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 factor1.97Show impact factor historyImpact factorYear
 5year impact2.01
 Cited halflife0.00
 Immediacy index0.63
 Eigenfactor0.04
 Article influence1.77
 WebsiteCommunications in Mathematical Physics website
 Other titlesCommunications in mathematical physics
 ISSN00103616
 OCLC1564493
 Material typePeriodical, Internet resource
 Document typeJournal / Magazine / Newspaper, Internet Resource
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Publications in this journal
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ABSTRACT: Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787–902, 1991) and Hitchin (Commun. Math. Phys. 131:347–380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle ${E \to Y}$ along a non–proper map ${Y \to S}$ . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367–374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.Communications in Mathematical Physics 04/2014; 327(1).  [show abstract] [hide abstract]
ABSTRACT: Given a Kähler manifold M endowed with a Hamiltonian Killing vector field Z, we construct a conical Kähler manifold such that M is recovered as a Kähler quotient of . Similarly, given a hyperKähler manifold ( M, g, J 1, J 2, J 3) endowed with a Killing vector field Z, Hamiltonian with respect to the Kähler form of J 1 and satisfying , we construct a hyperKähler cone such that M is a certain hyperKähler quotient of . In this way, we recover a theorem by Haydys. Our work is motivated by the problem of relating the supergravity cmap to the rigid cmap. We show that any hyperKähler manifold in the image of the cmap admits a Killing vector field with the above properties. Therefore, it gives rise to a hyperKähler cone, which in turn defines a quaternionic Kähler manifold. Our results for the signature of the metric and the sign of the scalar curvature are consistent with what we know about the supergravity cmap.Communications in Mathematical Physics 12/2013; 324(2).  [show abstract] [hide abstract]
ABSTRACT: We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes ${\beta \in \{1, 2, 4\}}$ of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for β = 1, 4, thus proving a number of conjectures of Khoruzhenko et al. (in Phys Rev B 80:(12)125301, 2009). We derive differential equations that characterize the cumulant generating functions for all ${\beta \in \{1, 2, 4 \} }$ . Furthermore, when β = 2 we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painlevé III′ transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit ${n \to \infty}$ . Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders.Communications in Mathematical Physics 12/2013; 324(2).  [show abstract] [hide abstract]
ABSTRACT: We study the BPS spectra of N=2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, ArgyresDouglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.Communications in Mathematical Physics 11/2013; 323(3). 
Article: Dynamic and Steady States for MultiDimensional KellerSegel Model with Diffusion Exponent m > 0
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ABSTRACT: This paper investigates infinitetime spreading and finitetime blowup for the KellerSegel system. For 0 < m ≤ 2 − 2 / d, the L p space for both dynamic and steady solutions are detected with ${p:=\frac{d(2m)}{2} }$ . Firstly, the global existence of the weak solution is proved for small initial data in L p . Moreover, when m > 1 − 2 / d, the weak solution preserves mass and satisfies the hypercontractive estimates in L q for any p < q < ∞. Furthermore, for slow diffusion 1 < m ≤ 2 − 2/d, this weak solution is also a weak entropy solution which blows up at finite time provided by the initial negative free energy. For m > 2 − 2/d, the hypercontractive estimates are also obtained. Finally, we focus on the L p norm of the steady solutions, it is shown that the energy critical exponent m = 2d/(d + 2) is the critical exponent separating finite L p norm and infinite L p norm for the steady state solutions.Communications in Mathematical Physics 11/2013; 323(3).  [show abstract] [hide abstract]
ABSTRACT: This paper is concerned with the VlasovPoissonBoltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular noncutoff with $3<\gamma<2s$ and $1/2\leq s<1$, where $\gamma$, $s$ are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in \cite{DYZh, DYZs} for the cutoff kernel with $2\leq \gamma\leq 1$ to the case $3<\gamma<2$ as long as the angular singularity exists instead and is strong enough, i.e., $s$ is close to 1. The proof is based on the timeweighted energy method building also upon the recent studies of the non cutoff Boltzmann equation in \cite{GR} and the VlasovPoissonLandau system in \cite{Guo5}.Communications in Mathematical Physics 10/2013; 324(1). 
