Recent zbMATH articles in MSC 82Bhttps://zbmath.org/atom/cc/82B2021-06-15T18:09:00+00:00WerkzeugIntegrability and braided tensor categories.https://zbmath.org/1460.820022021-06-15T18:09:00+00:00"Fendley, Paul"https://zbmath.org/authors/?q=ai:fendley.paulSummary: Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from ``discrete holomorphicity''. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of ``Baxterising'', i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.
Reviewer: Reviewer (Berlin)Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms.https://zbmath.org/1460.820012021-06-15T18:09:00+00:00"Cohen-Alloro, Omri"https://zbmath.org/authors/?q=ai:cohen-alloro.omri"Peled, Ron"https://zbmath.org/authors/?q=ai:peled.ronSummary: Motivated by questions on the delocalization of random surfaces, we prove that random surfaces satisfying a Lipschitz constraint rarely develop extremal gradients. Previous proofs of this fact relied on reflection positivity and were thus limited to random surfaces defined on highly symmetric graphs, whereas our argument applies to general graphs. Our proof makes use of a cluster algorithm and reflection transformation for random surfaces of the type introduced by \textit{R. H. Swendsen} and \textit{J.-S. Wang} [``Nonuniversal critical dynamics in Monte Carlo simulations'', Phys. Rev. Lett. 58, No. 2, 86--88 (1987; \url{doi:10.1103/PhysRevLett.58.86})], \textit{U. Wolff} [``Collective Monte Carlo updating for spin systems'', Phys. Rev. Lett. 62, No. 4, 361--364 (1989; \url{doi:10.1103/PhysRevLett.62.361})] and \textit{H. G. Evertz} et al. [``Stochastic cluster algorithms for discrete gaussian (SOS) models'', Phys. Lett. B 254, No. 1--2, 185--191 (1991; \url{doi:10.1016/0370-2693(91)90418-P})]. We discuss the general framework for such cluster algorithms, reviewing several particular cases with emphasis on their use in obtaining theoretical results. Two additional applications are presented: A reflection principle for random surfaces and a proof that pair correlations in the spin \(O(n)\) model have monotone densities, strengthening Griffiths' first inequality for such correlations.
Reviewer: Reviewer (Berlin)The classification of symmetry protected topological phases of one-dimensional fermion systems.https://zbmath.org/1460.811242021-06-15T18:09:00+00:00"Bourne, Chris"https://zbmath.org/authors/?q=ai:bourne.chris"Ogata, Yoshiko"https://zbmath.org/authors/?q=ai:ogata.yoshikoSummary: We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group \(G\). This index takes values in \(\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})\) with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.
Reviewer: Reviewer (Berlin)Hamilton-Jacobi equations for finite-rank matrix inference.https://zbmath.org/1460.820072021-06-15T18:09:00+00:00"Mourrat, Jean-Christophe"https://zbmath.org/authors/?q=ai:mourrat.jean-christopheSummary: We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in Mourrat (2018) which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of Mourrat (2018) using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the nonlinearity in the equation is convex.
Reviewer: Reviewer (Berlin)Perturbative algebraic quantum field theory on quantum spacetime: adiabatic and ultraviolet convergence.https://zbmath.org/1460.810472021-06-15T18:09:00+00:00"Doplicher, Sergio"https://zbmath.org/authors/?q=ai:doplicher.sergio"Morsella, Gerardo"https://zbmath.org/authors/?q=ai:morsella.gerardo"Pinamonti, Nicola"https://zbmath.org/authors/?q=ai:pinamonti.nicolaAuthors' abstract: The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the QuantumWick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which seems difficult to remove. We solve this problem here by another strategy: the fields at a point in the interaction Lagrangian are replaced by the fields at a quantum point, described by an optimally localized state on QST; the resulting Lagrangian density agrees with the previous one after spacetime integration, but gives rise to a different interaction hamiltonian. But now the methods of perturbative Algebraic Quantum Field Theory can be applied, and produce an ultraviolet finite perturbation expansion of the interacting observables. If the obtained theory is tested in an equilibrium state at finite temperature the adiabatic cutoff in time becomes immaterial, namely it has no effect on the correlation function at any order in perturbation theory. Moreover, the interacting vacuum state can be obtained in the vanishing temperature limit. It is nevertheless important to stress that the use of states which are optimally localized for a given observer brakes Lorentz invariance at the very beginning.
Reviewer: Daniel Beltiţă (Bucureşti)Cycles in random meander systems.https://zbmath.org/1460.050132021-06-15T18:09:00+00:00"Kargin, Vladislav"https://zbmath.org/authors/?q=ai:kargin.vladislavSummary: A meander system is a union of two arc systems that represent non-crossing pairings of the set \([2n] = \{1, \dots, 2n\}\) in the upper and lower half-plane. In this paper, we consider random meander systems. We show that for a class of random meander systems -- for simply-generated meander systems -- the number of cycles in a system of size \(n\) grows linearly with \(n\) and that the length of the largest cycle in a uniformly random meander system grows at least as \(c \log n\) with \(c > 0\). We also present numerical evidence suggesting that in a simply-generated meander system of size \(n\), (i) the number of cycles of length \(k \ll n\) is \(\sim n k^{-\beta}\), where \(\beta \approx 2\), and (ii) the length of the largest cycle is \(\sim n^\alpha\), where \(\alpha\) is close to 4/5. We compare these results with the growth rates in other families of meander systems, which we call rainbow meanders and comb-like meanders, and which show significantly different behavior.
