Communications in Mathematical Physics最新文献

We prove a nonlinear characteristic (C^k)-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum n-dimensional backgrounds, (nge 3), with any finite k, with cosmological constant ( Lambda in mathbb {R}), near Birmingham-Kottler backgrounds. This generalises the (C^2)-gluing of Aretakis, Czimek and Rodnianski, carried-out near light cones in four-dimensional Minkowski spacetime.

Smith homomorphisms are maps between bordism groups that change both the dimension and the tangential structure. We give a completely general account of Smith homomorphisms, unifying the many examples in the literature. We provide three definitions of Smith homomorphisms, including as maps of Thom spectra, and show they are equivalent. Using this, we identify the cofiber of the spectrum-level Smith map and extend the Smith homomorphism to a long exact sequence of bordism groups, which is a powerful computation tool. We discuss several examples of this long exact sequence, relating them to known constructions such as Wood’s and Wall’s sequences. Furthermore, taking Anderson duals yields a long exact sequence of invertible field theories, which has a rich physical interpretation. We developed the theory in this paper with applications in mind to symmetry breaking in quantum field theory, which we study in Debray-Devalapurkar-Krulewski-Liu-Pacheco-Tallaj-Thorngren (J High Energy Phys 2025(7):1–48, 2025)

This paper concerns the large Reynolds number limits and asymptotic behaviors of solutions to the 2D steady Navier–Stokes equations in an infinitely long convergent channel. It is shown that for a general convergent infinitely long nozzle whose boundary curves satisfy curvature-decreasing and any given finite negative mass flux, the Prandtl’s viscous boundary layer theory holds in the sense that there exists a Navier–Stokes flow with no-slip boundary condition for small viscosity, which is approximated uniformly by the superposition of an Euler flow and a Prandtl flow. Moreover, the singular asymptotic behaviors of the solution to the Navier–Stokes equations near the vertex of the nozzle and at infinity are determined by the given mass flux, which is also important for the construction of the Prandtl approximation solution due to the possible singularities at the vertex and non-compactness of the nozzle. One of the key ingredients in our analysis is that the curvature-decreasing condition on boundary curves of the convergent nozzle ensures that the limiting inviscid flow is pressure favorable and plays crucial roles in both the Prandtl expansion and the stability analysis.

We consider the Plancherel–Rotach type asymptotics of the biorthogonal polynomials associated with the biorthogonal ensemble having the joint probability density function

where

In the special case where the potential function V is linear, this biorthogonal ensemble arises in the quantum transport theory of disordered wires. We analyze the asymptotic problem via 2-component vector-valued Riemann–Hilbert problems and solve it under the one-cut regular with a hard edge condition. We use the asymptotics of the biorthogonal polynomials to establish sine universality for the correlation kernel in the bulk and provide a central limit theorem with a specific variance for holomorphic linear statistics. As an application of our theory, we establish Ohm’s law (1.13) and universal conductance fluctuation (1.14) for the disordered wire model, thereby rigorously confirming predictions from experimental physics (Washburn and Webb: Adv Phys 35(4):375–422, 1986).

We study the harmonic locus consisting of the monodromy-free Schrödinger operators with rational potential and quadratic growth at infinity. It is known after Oblomkov that it can be identified with the set of all partitions via the Wronskian map for Hermite polynomials. We show that the harmonic locus can also be identified with the subset of Wilson’s Calogero–Moser space that is fixed by the symplectic action of (mathbb C^times .) As a corollary, for the multiplicity-free part of the locus we effectively solve the inverse problem for the Wronskian map by describing the partition in terms of the spectrum of the corresponding Moser matrix. We also compute the characters of the (mathbb C^times )-action at the fixed points, proving, in particular, a conjecture of Conti and Masoero. In the Appendix written by N. Nekrasov there is an alternative proof of this result, based on the space of instantons and the ADHM construction.

Hadamard states were originally introduced for quantised Klein–Gordon fields and occupy a central position in the theory of quantum fields on curved spacetimes. Subsequently they have been developed for other linear theories, such as the Dirac, Proca and Maxwell fields, but the particular features of each require slightly different treatments. This paper gives a generalised definition of Hadamard states for linear bosonic and fermionic theories encompassing a range of theories that are described by Green-hyperbolic operators with ‘decomposable’ Pauli–Jordan propagators, including theories whose bicharacteristic curves are not necessarily determined by the spacetime metric. The new definition reduces to previous definitions for normally hyperbolic and Dirac-type operators. We develop the theory of Hadamard states in detail, showing that our definition propagates under the equation of motion, and is also stable under pullbacks and suitable pushforwards. There is an equivalent formulation in terms of Hilbert space valued distributions, and the generalised Hadamard condition on 2-point functions constrains the singular behaviour of all n-point functions. For locally covariant theories, the Hadamard states form a covariant state space. It is also shown how Hadamard states may be combined through tensor products or reduced by partial tracing while preserving the Hadamard property. As a particular application it is shown that state updates resulting from nonselective measurements preserve the Hadamard condition. The treatment we give was partly inspired by a recent work of Moretti, Murro and Volpe (MMV) (Ann H Poincaré 24: 3055–3111, 2023) on the neutral Proca field. Among the other applications, we revisit the neutral Proca field and prove a complete equivalence between the MMV definition of Hadamard states and an older work of Fewster and Pfenning (J Math Phys 44:4480–4513, 2003).

We consider the action of a finite group G by locality preserving automorphisms (quantum cellular automata) on quantum spin chains. We refer to such group actions as “symmetries”. The natural notion of equivalence for such symmetries is stable equivalence, which allows for stacking with factorized group actions. Stacking also endows the set of equivalence classes with a group structure. We prove that the anomaly of such symmetries provides an isomorphism between the group of stable equivalence classes of symmetries with the cohomology group (H^3(G,U(1))), consistent with previous conjectures. This amounts to a complete classification of locality preserving symmetries on spin chains. We further show that a locality preserving symmetry is stably equivalent to one that can be presented by finite depth quantum circuits with covariant gates if and only if the slant product of its anomaly is trivial in (H^2(G, U(1)[G])).

This paper presents a conceptual and efficient geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the n-dimensional lattice (mathbb {Z}^n). It is shown that, under the typical assumption of Haag duality, the monoidal (C^*)-categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of (mathbb {Z}^n). Employing techniques from higher algebra, one extracts from this datum an underlying locally constant prefactorization algebra defined on open disks in the cylinder (mathbb {R}^1times mathbb {S}^{n-1}). While the sphere (mathbb {S}^{n-1}) arises geometrically as the angular coordinates of cones, the origin of the line (mathbb {R}^1) is analytic and rooted in Haag duality. The usual braided (for (n=2)) or symmetric (for (nge 3)) monoidal (C^*)-categories of superselection sectors are recovered by removing a point of the sphere (mathbb {R}^1times (mathbb {S}^{n-1}setminus text {pt}) cong mathbb {R}^n) and using the equivalence between (mathbb {E}_n)-algebras and locally constant prefactorization algebras defined on open disks in (mathbb {R}^n). The non-trivial homotopy groups of spheres induce additional algebraic structures on these (mathbb {E}_n)-monoidal (C^*)-categories, which in the case of (mathbb {Z}^2) is given by a braided monoidal self-equivalence arising geometrically as a kind of ‘holonomy’ around the circle (mathbb {S}^1). The locally constant prefactorization algebra structures discovered in this work generalize, under some mild geometric conditions, to other discrete spaces and thereby provide a clear link between the geometry of the localization regions and the algebraic structures on the category of superselection sectors.

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.