Article: Stability of Peakons for an Integrable Modified CamassaHolm Equation with Cubic Nonlinearity
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ABSTRACT: Considered herein is the dynamical stability of the single peaked soliton and periodic peaked soliton for an integrable modified CamassaHolm equation with cubic nonlinearity. The equation is known to admit a single peaked soliton and multipeakon solutions, and is shown here to possess a periodic peaked soliton. By constructing certain Lyapunov functionals, it is demonstrated that the shapes of these waves are stable under small perturbations in the energy space.Communications in Mathematical Physics 09/2013; 322(3).  [show abstract] [hide abstract]
ABSTRACT: We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter ${0 < \kappa \ll 1}$ , and much smaller plaquette coupling ${\beta, 0 < \beta \ll \kappa}$ . In this regime, it is known that the lowlying energymomentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses ${m\approx3\ln\kappa}$ and ${m_m\approx2\ln\kappa}$ , respectively. We prove the existence of two (labelled by ±) twobaryon bound states for each of the total isospin sectors I = 0,1 and we obtain, in each case, the exact binding energies ${\epsilon_{I\,\pm} }$ (of order ${\kappa^2}$ ) which extend to jointly analytic function in ${\kappa}$ and β. We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for ${\alpha_0=\frac 14, \alpha_1=\frac 1{12}, \alpha_2=\frac12, \alpha_3=\frac 34}$ and small ${\delta >0 }$ , that the bound state masses ${2m\epsilon_{I\,\pm}}$ are the only points in the mass spectrum in ${(0,2m\epsilon_{I\,\pm}+\delta \alpha_I\kappa^2)}$ , for I = 0,1, and in ${(0,2m(1+\delta)\alpha_I\kappa^2)}$ , for I = 2,3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two and fourpoint correlations with spectral representations and a lattice BetheSalpeter equation. For I = 0,1, a quark, antiquark spacerange one potential of order ${\kappa^2}$ is found to be the dominant contribution to the twobaryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the twopoint correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.Communications in Mathematical Physics 08/2013; 321(1):249282.  [show abstract] [hide abstract]
ABSTRACT: Magnetic AharonovBohm effect (AB effect) was studied in hundreds of papers starting with the seminal paper of Aharonov and Bohm (Phys Rev 115:485, 1959). We give a new proof of the magnetic AharonovBohm effect without using the scattering theory and the theory of inverse boundary value problems. We consider separately the cases of one and several obstacles. The electric AB effect was studied much less. We give the first proof of the electric AB effect in domains with moving boundaries. When the boundary does not move with the time the electric AB effect is absent.Communications in Mathematical Physics 08/2013; 321(3).  [show abstract] [hide abstract]
ABSTRACT: We study the initial value problem for the conformal field equations with data given on a cone ${\cal N}_p$ with vertex $p$ so that in a suitable conformal extension the point $p$ will represent past timelike infinity $i^$, the set ${\cal N}_p \setminus \{p\}$ will represent past null infinity ${\cal J}^$, and the freely prescribed (suitably smooth) data will acquire the meaning of the incoming {\it radiation field} for the prospective vacuum spacetime. It is shown that: (i) On some coordinate neighbourhood of $p$ there exist smooth fields which satisfy the conformal vacuum field equations and induce the given data at all orders at $p$. The Taylor coefficients of these fields at $p$ are uniquely determined by the free data. (ii) On ${\cal N}_p$ there exists a unique set of fields which induce the given free data and satisfy the transport equations and the inner constraints induced on ${\cal N}_p$ by the conformal field equations. These fields and the fields which are obtained by restricting the functions considered in (i) to ${\cal N}_p$ coincide at all orders at $p$.Communications in Mathematical Physics 06/2013; 324(1).
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