Annales Henri Poincaré最新文献

For conformally Kähler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein–Maxwell. After deriving generic identities for the curvature of such manifolds without assuming field equations, we obtain (SU(infty )) Toda formulations for the Page-Pope, Plebański–Demiański, and Chen–Teo classes, we show how to solve the (modified) Toda equation, and we use this to find conformally self-dual and Einstein–Maxwell generalisations of these geometries.

Extending our previous works on the Cauchy problem for the (2+1) equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps equation coupled to the full set of the Einstein equations, for small data. A key ingredient in the proof is a nonlinear Morawetz estimate for the fully coupled equivariant Einstein-wave maps. The (2+1)-dimensional Einstein-wave map system occurs naturally in the (3+1) vacuum Einstein equations of general relativity.

We study a generic family of Lindblad master equations modeling bipartite open quantum systems, where one tries to stabilize a quantum system by carefully designing its interaction with another, dissipative, quantum system—a strategy known as quantum reservoir engineering. We provide sufficient conditions for convergence of the considered Lindblad equations; our setting accommodates the case where steady-states are not unique but rather supported on a given subspace of the underlying Hilbert space. We apply our result to a Lindblad master equation modeling engineered multi-photon emission and absorption processes, a setting that received considerable attention in recent years due to its potential applications for the stabilization of so-called cat qubits.

We construct quasi-periodic solutions of the universal hierarchy which includes the multi-component KP and Toda hierarchies and show how they fit into the bilinear formalism. The tau-function is expressed in terms of the Riemann theta-function multiplied by exponential function of a quadratic form in the hierarchical times.

We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon (mathbb Z)-periodic Lorentz gas and in view of future development, we establish our results in a general context of perturbation by (mathbb Z)-extension over chaotic probability preserving dynamical systems. As a by-product, we prove limit theorems for non-stationary Birkhoff sums for such infinite measure preserving dynamical systems.

We study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions, which implies the existence of the dynamics at the level of the CAR algebra. We then turn to the physical situation relevant to the (fractional) quantum Hall effect, namely the quasi-free second quantized Landau Hamiltonian to which electron–electron interactions can be added.

We consider a tight-binding model recently introduced by Timmel and Mele (Phys Rev Lett 125:166803, 2020) for strained moiré heterostructures. We consider two honeycomb lattices to which layer antisymmetric shear strain is applied to periodically modulate the tunneling between the lattices in one distinguished direction. This effectively reduces the model to one spatial dimension and makes it amenable to the theory of matrix-valued quasi-periodic operators. We then study the charge transport and spectral properties of this system, explaining the appearance of a Hofstadter-type butterfly and the occurrence of metal/insulator transitions that have recently been experimentally verified for non-interacting moiré systems (Wang et al. in Nature 577:42–46, 2020). For sufficiently incommensurable moiré lengths, described by a diophantine condition, as well as strong coupling between the lattices, which can be tuned by applying physical pressure, this leads to the occurrence of localization phenomena.

Starting from the Hawking–Page solutions of [14], we consider the corresponding Lorentzian cone metrics. These represent cone interior scale-invariant vacuum solutions, defined in the chronological past of the scaling origin. We extend the Lorentzian Hawking–Page solutions to the cone exterior region in the class of ((4+1))-dimensional scale-invariant vacuum solutions with an (SO(3)times U(1)) isometry, using the Kaluza–Klein reduction and the methods of Christodoulou in [5]. We prove that each Lorentzian Hawking–Page solution has extensions with a null curvature singularity, extensions with a spacelike curvature singularity, and extensions with a null Cauchy horizon of Taub–NUT type. These are all the possible extensions within our symmetry class. The extensions to spacetimes with a null curvature singularity can be used to construct ((4+1))-dimensional asymptotically flat vacuum spacetimes with locally naked singularities, where the null curvature singularity is not preceded by trapped surfaces. We prove the instability of such locally naked singularities using the blue-shift effect of Christodoulou in [6].

We give a functional characterization of a class of quasi-invariant determinantal processes corresponding to projection kernels in terms of de Branges spaces of entire functions.

By extending the gauge covariant magnetic perturbation theory to operators defined on half-planes, we prove that for 2d random ergodic magnetic Schrödinger operators, the zero-temperature bulk-edge correspondence can be obtained from a general bulk-edge duality at positive temperature involving the bulk magnetization and the total edge current. Our main result is encapsulated in a formula, which states that the derivative of a large class of bulk partition functions with respect to the external constant magnetic field equals the expectation of a corresponding edge distribution function of the velocity component which is parallel to the edge. Neither spectral gaps, nor mobility gaps, nor topological arguments are required. The equality between the bulk and edge indices, as stated by the conventional bulk-edge correspondence, is obtained as a corollary of our purely analytical arguments by imposing a gap condition and by taking a “zero-temperature” limit.