Reviewer: Reviewer (Berlin)Simulation studies of random sequential adsorption (RSA) of mixture of two-component circular discs.https://zbmath.org/1460.811202021-06-15T18:09:00+00:00"Wagaskar, K. V."https://zbmath.org/authors/?q=ai:wagaskar.k-v"Late, Ravikiran"https://zbmath.org/authors/?q=ai:late.ravikiran"Banpurkar, A. G."https://zbmath.org/authors/?q=ai:banpurkar.a-g"Limaye, A. V."https://zbmath.org/authors/?q=ai:limaye.a-v"Shelke, Pradip B."https://zbmath.org/authors/?q=ai:shelke.pradip-bSummary: We study Random Sequential Adsorption (RSA) of mixture of two-component circular discs on a two-dimensional continuum substrate by computer simulation for different values of radius ratio \(r_A/r_B\), \((r_A<r_B)\), and relative rate constant \(k = k_A/k_B\) between the discs. For smaller values of radius ratio and all values of relative rate constant between the discs, the approach of instantaneous surface coverage \(\theta (t)\) to the jammed state surface coverage \(\theta (\infty)\) of larger and smaller discs, is found to obey a power law behavior \(\theta \left(\infty \right)-\theta (t)\sim{t}^{-p},\) separately. For larger values of radius ratio and relative rate constant \(k\), the approach is found to obey same power law. Total surface coverage of binary mixture \(\theta (\infty)\) for all the cases is found always greater than 54.7\%, the one component jamming limit. Also, it is found that for a given radius ratio \(r_A/r_B \), there is an optimum value of relative rate constant \(k = k_A/k_B\) for which jamming coverage \(\theta (\infty)\) is maximum. Also, our study shows that in case of adsorption of a binary mixture of circular discs of a given radius ratio \(r_A/r_B\), relative rate constant \(k\) can be fixed in order to get maximum or desired surface coverage. Microstructural properties of the coverings formed by RSA of binary mixture of circular discs are studied by analyzing radial distribution function and volume distribution of pores.
Reviewer: Reviewer (Berlin)Mayer expansion for the Asakura-Oosawa model of colloid theory.https://zbmath.org/1460.820272021-06-15T18:09:00+00:00"Jansen, Sabine"https://zbmath.org/authors/?q=ai:jansen.sabine-c"Tsagkarogiannis, Dimitrios"https://zbmath.org/authors/?q=ai:tsagkarogiannis.dimitrios-kSummary: We present a convergence criterion for the activity expansion of the Asakura-Oosawa model of penetrable hard-spheres, a popular toy model in colloid theory. The model consists of a binary mixture of large and small spheres where small spheres may freely overlap with each other but the interaction is hard-core otherwise. Our convergence criterion is formulated in terms of an effective activity for large objects that takes into account excluded volume effects.
For the entire collection see [Zbl 1445.00026].
Reviewer: Reviewer (Berlin)Cluster expansion for the Ising model in the canonical ensemble.https://zbmath.org/1460.601112021-06-15T18:09:00+00:00"Scola, Giuseppe"https://zbmath.org/authors/?q=ai:scola.giuseppeSummary: We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare the lower bound of its radius of convergence with the one computed by the virial expansion working in the grand-canonical ensemble. Using the cluster expansion we give direct proofs with quantification of the higher order error terms for the decay of correlations, central limit theorem and large deviations.
Reviewer: Reviewer (Berlin)Limit theorems for the `laziest' minimal random walk model of elephant type.https://zbmath.org/1460.600362021-06-15T18:09:00+00:00"Miyazaki, Tatsuya"https://zbmath.org/authors/?q=ai:miyazaki.tatsuya"Takei, Masato"https://zbmath.org/authors/?q=ai:takei.masatoSummary: We consider a minimal model of one-dimensional discrete-time random walk with step-reinforcement, introduced by \textit{U. Harbola} et al. [``Memory-induced anomalous dynamics in a minimal random walk model'', Phys. Rev. E 90, 022136 (2014)]: The walker can move forward (never backward), or remain at rest. For each \(n = 1, 2, \ldots\), a random time \(U_n\) between 1 and \(n\) is chosen uniformly, and if the walker moved forward [resp. remained at rest] at time \(U_n\), then at time \(n+1\) it can move forward with probability \(p\) [resp. \(q]\), or with probability \(1 - p\) [resp. \(1 - q]\) it remains at its present position. For the case \(q > 0\), several limit theorems are obtained by \textit{C. F. Coletti} et al. [J. Stat. Mech. Theory Exp. 2019, No. 8, Article ID 083206, 13 p. (2019; Zbl 1457.82147)]. In this paper we prove limit theorems for the case \(q = 0\), where the walker can exhibit all three forms of asymptotic behavior as \(p\) is varied. As a byproduct, we obtain limit theorems for the cluster size of the root in percolation on uniform random recursive trees.
