Journal: Journal of Mathematical Physics

Abbreviation

J. Math. Phys.

Publisher

American Institute of Physics

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ISSN

1089-7658
0022-2488

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Publications 1 - 10 of 63
  • Two convergent NPA-like hierarchies for the quantum bilocal scenario
    Item type: Journal Article
    Renou, Marc-Olivier Anne; Xu, Xiangling; Ligthart, Laurens T. (2026)
    Journal of Mathematical Physics
    Characterising the correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory. The seminal work [M. Navascu & eacute;s et al., New J. Phys. 10, 073013 (2008)], known as the Navascu & eacute;s-Pironio-Ac & iacute;n (NPA) hierarchy, reformulated this question as a polynomial optimisation problem over noncommutative variables and proposed a convergent hierarchy of necessary conditions, each testable using semidefinite programming. More recently, the problem of characterising the quantum network correlations, which arise when locally measuring several independent quantum systems distributed in a network, has received considerable interest. Several generalisations of the NPA hierarchy, such as the scalar extension [A. Pozas-Kerstjens et al., Phys. Rev. Lett. 123, 140503 (2019)], were introduced while their converging sets remain unknown. In this work, we introduce a new bilocal factorisation NPA hierarchy, prove its equivalence to a modified bilocal scalar extension NPA hierarchy, and characterise its convergence in the case of the simplest network, the bilocal scenario. We further explore its relations with the other known generalisations.
  • Batalin-Vilkovisky integrals in finite dimensions
    Item type: Journal Article
    Albert, C.; Bleile, B.; Fröhlich, J. (2010)
    Journal of Mathematical Physics
  • The equivalence of the class of Rivlin-Sawyers equations and a class of stochastic models for polymer stress
    Item type: Journal Article
    Feigl, K.; Öttinger, Hans Christian (2001)
    Journal of Mathematical Physics
  • Local iterative block-diagonalization of gapped Hamiltonians: A new tool in singular perturbation theory
    Item type: Journal Article
    del Vecchio, Simone; Fröhlich, Jürg; Pizzo, Alessandro; et al. (2022)
    Journal of Mathematical Physics
    In this paper, the local iterative Lie–Schwinger block-diagonalization method, introduced and developed in our previous work for quantum chains, is extended to higher-dimensional quantum lattice systems with Hamiltonians that can be written as the sum of an unperturbed gapped operator, consisting of a sum of on-site terms, and a perturbation, consisting of bounded interaction potentials of short range multiplied by a real coupling constant t. Our goal is to prove that the spectral gap above the ground-state energy of such Hamiltonians persists for sufficiently small values of |t|, independently of the size of the lattice. New ideas and concepts are necessary to extend our method to systems in dimension d > 1: As in our earlier work, a sequence of local block-diagonalization steps based on judiciously chosen unitary conjugations of the original Hamiltonian is introduced. The supports of effective interaction potentials generated in the course of these block-diagonalization steps can be identified with what we call minimal rectangles contained in the lattice, a concept that serves to tackle combinatorial problems that arise in the course of iterating the block-diagonalization steps. For a given minimal rectangle, control of the effective interaction potentials generated in each block-diagonalization step with support in the given rectangle is achieved by exploiting a variety of rather subtle mechanisms, which include, for example, the use of weighted sums of paths consisting of overlapping rectangles and of large denominators, expressed in terms of sums of orthogonal projections, which serve to control analogous sums of projections in the numerators resulting from the unitary conjugations of the interaction potential terms involved in the local block-diagonalization step.
  • Construction of Lax connections by exponentiation
    Item type: Journal Article
    Beisert, Niklas; Lücker, Florian (2012)
    Journal of Mathematical Physics
  • Power series representations for complex bosonic effective actions. II. A small field renormalization group flow
    Item type: Journal Article
    Balaban, Tadeusz; Feldman, Joel; Knörrer, Horst; et al. (2010)
    Journal of Mathematical Physics
  • Relating different quantum generalizations of the conditional Renyi entropy
    Item type: Journal Article
    Tomamichel, Marco; Berta, Mario; Hayashi, Masahito (2014)
    Journal of Mathematical Physics
  • Successive elimination of shear layers by a hierarchy of constraints in inviscid spherical-shell flows
    Item type: Journal Article
    Livermore, Philip W.; Hollerbach, Rainer (2012)
    Journal of Mathematical Physics
  • On the development of shocks in fluids
    Item type: Review Article
    Christodoulou, Demetrios (2022)
    Journal of Mathematical Physics
    In my 2007 work, I studied the formation of shocks in the context of Eulerian equations of the mechanics of compressible fluids. That work studied the maximal classical development of smooth initial data. The present review article is a presentation of my 2019 work, which addresses the problem of the physical continuation of the solution past the point of shock formation. The problem requires the construction of a hypersurface, the shock hypersurface, originating from a given singular spacelike surface, which is acoustically spacelike as viewed from its past, and the construction of a new solution in the future of the union of a given regular null hypersurface with the shock hypersurface, a solution which extends continuously the prior maximal classical solution across the given regular null hypersurface, but which displays discontinuities in physical variables across the shock hypersurface in accordance with the mass, momentum, and energy conservation laws. Moreover, the shock hypersurface is to be acoustically timelike as viewed from its future. Mathematically, this is a free boundary problem, with nonlinear conditions at the free boundary, for a first order quasilinear hyperbolic system of PDE, with characteristic initial data, which are singular at the past boundary of the initial null hypersurface, that boundary being the singular surface of origin. My 2019 work solved a restricted form of the problem through the introduction of new geometric and analytic methods. This Review is focused on the presentation of these methods.
  • Some Hamiltonian models of friction
    Item type: Journal Article
    Fröhlich, Jürg; Gang, Zhou; Soffer, Avy (2011)
    Journal of Mathematical Physics
Publications 1 - 10 of 63