# Communications in Mathematical Physics (COMMUN MATH PHYS)

Publisher: Springer Verlag

## Journal 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 Factor Rankings

2016 Impact Factor Available summer 2017 2.086 1.901 1.971 1.941 2 2.067 2.075 2.07 2.077 2.007 1.741 1.65 1.851 1.729 1.721 1.537 1.737 1.651 1.718 1.936 2.282 2.055 1.942

## Impact factor over time

Impact factor
.
Year

5-year impact 2.08 >10.0 0.92 0.04 2.01 Communications in Mathematical Physics website Communications in mathematical physics 0010-3616 1564493 Periodical, Internet resource Journal / Magazine / Newspaper, Internet Resource

## Publisher details

• Pre-print
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• Author can archive a post-print version
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• Author's pre-print on pre-print servers such as arXiv.org
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• Articles in some journals can be made Open Access on payment of additional charge
• Classification
green

## Publications in this journal

• ##### Article: The Steep Nekhoroshev’s Theorem
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ABSTRACT: Revising Nekhoroshev’s geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev’s theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be (Formula presented.)) ((Formula presented.)’s being Nekhoroshev’s steepness indices and (Formula presented.) the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
No preview · Article · Jan 2016 · Communications in Mathematical Physics
• ##### Article: Parabolic Presentations of the Super Yangian $${Y(\mathfrak{gl}_{M|N})}$$ Y ( gl M | N ) Associated with Arbitrary 01-Sequences
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ABSTRACT: Let μ be an arbitrary composition of M + N and let $${\mathfrak{s}}$$ be an arbitrary $${0^{M}1^{N}}$$- sequence. A new presentation, depending on $${\mu \rm and \mathfrak{s}}$$, of the super Yangian Y M|N associated to the general linear Lie superalgebra $${\mathfrak{gl}_{M|N}}$$ is obtained.
No preview · Article · Jan 2016 · Communications in Mathematical Physics
• ##### Article: On the Spectral Problem $${\mathcal{L} u=\lambda u'}$$ L u = λ u ′ and Applications
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ABSTRACT: We develop a general instability index theory for an eigenvalue problem of the type $${\mathcal{L} u=\lambda u'}$$, for a class of self-adjoint operators $${\mathcal{L}}$$ on the line R 1. More precisely, we construct an Evans-like function to show (a real eigenvalue) instability in terms of a Vakhitov–Kolokolov type condition on the wave. If this condition fails, we show by means of Lyapunov–Schmidt reduction arguments and the Kapitula–Kevrekidis–Sandstede index theory that spectral stability holds. Thus, we have a complete spectral picture, under fairly general assumptions on $${\mathcal{L}}$$. We apply the theory to a wide variety of examples. For the generalized Bullough–Dodd–Tzitzeica type models, we give instability results for travelling waves. For the generalized short pulse/Ostrovsky/Vakhnenko model, we construct (almost) explicit peakon solutions, which are found to be unstable, for all values of the parameters.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: Localization in the Ground State of an Interacting Quasi-Periodic Fermionic Chain
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ABSTRACT: We consider a one dimensional many body fermionic system with a large incommensurate external potential and a weak short range interaction. We prove, for chemical potentials in a gap of the non interacting spectrum, that the zero temperature thermodynamical correlations are exponentially decaying for large distances, with a decay rate much larger than the gap; this indicates the persistence of localization in the interacting ground state. The analysis is based on the renormalization group, and convergence of the renormalized expansion is achieved using fermionic cancellations and controlling the small divisor problem assuming a Diophantine condition for the frequency.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: Mixed Type Solutions of the $${SU(3)}$$ S U ( 3 ) Models on a Torus