Reviewer: Reviewer (Berlin)Exact steady solutions for a fifteen velocity model of gas.https://zbmath.org/1460.766782021-06-15T18:09:00+00:00"d'Ameida, Amah"https://zbmath.org/authors/?q=ai:dameida.amahSummary: Existence and boundedness of the solutions of the boundary value problem for a fifteen velocity tridimensional discrete model of gas is proved for bounded boundary conditions and exact analytic solutions are built. An application to the determination of the accommodation coefficients on the boundaries of a flow in a rectangular box is performed.
For the entire collection see [Zbl 1458.00035].
Reviewer: Reviewer (Berlin)Crossing a large-\(N\) phase transition at finite volume.https://zbmath.org/1460.810752021-06-15T18:09:00+00:00"Bea, Yago"https://zbmath.org/authors/?q=ai:bea.yago"Dias, Oscar J. C."https://zbmath.org/authors/?q=ai:dias.oscar-j-c"Giannakopoulos, Thanasis"https://zbmath.org/authors/?q=ai:giannakopoulos.thanasis"Mateos, David"https://zbmath.org/authors/?q=ai:mateos.david"Sanchez-Garitaonandia, Mikel"https://zbmath.org/authors/?q=ai:sanchez-garitaonandia.mikel"Santos, Jorge E."https://zbmath.org/authors/?q=ai:santos.jorge-e"Zilhão, Miguel"https://zbmath.org/authors/?q=ai:zilhao.miguelSummary: The existence of phase-separated states is an essential feature of infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the phase transition takes place, equilibrium homogeneous states are either metastable or suffer from a spinodal instability. In this range the stable states are inhomogeneous, phase-separated states. We use holography to investigate how this picture is modified at finite volume in a strongly coupled, four-dimensional gauge theory. We work in the planar limit, \( N \rightarrow \infty \), which ensures that we remain in the thermodynamic limit. We uncover a rich set of inhomogeneous states dual to lumpy black branes on the gravity side, as well as first- and second-order phase transitions between them. We establish their local (in)stability properties and show that fully non-linear time evolution in the bulk takes unstable states to stable ones.
Reviewer: Reviewer (Berlin)Application of bat-inspired computing algorithm and its variants in search of near-optimal Golomb rulers for WDM systems: a comparative study.https://zbmath.org/1460.780192021-06-15T18:09:00+00:00"Bansal, Shonak"https://zbmath.org/authors/?q=ai:bansal.shonak"Gupta, Neena"https://zbmath.org/authors/?q=ai:gupta.neena"Singh, Arun K."https://zbmath.org/authors/?q=ai:singh.arun-kumarSummary: The algorithms inspired by the nature are the powerful computing algorithms in solving various NP-complete industrial and engineering design problems. This chapter presents a comparative study of bat-inspired computing algorithm and its hybrid variants in order to discover near-optimal Golomb rulers (OGRs). Near-OGR sequences can be used as a channel allocation scheme to reduce one of the important nonlinear crosstalk generated via four-wave mixing (FWM) signals in an optical wavelength division multiplexing (WDM) systems. The OGRs provide unequally spaced channel allocation, a bandwidth-efficient scheme, then the uniformly spaced channel allocation methods to minimize the FWM crosstalk signals. To explore the search space, the bat-inspired computing algorithm is hybrid in its simple form with differential evolution (DE) mutation and random walk characteristics. The algorithms solve the two parameters, namely, the length of the Golomb ruler and total unequally spaced channel bandwidth occupied by OGRs in the optical WDM systems. The results reveal that the presented bat-inspired computing algorithm and its variants are better than other classical computing methods such as extended quadratic congruence (EQC) and search algorithm (SA) and nature-inspired computing algorithms, namely, genetic algorithms (GAs), and simple big bang-big crunch (BB-BC) computing algorithm to generate near-OGRs in terms of the length of ruler, the total occupied channel bandwidth, the bandwidth expansion factor (BEF), the CPU time and the computational complexity. This comparative study also concludes that the hybridization with both DE mutation and random walk schemes likely outperforms other methods for large mark values.
For the entire collection see [Zbl 1457.92003].
Reviewer: Reviewer (Berlin)Edge scaling limit of the spectral radius for random normal matrix ensembles at hard edge.https://zbmath.org/1460.600072021-06-15T18:09:00+00:00"Seo, Seong-Mi"https://zbmath.org/authors/?q=ai:seo.seong-miSummary: We investigate local statistics of eigenvalues for random normal matrices, represented as 2D determinantal Coulomb gases, in the case when the eigenvalues are forced to be in the support of the equilibrium measure associated with an external field. For radially symmetric external fields with sufficient growth at infinity, we show that the fluctuations of the spectral radius around a hard edge tend to follow an exponential distribution as the number of eigenvalues tends to infinity. As a corollary, we obtain the order statistics of the moduli of eigenvalues.
