# Communications in Mathematical Physics (COMMUN MATH PHYS )

## Description

Subjects: Quantum physics and differential geometry; Flow equations, nonlinear PDE of mathematical physics; String theory, nonperturbative field theory and related topics; Field theory, mechanics and condensed matter; nonequilibrium and dynamical systems; General relativity, mathematical aspects of M/string theory, applications of differential geometry to physics; Field theory, constructive methods; statistical mechanics; Algebraic quantum field theory and related issues of operator algebras; Turbulence, disordered systems, and rigorous studies of field theory; Nonequilibrium statistical mechanics; Algebraic geometry in physics, mathematical aspects of string theory; Quantum information theory; Quantum chaos; Schrödinger operators and atomic physics; Statistical physics; Classical and quantum integrable systems, conformal field theory and related topics; Quantum dynamics and nonequilibrium statistical mechanics.

- Impact factor1.97Hide impact factor historyImpact factorYear
- 5-year impact2.01
- Cited half-life0.00
- Immediacy index0.63
- Eigenfactor0.04
- Article influence1.77
- WebsiteCommunications in Mathematical Physics website
- Other titlesCommunications in mathematical physics
- ISSN0010-3616
- OCLC1564493
- Material typePeriodical, Internet resource
- Document typeJournal / Magazine / Newspaper, Internet Resource

## Publisher details

- Pre-print
- Author can archive a pre-print version

- Post-print
- Author can archive a post-print version

- Conditions
- Author's pre-print on pre-print servers such as arXiv.org
- Author's post-print on author's personal website immediately
- Author's post-print on any open access repository after 12 months after publication
- Publisher's version/PDF cannot be used
- Published source must be acknowledged
- Must link to publisher version
- Set phrase to accompany link to published version (see policy)
- Articles in some journals can be made Open Access on payment of additional charge

- Classification green

## Publications in this journal

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**ABSTRACT:**This paper is devoted to a new integrable two-component Camassa–Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable system that admits weak kink and kink–peakon interactional solutions. In addition, the new system includes both standard (quadratic) and cubic Camassa–Holm equations as two special cases. In the paper, we first establish the local well-posedness for the Cauchy problem of the system, and then derive a precise blow-up scenario and a new blow-up result for strong solutions to the system with both quadratic and cubic nonlinearity. Furthermore, its peakon and weak kink solutions are discussed as well.Communications in Mathematical Physics 12/2014; - Communications in Mathematical Physics 12/2014; 332(2).
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**ABSTRACT:**The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being dynamically reflectionless, thus providing a short proof of an important result of Breuer et al. (Commun Math Phys 295:531–550, 2010). The motivation for the new characterization comes from recent studies of the non-equilibrium statistical mechanics of the electronic black box model and we elaborate on this connection.Communications in Mathematical Physics 12/2014; 332(2). - Communications in Mathematical Physics 11/2014; 332(1).
- Communications in Mathematical Physics 11/2014; 332(1).
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**ABSTRACT:**In this paper we introduce the “interpolation–degeneration” strategy to study Kähler–Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By “interpolation” we show the angles in (0, 2π] that admit a conical Kähler–Einstein metric form a connected interval, and by “degeneration” we determine the boundary of the interval in some important cases. As a first application, we show that there exists a Kähler–Einstein metric on \({\mathbb{P}^2}\) with cone singularity along a smooth conic (degree 2) curve if and only if the angle is in (π/2, 2π]. When the angle is 2π/3 this proves the existence of a Sasaki–Einstein metric on the link of a three dimensional A 2 singularity, and thus answers a question posed by Gauntlett–Martelli–Sparks–Yau. As a second application we prove a version of Donaldson’s conjecture about conical Kähler–Einstein metrics in the toric case using Song–Wang’s recent existence result of toric invariant conical Kähler–Einstein metrics.Communications in Mathematical Physics 11/2014; 331(3). -
##### Article: Higgs Bundles and (A, B, A)-Branes

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**ABSTRACT:**Through the action of anti-holomorphic involutions on a compact Riemann surface Σ we construct families of (A, B, A)-branes \({\mathcal{L}_{G_{c}}}\) in the moduli spaces \({\mathcal{M}_{G_{c}}}\) of G c -Higgs bundles on Σ. We study the geometry of these (A, B, A)-branes in terms of spectral data and show they have the structure of real integrable systems.Communications in Mathematical Physics 11/2014; 331(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate a multiple mirror phenomenon arising from Berglund–Hübsch–Krawitz mirror symmetry. We prove that the different mirror Calabi–Yau orbifolds which arise in this context are in fact birational to one another.Communications in Mathematical Physics 10/2014; 331(2). -
##### Article: Generalized Kähler Geometry