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ABSTRACT: In this paper, we study mixed-type solutions of $${SU(3)}$$ Chern–Simons system (see (1.4) below) on a two dimensional flat torus. Nolasco and Tarantello (Commun Math Phys 213:599–639, 2000), among other things, Nolasco and Tarantello obtained solutions of (1.4) as minimizers of several functionals closely related to (1.4), and showed that if $${N_1+N_2=1}$$, then one of those minimizers turns out to be a mixed-type solution, that is, one component tends to $${\ln\frac{1}{2}}$$ pointwise a.e. and the other component converges to a solution of a mean field equation. We call these kinds of solutions mixed-type (I) solutions. In this paper, we prove two main results: (i) the asymptotic analysis of mixed-type (I) solutions with arbitrary configuration of vortex points, and (ii) the existence of mixed-type (I) solutions under a non-degenerate condition. This non-degenerate condition also ensures some uniqueness result. In particular, our results imply that when $${N_1+N_2=1}$$, there are only two mixed-type (I) solutions of (1.4).
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: The Operator Product Expansion Converges in Massless $${\varphi_{4}^{4}}$$ φ 4 4 -Theory
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ABSTRACT: It has been shown recently (Hollands and Kopper, Commun. Math. Phys. 313:257–290, 2012) that the mathematical status of the operator product expansion (OPE) is better than had previously been expected: namely considering massive Euclidean $${\varphi_4^4}$$-theory in the perturbative loop expansion, the OPE converges at any loop order when considering (as is usually done) composite operator insertions into correlation functions. In the present paper we prove the same result for the massless theory. While the short-distance properties of massive and massless theories may be expected to be similar on physical grounds, the proof in the massless case requires entirely new techniques, because we have to control with sufficient precision the exceptional momentum singularities of the massless correlation functions. The bounds we state are organised in terms of weight factors associated to certain tree graphs (“tree dominance”). Our proof is again based on the flow equations of the renormalisation group, which we combine with such graph structures.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: Weakly Asymmetric Non-Simple Exclusion Process and the Kardar–Parisi–Zhang Equation
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ABSTRACT: We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. We identify the main non-linearity and eliminate it by imposing a gradient type condition. For hopping range at most 3, using the generalized transformation, we prove the convergence of the exclusion process toward the Kardar-Parisi-Zhang (KPZ) equation. This is the first universality result concerning interacting particle systems in the context of KPZ universality class. While this class of exclusion processes are not explicitly solvable, we obtain the exact one-point limiting distribution for the step initial condition by using the previous result of Amir et al. (2011) and our convergence result.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: On the Gromov–Witten/Donaldson–Thomas Correspondence and Ruan’s Conjecture for Calabi–Yau 3-Orbifolds
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ABSTRACT: For any toric Calabi-Yau 3-orbifold with transverse A-singularities, we prove the Gromov-Witten/Donaldson-Thomas correspondence and Ruan's crepant resolution conjecture in all genera.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: A Finite Dimensional Integrable System Arising in the Study of Shock Clustering
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ABSTRACT: In this work, we consider a finite dimensional Hamiltonian system that contains as a special case an exact discretization of the Lax equation for shock clustering. We characterize the generic coadjoint orbits of the underlying Lie group and establish the Liouville integrability of the system on such orbits. We also solve the Hamiltonian equation explicitly via Riemann–Hilbert factorization problems.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: Nondegeneracy of Nodal Solutions to the Critical Yamabe Problem
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ABSTRACT: We prove the existence of a sequence of nondegenerate, in the sense of Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem $$-\Delta Q= |Q|^{\frac{2}{n-2}} Q, \quad Q \in {\mathcal D}^{1,2}(\mathbb{R}^n).$$This is the first example in the literature of nondegeneracy for nodal nonradial solutions of nonlinear elliptic equations and it is also the only nontrivial example for which the result of Duyckaerts–Kenig–Merle [9] applies.
No preview · Article · Dec 2015 · Communications in Mathematical Physics
• ##### Article: The Structure of the Kac–Wang–Yan Algebra