Reviewer: Reviewer (Berlin)The free-fermion eight-vertex model: couplings, bipartite dimers and \(Z\)-invariance.https://zbmath.org/1460.820032021-06-15T18:09:00+00:00"Melotti, Paul"https://zbmath.org/authors/?q=ai:melotti.paulIn this present paper, the author studies the eight-vertex model (or 8V-model for short) introduced by \textit{B. Sutherland} [``Two-dimensional hydrogen bonded crystals without the ice rule'', Math. Phys. 11, No. 11, 3183--3186 (1970; \url{doi:10.1063/1.1665111})]. Denote by \(X_{\alpha, \beta}\) the whole set of weights corresponding to parameters \(\alpha\), \(\beta\) and by \(Z_{8V} (Q,X_{\alpha, \beta})\) the partition function. Let \(Q\) be a quadrangulation of the sphere. For any parameters \(\alpha, \beta,\alpha ',\beta ':\mathcal{F}\rightarrow (0,\frac{\pi}{2})\), the author proves the equation \[\frac{Z_{8V}(Q,X_{\alpha ,\beta })}{\sqrt{c_{\alpha ,\beta }}}\frac{Z_{8V}(Q,X_{\alpha ',\beta '})}{\sqrt{c_{\alpha ',\beta '}}}=\frac{Z_{8V}(Q,X_{\alpha ,\beta '})}{\sqrt{c_{\alpha ,\beta'}}}\frac{Z_{8V}(Q,X_{\alpha ',\beta })}{\sqrt{c_{\alpha ',\beta }}},\] where \(\mathcal{F}\) is set of faces. The author presents a local formula for the inverse of Kasteleyn matrix \(K_{\alpha,\beta}\). The author then defines a probability measure \(\mathcal{P}_{8V}\) on the space of 8V-configurations equipped with the \(\sigma\)-field generated by cylinders. Under some conditions, the author proves that the probability \(\mathcal{P}_{8V}\) is a translation invariant ergodic Gibbs measure. The author computes correlators of free-fermion 8V models and relate them to Ising ones. The dimer model associated to the 8V-model is defined. The author proves that the edge correlations can be expressed as minors of the inverse Kasteleyn matrices. Finally the author constructs an ergodic Gibbs measure in the \(Z\)-invariant case.
Reviewer: Hasan Akin (Gaziantep)Non-universal Casimir forces at approach to Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions.https://zbmath.org/1460.810962021-06-15T18:09:00+00:00"Napiórkowski, M."https://zbmath.org/authors/?q=ai:napiorkowski.marek"Piasecki, J."https://zbmath.org/authors/?q=ai:piasecki.jaroslaw"Turner, J. W."https://zbmath.org/authors/?q=ai:turner.john-wmSummary: We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance \(D\). The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is \(\sim 1/D^2\) with a non-universal amplitude. The next order correction is \(\sim \ln D/D^3\). These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is \(\sim 1/D^3\) with a universal amplitude. We associate this discrepancy with the D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.
Reviewer: Reviewer (Berlin)The Green's function on the double cover of the grid and application to the uniform spanning tree trunk.https://zbmath.org/1460.820052021-06-15T18:09:00+00:00"Kenyon, Richard W."https://zbmath.org/authors/?q=ai:kenyon.richard-w"Wilson, David B."https://zbmath.org/authors/?q=ai:wilson.david-bruceIn this present paper, the authors investigate the Green's function and a closely related operator, the inverse Kasteleyn matrix, on the double cover of \(\mathbb{Z}^{2}\) branched over a face or a vertex. The authors define the Green's function as a limit of the Green's function \(G_n\) on the graphs \(\mathcal{G}_n=\mathbb{Z}^{2}\cap[-n,n]\times [-n,n]\) with Dirichlet boundary conditions. An exact expression for the Green's functions for the double branched covers of \(\mathbb{Z}^{2}\) is computed. The authors show that the spanning tree edge probabilities near the two-ended loop-erased random walk on \(\mathbb{Z}^{2}\) form a determinantal process. Then, the authors study the Kasteleyn matrix on regions with a hole (a monomer) at the origin, and how this relates to the uniform spanning tree trunk measure. They compute the inverse Kasteleyn matrix using the Green's function on the double cover of the square lattice \(\mathbb{Z}^{2}\). They illustrate with an example calculation. In the spanning tree trunk measure for the square lattice, the authors prove that the probability that the trunk contains the path \((1, 0)(3, 0)\cdots (2k +1, 0)\) is \((\sqrt{2}-1)^k\). In the last section, similar calculations for the triangular lattice are obtained.
Reviewer: Hasan Akin (Gaziantep)Relaxation dynamics of non-Brownian spheres below jamming.https://zbmath.org/1460.768822021-06-15T18:09:00+00:00"Nishikawa, Yoshihiko"https://zbmath.org/authors/?q=ai:nishikawa.yoshihiko"Ikeda, Atsushi"https://zbmath.org/authors/?q=ai:ikeda.atsushi"Berthier, Ludovic"https://zbmath.org/authors/?q=ai:berthier.ludovicSummary: We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless soft spheres below jamming in spatial dimensions \(d=2, 3, 4\), and 8, and in the mean-field Mari-Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite \(d\) logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all \(d\) in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.