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**ABSTRACT:**Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.Communications in Mathematical Physics 10/2014; 331(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**A quantum system \({\mathcal S}\) undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a quantum filtering equation (or quantum stochastic master equation) and its solution is called a quantum filter (or quantum trajectory). This solution describes the evolution of the state of \({\mathcal S}\) . In the context of quantum non demolition measurement, we investigate the large time behavior of this solution. It is rigorously shown that, for large time, this solution behaves as if a direct Von Neumann measurement has been performed at time 0. In particular the solution converges to a random pure state which can be directly linked to the wave packet reduction postulate. Using the theory of Girsanov transformation, we obtain the explicit rate of convergence towards this random state. The problem of state estimation (used in experiment) is also investigated.Communications in Mathematical Physics 10/2014; 331(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel. Along with a corresponding achievability statement for rates below the capacity, such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication. Here, we show that such a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former). These results follow by bounding the success probability in terms of a “sandwiched” Rényi relative entropy, by showing that this quantity is subadditive for all entanglement-breaking and Hadamard channels, and by relating this quantity to the Holevo capacity. Prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results.Communications in Mathematical Physics 10/2014; 331(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto–Hydrodynamic equations. First we prove that these solutions satisfy some weak-strong uniqueness property. Then we investigate the validity of energy identities. In particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation. In the case of the Hall–Magneto–Hydrodynamic equations we also give a sufficient condition to guarantee the magneto-helicity identity. Our conditions correspond to the same heuristic scaling as the one introduced by Onsager in hydrodynamic theory. Finally we examine the sign, locally, of the anomalous dissipations of weak solutions obtained by some natural approximation processes.Communications in Mathematical Physics 09/2014; 330(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Communications in Mathematical Physics 09/2014; 330(3). -
##### Article: W 1, p(·)-Regularity for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

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**ABSTRACT:**We establish global W 1, p(·)-estimates for second order elliptic equations in divergence form under the natural assumption that p(·) is log-Hölder continuous. To this end, we assume that the coefficients are measurable in one variable and have small BMO semi-norms in the other variables and the boundary of the domain is Reifenberg flat. Our work is an optimal and natural extension of W 1,p -regularity for such equations with merely measurable coefficients beyond Lipschitz domains.Communications in Mathematical Physics 08/2014; 329(3). -
##### Article: Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the (k + 1)-Equals Ideal

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**ABSTRACT:**We show that for Jack parameter α = −(k + 1)/(r − 1), certain Jack polynomials studied by Feigin–Jimbo–Miwa–Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read–Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S n -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein–Gelfand–Gelfand type; we prove this for the ideal of the (k + 1)-equals arrangement in the case when the number of coordinates n is at most 2k + 1. In general, our conjecture predicts the graded S n -equivariant Betti numbers of the ideal of the (k + 1)-equals arrangement with no restriction on the number of ambient dimensions.Communications in Mathematical Physics 08/2014; 330(1). -
##### Article: An Isospectral Problem for Global Conservative Multi-Peakon Solutions of the Camassa–Holm Equation

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**ABSTRACT:**We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa–Holm equation is integrable by the inverse spectral transform in the multi-peakon case.Communications in Mathematical Physics 08/2014; 329(3). -
##### Article: On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons

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**ABSTRACT:**In this paper we prove that the solutions of the isotropic, spatially homogeneous Nordheim equation for bosons with bounded initial data blow up in finite time in the L ∞ norm if the values of the energy and particle density are in the range of values where the corresponding equilibria contain a Dirac mass. We also prove that, in the weak solutions, whose initial data are measures with values of particle and energy densities satisfying the previous condition, a Dirac measure at the origin forms in finite time.Communications in Mathematical Physics 08/2014; 330(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the long time behavior of solutions of the d-dimensional linear Boltzmann equation that arises in the weak coupling limit for the Schrödinger equation with a time-dependent random potential. We show that the intermediate mesoscopic time limit satisfies a Fokker–Planck type equation with the wave vector performing a Brownian motion on the (d − 1)-dimensional sphere of constant energy, as in the case of a time-independent Schrödinger equation. However, the long time limit of the solution with an isotropic initial data satisfies an equation corresponding to the energy being the square root of a Bessel process of dimension d/2.Communications in Mathematical Physics 08/2014; 329(3).

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