Annales Henri Poincaré最新文献

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.

In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched Rényi divergences such as the sandwiched Rényi conditional entropy. We follow three different approaches: The first one is the “almost additive approach”, which exploits the sub-/superadditivity and joint concavity/convexity of the exponential of the divergence. In our second approach, termed the “operator space approach”, we express the entropic measures as norms and utilize their properties for establishing the bounds. These norms draw inspiration from interpolation space norms. We not only demonstrate the norm properties solely relying on matrix analysis tools but also extend their applicability to a context that holds relevance in resource theories. By this, we extend the strategies of Marwah and Dupuis as well as Beigi and Goodarzi employed in the sandwiched Rényi conditional entropy context. Finally, we merge the approaches into a mixed approach that has some advantageous properties and then discuss in which regimes each bound performs best. Our results improve over the previous best continuity bounds or sometimes even give the first continuity bounds available. In a separate contribution, we use the ALAFF method, developed in a previous article by some of the authors, to study the stability of approximate quantum Markov chains.

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.”

Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses and boundary conditions. We show that the relative entropy depends crucially on d, the dimension of Euclidean space. Furthermore, we demonstrate that the mutual information between two disjoint regions in (mathbb {R}^d) is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of “touching” regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories.

Drinfeld defined the Knizhnik–Zamolodchikov (KZ) associator (Phi _{textrm{KZ}}) by considering the regularized holonomy of the KZ connection along the droit chemin [0, 1]. The KZ associator is a group-like element of the free associative algebra with two generators, and it satisfies the pentagon equation. In this paper, we consider paths on ({mathbb {C}}backslash { z_1, dots , z_n}) which start and end at tangential base points. These paths are not necessarily straight, and they may have a finite number of transversal self-intersections. We show that the regularized holonomy H of the KZ connection associated with such a path satisfies a generalization of Drinfeld’s pentagon equation. In this equation, we encounter H, (Phi _{textrm{KZ}}), and new factors associated with self-intersections, tangential base points, and the rotation number of the path.