Reviewer: Reviewer (Berlin)Exponential dynamical localization in expectation for the one dimensional Anderson model.https://zbmath.org/1460.810272021-06-15T18:09:00+00:00"Ge, Lingrui"https://zbmath.org/authors/?q=ai:ge.lingrui"Zhao, Xin"https://zbmath.org/authors/?q=ai:zhao.xinSummary: We prove exponential dynamical localization in expectation for the one dimensional Anderson model via positivity and uniform LDT for the Lyapunov exponent. The ideas are based on the methods developed in [\textit{S. Jitomirskaya} and \textit{X. Zhu}, Commun. Math. Phys. 370, No. 1, 311--324 (2019; Zbl 07083976)].
Reviewer: Reviewer (Berlin)Drag and thermophoresis on a sphere in a rarefied gas based on the Cercignani-Lampis model of gas-surface interaction.https://zbmath.org/1460.766822021-06-15T18:09:00+00:00"Kalempa, Denize"https://zbmath.org/authors/?q=ai:kalempa.denize"Sharipov, Felix"https://zbmath.org/authors/?q=ai:sharipov.felix-mSummary: In the present work, the influence of the gas-surface interaction law on the classical problems of viscous drag and thermophoresis on a spherical particle with high thermal conductivity immersed in a monatomic rarefied gas is investigated on the basis of the solution of a kinetic model to the linearized Boltzmann equation. The scattering kernel proposed by Cercignani and Lampis is employed to model the gas-surface interaction law via the setting of two accommodation coefficients, namely the tangential momentum accommodation coefficient and the normal energy accommodation coefficient. The viscous drag and thermophoretic forces acting on the sphere are calculated in a range of the rarefaction parameter, defined as the ratio of the sphere radius to an equivalent free path of gaseous particles, which covers the free molecular, transition and continuum regimes. In the free molecular regime the problem is solved analytically via the method of the characteristics to solve the collisionless kinetic equation, while in the transition and continuum regimes the discrete velocity method is employed to solve the kinetic equation numerically. The numerical calculations are carried out in a range of accommodation coefficients which covers most situations encountered in practice. The macroscopic characteristics of the gas flow around the sphere, namely the density and temperature deviations from thermodynamic equilibrium far from the sphere, the bulk velocity and the heat flux are calculated and their profiles as functions of the radial distance from the sphere are presented for some values of rarefaction parameter and accommodation coefficients. The results show the appearance of the negative thermophoresis in the near-continuum regime and the dependence of this phenomenon on the accommodation coefficients. To verify the reliability of the calculations, the reciprocity relation between the cross phenomena which is valid at an arbitrary distance from the sphere was found and then verified numerically within an accuracy of 0.1\%. The results for the thermophoretic force are compared to the more recent experimental data found in the literature for a copper sphere in argon gas.
Reviewer: Reviewer (Berlin)Long-time Anderson localization for the nonlinear Schrödinger equation revisited.https://zbmath.org/1460.820062021-06-15T18:09:00+00:00"Cong, Hongzi"https://zbmath.org/authors/?q=ai:cong.hongzi"Shi, Yunfeng"https://zbmath.org/authors/?q=ai:shi.yunfeng"Zhang, Zhifei"https://zbmath.org/authors/?q=ai:zhang.zhifei.1|zhang.zhifeiSummary: In this paper, we confirm the conjecture of \textit{W. M. Wang} and \textit{Z. Zhang} [ibid. 134, No. 5--6, 953--968 (2009; Zbl 1193.82022)] in a long time scale, i.e., the displacement of the wavefront for \(1D\) nonlinear random Schrödinger equation is of logarithmic order in time \(|t|\).
Reviewer: Reviewer (Berlin)Phase transition in JT gravity and \(T\overline{T}\) deformation.https://zbmath.org/1460.830602021-06-15T18:09:00+00:00"Kim, Kyung Kiu"https://zbmath.org/authors/?q=ai:kim.kyung-kiu"Baek, Jong-Hyun"https://zbmath.org/authors/?q=ai:baek.jong-hyun"Seo, Yunseok"https://zbmath.org/authors/?q=ai:seo.yunseokSummary: In this paper we study a black hole phase transition in a generalized JT gravity noticed in arXiv:2006.03494. We investigate the effect of the phase transition on the Euclidean geodesic and holographic two-point function in models with dilaton potential which interpolates two ordinary JT gravities with different cosmological constants. It is noted that there exists a closed geodesic with a new scale at low temperature phase when the potential has a locally negative region. This scale causes several peaks in the two-point function. We also comment on the phase transition of charged black holes. We then consider coupling generalized JT gravity to a matter and study its relation to a \(T\overline{T}\) deformation of CFT at the classical level. We find the deformation parameter as a function of the dilaton and provide examples showing Janus-type couplings.
