Annales Henri Poincaré最新文献

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 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 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}).

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).

We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential equation describing isospectral deformations of a Sturm–Liouville equation. We also derive identities relating solutions to the integrable partial differential equation and to the Sturm–Liouville equation which imply an analogue for Painlevé V of Amir–Corwin–Quastel “integro-differential Painlevé II equation”. This equation reduces, in a degenerate limit, to the system of coupled Painlevé V equations derived by Charlier and Doeraene for the generating function of the Bessel process and to the Painlevé V equation derived by Tracy and Widom for the gap probability of the Bessel process. Finally, we study an initial value problem for the integrable partial differential equation. The approach is based on Its–Izergin–Korepin–Slavnov theory of integrable operators and their associated Riemann–Hilbert problems.

We prove that a class of weakly perturbed Hamiltonians of the form (H_lambda = H_0 + lambda W), with W being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by (H_lambda ) relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order (lambda ^{-2}). Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix (H_lambda ).

While it has become widely appreciated that defining (higher) gauge theories requires, in addition to ordinary phase space data, also “flux quantization” laws in generalized differential cohomology, there has been little discussion of the general rules, if any, for lifting Poisson brackets of (flux-)observables and their quantization from traditional phase spaces to the resulting higher moduli stacks of flux-quantized gauge fields. In this short note, we present a systematic analysis of (i) the canonical quantization of flux observables in Yang–Mills theory and (ii) of valid flux quantization laws in abelian Yang–Mills, observing (iii) that the resulting topological quantum observables form the homology Pontrjagin algebra of the loop space of the moduli space of flux-quantized gauge fields. This is remarkable because the homology Ponrjagin algebra on loops of moduli makes immediate sense in broad generality for higher and non-abelian (nonlinearly coupled) gauge fields, such as for the C field in 11d supergravity, where it recovers the quantum effects previously discussed in the context of “Hypothesis H.”