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ABSTRACT: The Lie algebra (Formula presented.) of regular differential operators on the circle has a universal central extension (Formula presented.). The invariant subalgebra (Formula presented.) under an involution preserving the principal gradation was introduced by Kac, Wang, and Yan. The vacuum (Formula presented.)-module with central charge (Formula presented.), and its irreducible quotient (Formula presented.), possess vertex algebra structures, and (Formula presented.) has a nontrivial structure if and only if (Formula presented.). We show that for each integer (Formula presented.), (Formula presented.) and (Formula presented.) are (Formula presented.)-algebras of types (Formula presented.) and (Formula presented.), respectively. These results are formal consequences of Weyl’s first and second fundamental theorems of invariant theory for the orthogonal group (Formula presented.) and the symplectic group (Formula presented.), respectively. Based on Sergeev’s theorems on the invariant theory of (Formula presented.) we conjecture that (Formula presented.) is of type (Formula presented.), and we prove this for (Formula presented.). As an application, we show that invariant subalgebras of (Formula presented.)-systems and free fermion algebras under arbitrary reductive group actions are strongly finitely generated.
No preview · Article · Nov 2015 · Communications in Mathematical Physics
• ##### Article: Hyperkähler Implosion and Nahm’s Equations
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ABSTRACT: We use Nahm data to describe candidates for the universal hyperkähler implosion with respect to a compact Lie group.
No preview · Article · Nov 2015 · Communications in Mathematical Physics
• ##### Article: The Cubic Dirac Equation: Small Initial Data in $${{H^{\frac{1}{2}}} (\mathbb{R}^{2}}$$ H 1 2 ( R 2 )
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ABSTRACT: Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $${{H^{\frac{1}{2}}} (\mathbb{R}^{2}}$$) is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein–Gordon equation in dimension n = 2, which is captured by constructing an adapted systems of coordinate frames.
No preview · Article · Nov 2015 · Communications in Mathematical Physics
• ##### Article: Singularity of the Velocity Distribution Function in Molecular Velocity Space
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ABSTRACT: We study the boundary singularity of the solutions to the Boltzmann equation in the kinetic theory. The solution has a jump discontinuity in the microscopic velocity $${\zeta}$$ on the boundary and a secondary singularity of logarithmic type around the velocity tangential to the boundary, $${\zeta_{n} \sim 0_{-}}$$, where $${\zeta_{n}}$$ is the component of molecular velocity normal to the boundary, pointing to the gas. We demonstrate this secondary singularity by obtaining an asymptotic formula for the derivative of the solution on the boundary with respect to $${\zeta_{n}}$$ that diverges logarithmically when $${\zeta_{n} \sim 0_{-}}$$. Our study is for the thermal transpiration problem between two plates for the hard sphere gases with sufficiently large Knudsen number and with the diffuse reflection boundary condition. The solution is constructed and its singularity is studied by an iteration procedure.
No preview · Article · Nov 2015 · Communications in Mathematical Physics
• ##### Article: Painlevé Representation of Tracy–Widom $${_\beta}$$ β Distribution for $${\beta}$$ β = 6
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ABSTRACT: In Rumanov (J Math Phys 56:013508, 2015), we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of (Formula presented.). Using this general result, the case (Formula presented.) is further considered here. This is the smallest even (Formula presented.), when the corresponding Lax pair and its relation to Painlevé II (PII) have not been known before, unlike cases (Formula presented.) and 4. It turns out that again everything can be expressed in terms of the Hastings–McLeod solution of PII. In particular, a second order nonlinear ordinary differential equation (ODE) for the logarithmic derivative of Tracy–Widom distribution for (Formula presented.) involving the PII function in the coefficients is found, which allows one to compute asymptotics for the distribution function. The ODE is a consequence of a linear system of three ODEs for which the local singularity analysis yields series solutions with exponents in the set 4/3, 1/3 and −2/3.
No preview · Article · Nov 2015 · Communications in Mathematical Physics