Reviewer: Reviewer (Berlin)Mini-workshop: one-sided and two-sided stochastic descriptions. Abstracts from the mini-workshop held February 23--29, 2020.https://zbmath.org/1460.000332021-06-15T18:09:00+00:00"Berger, Noam (ed.)"https://zbmath.org/authors/?q=ai:berger.noam"Bethuelsen, Stein Andreas (ed.)"https://zbmath.org/authors/?q=ai:bethuelsen.stein-andreas"Conache, Diana (ed.)"https://zbmath.org/authors/?q=ai:conache.diana"Le Ny, Arnaud (ed.)"https://zbmath.org/authors/?q=ai:le-ny.arnaudSummary: We consider the set of discrete time stochastic processes which are dependent on their past, and the set of those that depend on both their past and their future. As long as we only allow dependence on a finite number of variables, those two sets are the same. However interesting questions appear when the dependence becomes infinite, and some of them were discussed during our mini-workshop.
Reviewer: Reviewer (Berlin)Quantum Hamiltonians with weak random abstract perturbation. II: Localization in the expanded spectrum.https://zbmath.org/1460.352402021-06-15T18:09:00+00:00"Borisov, Denis"https://zbmath.org/authors/?q=ai:borisov.denis-i"Täufer, Matthias"https://zbmath.org/authors/?q=ai:taufer.matthias"Veselić, Ivan"https://zbmath.org/authors/?q=ai:veselic.ivanSummary: We consider multi-dimensional Schrödinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on a random variable. The random variables, indexed by the lattice, are assumed to be independent and identically distributed according to an absolutely continuous probability density. A small global coupling constant tunes the strength of the perturbation. We treat analogous random Hamiltonians defined on multi-dimensional layers, as well. For such models we determine the location of the almost sure spectrum and its dependence on the global coupling constant. In this paper we concentrate on the case that the spectrum expands when the perturbation is switched on. Furthermore, we derive a Wegner estimate and an initial length scale estimate, which together with Combes-Thomas estimate allow to invoke the multi-scale analysis proof of localization. We specify an energy region, including the bottom of the almost sure spectrum, which exhibits spectral and dynamical localization. Due to our treatment of general, abstract perturbations our results apply at once to many interesting examples both known and new.
For Part I, see [the first author et al., Ann. Henri Poincaré 17, No. 9, 2341--2377 (2016; Zbl 1348.82039)].
Reviewer: Reviewer (Berlin)Canonical decomposition of irreducible linear differential operators with symplectic or orthogonal differential Galois groups.https://zbmath.org/1460.120022021-06-15T18:09:00+00:00"Boukraa, S."https://zbmath.org/authors/?q=ai:boukraa.salah"Hassani, S."https://zbmath.org/authors/?q=ai:hassani.saoud"Maillard, J.-M."https://zbmath.org/authors/?q=ai:maillard.jean-marie"Weil, J.-A."https://zbmath.org/authors/?q=ai:weil.jacques-arthurSummary: We first revisit an order-six linear differential operator, already introduced in our previous paper [ibid. 47, No. 9, Article ID 095203, 37 p. (2014; Zbl 1288.82007)], having a solution which is a diagonal of a rational function of three variables. This linear differential operator is such that its exterior square has a rational solution, indicating that it has a selected differential Galois group, and is actually homomorphic to its adjoint. We obtain the two corresponding intertwiners giving this homomorphism to the adjoint. We show that these intertwiners are also homomorphic to their adjoint and have a simple decomposition, already underlined in [loc. cit.], in terms of order-two self-adjoint operators. From these results, we deduce a new form of decomposition of operators for this selected order-six linear differential operator in terms of three order-two self-adjoint operators. We generalize this decomposition to decomposition in terms of three self-adjoint operators of arbitrary orders, provided the three orders have the same parity. We then generalize the previous decomposition to decompositions in terms of an arbitrary number of self-adjoint operators of the same parity order. This yields an infinite family of linear differential operators homomorphic to their adjoint, and, thus, with a selected differential Galois group. We show that the equivalence of such operators, with selected differential Galois groups, is compatible with these canonical decompositions. The rational solutions of the symmetric, or exterior, squares of these selected operators are, noticeably, seen to depend only on the rightmost self-adjoint operator in the decomposition. These results, and tools, are applied on operators of large orders. For instance, it is seen that a large set of (quite massive) operators, associated with reflexive 4-polytopes defining Calabi-Yau three-folds, obtained recently by \textit{P. Lairez} [Math. Comput. 85, No. 300, 1719--1752 (2016; Zbl 1337.68301); supplementary material \url{http://pierre.lairez.fr/supp/periods}], correspond to a particular form of the decomposition detailed in this paper. All the results of this paper can be seen as providing an algebraic characterization of linear differential operators with selected symplectic or orthogonal differential Galois groups.
Reviewer: Reviewer (Berlin)Kitaev lattice models as a Hopf algebra gauge theory.https://zbmath.org/1460.810642021-06-15T18:09:00+00:00"Meusburger, Catherine"https://zbmath.org/authors/?q=ai:meusburger.catherineIn my opinion the paper it is very deep and wide from the conceptual point of view, with very hard work of the author. The author shows many diagrams that explain very well the explained structures. The diagram of page 467 is fantastic. Anyway, I would suggest in the Introduction other diagram with the definitions and relations among the different concepts indicated.
