Annales Henri Poincaré最新文献

In the perturbative treatment of interacting quantum field theories, if the interaction Lagrangian changes adiabatically in a finite interval of time, secular growths may appear in the truncated perturbative series also when the interaction Lagrangian density is returned to be constant. If this happens, the perturbative approach does not furnish reliable results in the evaluation of scattering amplitudes or expectation values. In this paper we show that these effects can be avoided for adiabatically switched-on interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. We start considering equilibrium background states and show that, when thermalisation occurs (interaction Lagrangian of spatial compact support), secular effects are avoided. Furthermore, no secular effects pop up if the limit where the Lagrangian is supported everywhere in space is taken after thermalisation (large time limit), in contrast to the reversed order. This result is generalized showing that if the interaction Lagrangian is spatially compact, secular growths are avoided for generic background states which are only invariant under time translation and to states whose explicit dependence of time is not too strong. Finally, as an application, the presented theorems are used to study a complex scalar and a Dirac field, on a background KMS state, in a classical external electromagnetic potential and the contribution to the two point-function given by a generic loop diagram arising from a second order perturbative expansion.

Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calderón projectors for the Wick-rotated equations induce Hadamard bi-solutions on the Lorentzian level. On the other hand, we find smoothing obstructions to gauge-invariance and positivity conditions needed in quantization. These obstructions are primarily due to boundary terms arising in the Wick-rotated theory and depend on the boundary conditions.

We study the time evolution of single-particle quantum states described by a Lindblad master equation with local terms. By means of a geometric resolvent equation derived for Lindblad generators, we establish a finite-volume-type criterion for the decay of the off-diagonal matrix elements in the position basis of the time-evolved or steady states. This criterion is shown to yield exponential decay for systems where the non-hermitian evolution is either gapped or strongly disordered. The gap exists, for example, whenever any level of local dephasing is present in the system. The result in the disordered case can be viewed as an extension of Anderson localization to open quantum systems.

The general classification of (3+1)-static black hole solutions of the Einstein equations, with or without matter, is central in general relativity and important in geometry. In the realm of (textrm{S}^{1})-symmetric vacuum spacetimes, a recent classification proved that, without restrictions on the topology or the asymptotic behavior, black hole solutions can be only of three kinds: (i) Schwarzschild black holes, (ii) Boost black holes or (iii) Myers–Korotkin–Nicolai black holes, each one having its distinct asymptotic and topological type. In contrast to this, very little is known about the general classification of (textrm{S}^{1})-symmetric static electrovacuum black holes although examples show that, on the large picture, there should be striking differences with respect to the vacuum case. A basic question then is whether or not there are charged analogs to the static vacuum black holes of types (i), (ii) and (iii). In this article, we prove the remarkable fact that, while one can ‘charge’ the Schwarzschild solution (resulting in a Reissner–Nordström spacetime) preserving the asymptotic, one cannot do the same to the Boosts and to the Myers–Korotkin–Nicolai solutions: The addition of a small or large electric charge, if possible at all, would transform entirely their asymptotic behavior. In particular, such vacuum solutions cannot be electromagnetically perturbed. The results of this paper are consistent but go far beyond the works of Karlovini and Von Unge on periodic analogs of the Reissner–Nordström black holes. The type of result as well as the techniques used is based on comparison geometry a la Bakry–Émery and appears to be entirely novel in this context. The findings point to a complex interplay between asymptotic, topology and charge in spacetime dimension (3+1), markedly different from what occurs in higher dimensions.

In this paper, we study the long-time dynamics of solutions to the defocusing semilinear wave equation (Box _gphi =|phi |^{p-1}phi ) on the Schwarzschild black hole spacetimes. For (frac{1+sqrt{17}}{2}<p<5) and compactly supported initial data, we show that the solution decays like (|phi |lesssim t^{-1+epsilon }) in the domain of outer communication. The proof relies on the r-weighted vector field method of Dafermos–Rodnianski together with the Strichartz estimates for linear waves by Marzuola–Metcalfe–Tataru–Tohaneanu.

We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a three-dimensional box with periodic boundary condition. For large Fermi momentum (k_{text {F}}), we prove that the effective dynamics is generated by a Fröhlich-type polaron Hamiltonian, which linearly couples the impurity particle to an almost-bosonic excitation field. Moreover, we prove that the effective dynamics can be approximated by an explicit coupled coherent state. Our method is applicable to a range of interaction couplings, in particular including interaction couplings of order 1 and time scales of the order (k_{text {F}}^{-1}).

In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation governs the flow of the effective average action, under changes of a mass parameter k. Here we introduce an analogous flow equation for gauge theories, with the aid of the Batalin–Vilkovisky (BV) formalism. We also show that the corresponding effective average action satisfies a Slavnov–Taylor identity in Zinn-Justin form. We interpret the equation as a cohomological constraint on the functional form of the effective average action, and we show that it is consistent with the flow.

We prove a correspondence between Ising models in a torus and the algebro-geometric data of a Harnack curve with a certain symmetry and a point in the real part of its Prym variety, extending the correspondence between dimer models and Harnack curves and their Jacobians due to Kenyon and Okounkov.

It has been observed that, given an algebraic quantum field theory (AQFT) on a manifold M and an open cover ({M_alpha }) of M, it is typically not possible to recover the global algebra of observables on M by simply gluing the underlying local algebras subordinate to ({M_alpha }). Instead of gluing local algebras, we introduce a gluing construction for AQFTs subordinate to ({M_alpha }) and we show that for simple examples of AQFTs, constructed out of geometric data, gluing the local AQFTs subordinate to ({M_alpha }) recovers the global AQFT on M.

In this paper, we consider the time (quasi)-periodic quantum Hamiltonian of the form (textrm{H}(t)=textrm{H}_gamma +textrm{V}(omega t)), where (textrm{H}_gamma ) is a power-law long-range lattice operator with uniform electric fields on (mathbb {Z}), (textrm{V}(omega t)) is a time quasi-periodic perturbation. In particular, we can obtain the uniform power-law localization of the Floquet Hamiltonian operator (-{textbf{i}}omega cdot partial _{phi }+textrm{H}(phi )), and the dynamical localization of the Hamiltonian operator (textrm{H}(t)). No assumptions are made on the size of the perturbation; however, we require the time quasi-periodic perturbation is a “quasi-Töplitz” operator (close to a Töplitz operator).