Bóna developed a non-linear generalization of quantum mechanics, which is based on symplectic structures for normal states. One important application of such a generalization is a general setting that is very convenient to study the emergence of macroscopic classical dynamics from microscopic quantum processes. We propose here a new mathematical approach to Bóna’s non-linear quantum mechanics. It is based on C0-semigroup theory and has a domain of applicability that is much broader than Bóna’s original one. It highlights the central role of self-consistency. This leads to a mathematical framework in which the classical and quantum worlds are naturally entangled. In this new mathematical approach, we build a Poisson bracket for the polynomial functions on the Hermitian weak*-continuous functionals on any C*-algebra. This is reminiscent of a well-known construction for finite-dimensional Lie algebras. We then restrict this Poisson bracket to states of this C*-algebra by taking quotients with respect to Poisson ideals. This leads to densely defined symmetric derivations on the commutative C*-algebras of real-valued functions on the set of states. Up to a closure, these are proven to generate C0-groups of contractions. As a matter of fact, in generic commutative C*-algebras, even the closableness of unbounded symmetric derivations is a non-trivial issue. Some new mathematical concepts are introduced, which are possibly interesting by themselves: the convex weak* Gâteaux derivative and the state-dependent C*-dynamical systems. Our recent results on macroscopic dynamical properties of lattice-fermion and quantum-spin systems with long-range, or mean-field, interactions corroborate the relevance of the general approach we present here.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-09T10:32:22Z
DOI: 10.1063/5.0039339
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- Asymptotically autonomous dynamics for non-autonomous stochastic 2D
g-Navier–Stokes equation in regular spaces-
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Authors: Dongmei Xu, Fuzhi Li
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
This work is a continuation of our previous work [Li et al., Commun. Pure Appl. Anal. 19, 3137 (2020)] on the regular backward compact random attractor. We prove that under certain conditions, the components of the random attractor of a non-autonomous dynamical system can converge in time to those of the random attractor of the limiting autonomous dynamical system in more regular spaces rather than the basic phase space. As an application of the abstract theory, we show that the backward compact random attractors [[math] is precompact for each [math]] for the non-autonomous stochastic g-Navier–Stokes (g-NS) equation is backward asymptotically autonomous to a random attractor of the autonomous g-NS equation under the topology of [math].
Citation: Journal of Mathematical Physics
PubDate: 2022-05-06T10:12:25Z
DOI: 10.1063/5.0084148
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- Modified DKP hierarchy as modified BKP hierarchy
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Authors: Wenchuang Guan, Shen Wang, Weici Guo, Jipeng Cheng
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
In this paper, we investigate some topics involving the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. Note that the modified DKP (mDKP) hierarchy is just the modified B-type Kadomtsev-Petviashvili (BKP) hierarchy in the bosonic forms. Based on this fact, we first proved the conjecture in You [Physica D 50, 429–462 (1991)], that is, the product of the two tau functions of the mDKP hierarchy is some tau function of the KP hierarchy. Then, we investigate the Darboux transformations of the DKP and mDKP hierarchy. Finally, the solutions of the constrained BKP hierarchy are given in the context of the fermionic representation of infinite Lie algebra d∞.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-05T11:36:15Z
DOI: 10.1063/5.0086983
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- Spectral decimation of a self-similar version of almost Mathieu-type
operators-
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Authors: Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou, Alexander Teplyaev
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
We introduce and study self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians [math] instead of the standard discrete Laplacian and includes the classical almost Mathieu operators as a particular case, namely, when the Laplacian’s parameter is [math]. Our main result establishes that the spectra of these self-similar almost Mathieu operators can be described by the spectra of the corresponding self-similar Laplacians through the spectral decimation framework used in the context of spectral analysis on fractals. The spectral-type of the self-similar Laplacians used in our model is singularly continuous when [math]. In these cases, the self-similar almost Mathieu operators also have singularly continuous spectra despite the periodicity of the potentials. In addition, we derive an explicit formula of the integrated density of states of the self-similar almost Mathieu operators as the weighted pre-images of the balanced invariant measure on a specific Julia set.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-04T09:52:42Z
DOI: 10.1063/5.0078939
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- Asymptotic charges for spin-1 and spin-2 fields at the critical sets of
null infinity-
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Authors: Mariem Magdy Ali Mohamed, Juan A. Valiente Kroon
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
The asymptotic charges of spin-1 and spin-2 fields are studied near spatial infinity. We evaluate the charges at the critical sets where spatial infinity meets null infinity with the aim of finding the relation between the charges at future and past null infinities. To this end, we make use of Friedrich’s framework of the cylinder at spatial infinity to obtain asymptotic expansions of the Maxwell and spin-2 fields near spatial infinity, which are fully determined in terms of initial data on a Cauchy hypersurface. With expanding the initial data in terms of spin-weighted spherical harmonics, it is shown that only a subset of the initial data, which satisfy certain regularity conditions, gives rise to well-defined charges at the point where future (past) infinity meets spatial infinity. Given such initial data, the charges are shown to be fully expressed in terms of the freely specifiable part of the data. Moreover, it is shown that there exists a natural correspondence between the charges defined at future and past null infinities.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-02T10:22:47Z
DOI: 10.1063/5.0081834
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- Affine super Yangians and rectangular W-superalgebras
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Authors: Mamoru Ueda
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian [math] to the universal enveloping algebra of the rectangular W-superalgebra [math] for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + (m − n)(l − 1) ≠ 0.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-02T10:22:46Z
DOI: 10.1063/5.0076638
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- Introduction to the Special Issue: In memory of Jean Bourgain
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Authors: Semyon Dyatlov, Svetlana Jitomirskaya, Zeev Rudnick
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-02T10:22:28Z
DOI: 10.1063/5.0084218
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- Existence analysis of a stationary compressible fluid model for
heat-conducting and chemically reacting mixtures-
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Authors: Miroslav Bulíček, Ansgar Jüngel, Milan Pokorný, Nicola Zamponi
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
The existence of large-data weak solutions to a steady compressible Navier–Stokes–Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure containing a γ-power law. The model is thermodynamically consistent and contains the Maxwell–Stefan cross-diffusion equations in the Fick–Onsager form as a special case. Compared to previous works, a very general model class is analyzed, including cross-diffusion effects, temperature gradients, compressible fluids, and different molar masses. A priori estimates are derived from the entropy balance and the total energy balance. The compactness for the total mass density follows from an estimate for the pressure in Lp with p> 1, the effective viscous flux identity, and uniform bounds related to Feireisl’s oscillation defect measure. These bounds rely heavily on the convexity of the free energy and the strong convergence of the relative chemical potentials.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-02T10:22:27Z
DOI: 10.1063/5.0041053
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- On self-dual Yang–Mills fields on special complex surfaces
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Authors: Bernardo Araneda
Abstract: Journal of Mathematical Physics, Volume 63, Issue 5, May 2022.
We derive a generalization of the flat space equations of Yang and Newman for self-dual Yang–Mills fields to (locally) conformally Kähler Riemannian four-manifolds. The results also apply to Einstein metrics (whose full curvature is not necessarily self-dual). We analyze the possibility of hidden symmetries in the form of Bäcklund transformations, and we find a continuous group of hidden symmetries only for the case in which the geometry is conformally half-flat. No isometries are assumed.
Citation: Journal of Mathematical Physics
PubDate: 2022-05-02T10:22:26Z
DOI: 10.1063/5.0087276
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