Reviewer: Luis Vazquez (Madrid)Mesoscopic description of the adiabatic piston: kinetic equations and \(\mathcal{H}\)-theorem.https://zbmath.org/1460.820042021-06-15T18:09:00+00:00"Khalil, Nagi"https://zbmath.org/authors/?q=ai:khalil.nagiSummary: The adiabatic piston problem is solved at the mesoscale using a kinetic theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston). A closed system of equations for the distribution functions of the gases conditioned to a position of the piston and the distribution function of the piston is derived, under the assumption of a generalized molecular chaos. It is shown that the resulting kinetic description has the canonical equilibrium as a steady-state solution. Moreover, the Boltzmann entropy, which includes the motion of the piston, verifies the \(\mathcal{H}\)-theorem. The kinetic description is not limited to the thermodynamic limit nor to a small ratio between the masses of the particle and the piston, and collisions among particles are explicitly considered.
Reviewer: Reviewer (Berlin)Crossover phenomena in the critical behavior for long-range models with power-law couplings.https://zbmath.org/1460.601102021-06-15T18:09:00+00:00"Sakai, Akira"https://zbmath.org/authors/?q=ai:sakai.akiraSummary: This is a short review of the two papers \textit{L.-C. Chen} and \textit{A. Sakai} [Ann. Probab. 43, No. 2, 639--681 (2015; Zbl 1342.60162), ``The marginal case for \(d\ge d_c\)'', to appear in Common. Math. Phys.] on the \(x\)-space asymptotics of the critical two-point function \(G_{p_c}(x)\) for the long-range models of self-avoiding walk, percolation and the Ising model on \(\mathbb{Z}^d\), defined by the translation-invariant power-law step-distribution/coupling \(D(x)\propto|x|^{-d-\alpha}\) for some \(\alpha>0\). Let \(S_1(x)\) be the random-walk Green function generated by \(D\). We have shown that \begin{itemize} \item \(S_1(x)\) changes its asymptotic behavior from Newton \((\alpha>2)\) to Riesz \((\alpha<2)\), with log correction at \(\alpha=2\); \item \(G_{p_c}(x)\sim\frac{A}{p_c}S_1(x)\text{ as }|x|\to\infty\) in dimensions higher than (or equal to, if \(\alpha=2)\) the upper critical dimension \(d_c\) (with sufficiently large spread-out parameter \(L)\). The model-dependent \(A\) and \(d_c\) exhibit crossover at \(\alpha=2\). \end{itemize} The keys to the proof are (i) detailed analysis on the underlying random walk to derive sharp asymptotics of \(S_1\), (ii) bounds on convolutions of power functions (with log corrections, if \(\alpha=2)\) to optimally control the lace-expansion coefficients \(\pi^{(n)}_p\), and (iii) probabilistic interpretation (valid only when \(\alpha\le 2)\) of the convolution of \(D\) and a function \(\Pi_p\) of the alternating series \(\sum^\infty_{n=0}(-1)^n\pi^{(n)}_p\). We outline the proof, emphasizing the above key elements for percolation in particular.
Reviewer: Reviewer (Berlin)A proof of the Gaudin Bethe ansatz conjecture.https://zbmath.org/1460.370572021-06-15T18:09:00+00:00"Rybnikov, Leonid"https://zbmath.org/authors/?q=ai:rybnikov.leonid-gSummary: The Gaudin algebra is the commutative subalgebra in \(U({\mathfrak g})^{\otimes N}\) generated by higher integrals of the quantum Gaudin magnet chain attached to a semisimple Lie algebra \({\mathfrak g}\). This algebra depends on a collection of pairwise distinct complex numbers \(z_1,\ldots ,z_N\). We prove that this subalgebra has a cyclic vector in the space of singular vectors of the tensor product of any finite-dimensional irreducible \({\mathfrak g}\)-modules, for all values of the parameters \(z_1,\ldots ,z_N\). We deduce from this result the Bethe Ansatz conjecture in the Feigin-Frenkel form that states that the joint eigenvalues of the higher Gaudin Hamiltonians on the tensor product of irreducible finite-dimensional \({\mathfrak g}\)-modules are in 1-1 correspondence with monodromy-free \(^LG\)-opers on the projective line with regular singularities at the points \(z_1,\ldots ,z_N,\infty \), and the prescribed residues at the singular points.
Reviewer: Reviewer (Berlin)Exponential decay of correlations in the \(2D\) random field Ising model.https://zbmath.org/1460.601052021-06-15T18:09:00+00:00"Aizenman, Michael"https://zbmath.org/authors/?q=ai:aizenman.michael"Harel, Matan"https://zbmath.org/authors/?q=ai:harel.matan"Peled, Ron"https://zbmath.org/authors/?q=ai:peled.ronSummary: An extension of the Ising spin configurations to continuous functions is used for an exact representation of the random field Ising model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent analyses of the decay of correlations to positive temperatures, at homogeneous but arbitrarily weak disorder.
Reviewer: Reviewer (Berlin)Random band matrices in the delocalized phase. III: Averaging fluctuations.https://zbmath.org/1460.600092021-06-15T18:09:00+00:00"Yang, Fan"https://zbmath.org/authors/?q=ai:yang.fan.1|yang.fan.4|yang.fan.2|yang.fan.6"Yin, Jun"https://zbmath.org/authors/?q=ai:yin.jun.1|yin.junSummary: We consider a general class of symmetric or Hermitian random band matrices \(H=(h_{xy})_{x,y \in\lbrack\lbrack 1,N\rbrack\rbrack^d}\) in any dimension \(d\ge 1\), where the entries are independent, centered random variables with variances \(s_{xy}=\mathbb{E}|h_{xy}|^2\). We assume that \(s_{xy}\) vanishes if \(|x-y|\) exceeds the band width \(W\), and we are interested in the mesoscopic scale with \(1\ll W\ll N\). Define the generalized resolvent of \(H\) as \(G(H,Z):=(H-Z)^{-1}\), where \(Z\) is a deterministic diagonal matrix with entries \(Z_{xx}\in\mathbb{C}_+\) for all \(x\). Then we establish a precise high-probability bound on certain averages of polynomials of the resolvent entries. As an application of this fluctuation averaging result, we give a self-contained proof for the delocalization of random band matrices in dimensions \(d\ge 2\). More precisely, for any fixed \(d\ge 2\), we prove that the bulk eigenvectors of \(H\) are delocalized in certain averaged sense if \(N\le W^{1+\frac{d}{2}}\). This improves the corresponding results in [\textit{Y. He} and \textit{M. Marcozzi}, J. Stat. Phys. 177, No. 4, 666--716 (2019; Zbl 1448.60023)] that imposed the assumption \(N\ll W^{1+\frac{d}{d+1}}\), and the results in [\textit{L. Erdős} and \textit{A. Knowles}, Ann. Henri Poincaré 12, No. 7, 1227--1319 (2011; Zbl 1247.15033); Commun. Math. Phys. 303, No. 2, 509--554 (2011; Zbl 1226.15024)] that imposed the assumption \(N\ll W^{1+\frac{d}{6}}\). For 1D random band matrices, our fluctuation averaging result was used in Part II and Part I [\textit{P. Bourgade} et al., J. Stat. Phys. 174, No. 6, 1189--1221 (2019; Zbl 1447.60018); Commun. Pure Appl. Math. 73, No. 7, 1526--1596 (2020; Zbl 1446.60005)] to prove the delocalization conjecture and bulk universality for random band matrices with \(N\ll W^{4/3}\).
Reviewer: Reviewer (Berlin)The trimmed Anderson model at strong disorder: localisation and its breakup.https://zbmath.org/1460.470202021-06-15T18:09:00+00:00"Elgart, Alexander"https://zbmath.org/authors/?q=ai:elgart.alexander"Sodin, Sasha"https://zbmath.org/authors/?q=ai:sodin.sashaSummary: We explore the properties of discrete random Schrödinger operators in which the random part of the potential is supported on a sub-lattice (the trimmed Anderson model). In this setting, Anderson localisation at strong disorder does not always occur; alternatives include anomalous localisation and, possibly, delocalisation. We establish two new sufficient conditions for localisation at strong disorder as well as a sufficient condition for its absence, and provide examples for both situations. The main technical ingredient is a pair of Wegner-type estimates which are applicable when the covering condition does not hold. Finally, we discuss a coupling between random operators at weak and strong disorder. This coupling is used in a heuristic discussion of the properties of the trimmed Anderson model for sparse sub-lattices, and also in a new rigorous proof of a result of \textit{M. Aizenman} [Rev. Math. Phys. 6, No. 5a, 1163--1182 (1994; Zbl 0843.47039)] pertaining to weak disorder localisation for the usual Anderson model.
Reviewer: Reviewer (Berlin)Thermodynamic criticality of d-dimensional charged AdS black holes surrounded by quintessence with a cloud of strings background.https://zbmath.org/1460.830392021-06-15T18:09:00+00:00"Chabab, M."https://zbmath.org/authors/?q=ai:chabab.mohamed"Iraoui, Samir"https://zbmath.org/authors/?q=ai:iraoui.samirSummary: We focus on the study of exact solutions corresponding to charged AdS black holes surrounded by quintessence with a cloud of strings present in higher dimensional spacetime. We then investigate its corresponding thermodynamic criticality in the extended phase space and show that the spacetime dimension has no effect on the existence of small/large phase transition for such black holes. The heat capacity is evaluated and the geothermodynamics of \textit{H. Quevedo} [J. Math. Phys. 48, No. 1, 013506, 14 p. (2007; Zbl 1121.80011)] analyzed for different spacetime dimensions with the cloud of strings and quintessence parameters. We calculate the critical exponents describing the behavior of relevant thermodynamic quantities near the critical point. Finally, we also discuss the uncharged case, show how it is sensitive to the quintessence and strings cloud parameters, and when the thermodynamic behavior of the uncharged black holes is similar to Van der Waals fluid.
Reviewer: Reviewer (Berlin)