Annales Henri Poincaré最新文献

We consider a frictionless system coupled to an external Markovian environment. The quantum and classical evolution of such systems are described by the Lindblad and the Fokker–Planck equation, respectively. We show that when such a system is given by an at most quadratically growing Hamiltonian and at most linearly growing real jump functions, the quantum and classical evolutions remain close on time scales much longer than Ehrenfest time. In particular, we show that the evolution of a density matrix by the Lindblad equation is close in trace norm to the quantization of the corresponding evolution by the Fokker–Planck equation. Such agreement improves upon recent results (Galokowski and Zworski in Classical quantum correspondence in Lindblad evolution, 2024. arXiv:2403.09345; Hernández et al. in Decoherence ensures classicality beyond the Ehrenfest time as (hbar rightarrow 0), 2023. arXiv:2306.13717, Hernández et al. in The limit of open quantum systems with general Lindbladians: vanishing noise ensures classicality beyond the ehrenfest time, 2023. arXiv:2307.05326), which proved long-time agreement in weaker norms.

We analyze the discrete-time dynamics of a model of non-interacting fermions coupled to an infinite reservoir formed by a bosonic quantum walk on ({{mathbb {Z}}}). This dynamics consists of consecutive applications of free evolutions of the fermions and bosons followed by a local coupling between them. The unitary operator implementing this coupling accounts for energy exchanges between the system and reservoir, while it preserves the number of fermions. The free fermion evolution is given by a second-quantized single-particle unitary operator satisfying some genericity assumptions. The free boson evolution is given by the second-quantized shift operator on ({{mathbb {Z}}}). We derive explicitly the Heisenberg dynamics of fermionic observables and obtain a systematic expansion in the large-coupling regime, which we control by using spectral methods. We also prove that the reduced state of the fermions converges in the large time limit to a mixture of infinite-temperature Gibbs states in each particle sector.

We show that two natural and a priori unrelated structures encapsulate the same data, namely certain commutative and associative product structures and a class of superintegrable Hamiltonian systems. More precisely, consider a Euclidean space of dimension at least three, equipped with a commutative and associative product structure that satisfies the conditions of a Manin-Frobenius manifold, plus one additional compatibility condition. We prove that such a product structure encapsulates precisely the conditions of a so-called abundant structure. Such a structure provides the data needed to construct a family of second-order (maximally) superintegrable Hamiltonian systems of second order. We prove that all abundant superintegrable Hamiltonian systems on Euclidean space of dimension at least three arise in this way. As an example, we present the Smorodinski-Winternitz Hamiltonian system.

We consider a d–dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. With the help of self-duality and Mosco convergence of Dirichlet forms, we extend structural parallels between exclusion and inclusion dynamics from the short-range scenario to the long-range setting. The hydrodynamic equation for the symmetric inclusion process turns out to be of non-local type. At the level of fluctuations from the hydrodynamic limit, we demonstrate that the density fluctuation field converges to a time-dependent generalized Ornstein–Uhlenbeck process whose characteristics are again non-local.

In this work, the description of the moduli space of principal (G)-bundles as double quotient of loop groups is used to construct an étale local (r)-matrix for the Hitchin integrable system.

We demonstrate that the integration-out step of the renormalization group transformation preserves the quasilocality of the effective action. This is shown in the case of a single, real, scalar field on a torus, but the proof holds more generally. The main result can be thought of as showing the flow invariance of the quasilocal subset under the flow generated by the Polchinski equation.

The quantum central limit theorem for bosonic quantum systems states that the sequence of states (rho ^{boxplus n}) obtained from the n-fold convolution of a centered quantum state (rho ) converges to a quantum Gaussian state (rho _textrm{G}) that has the same first and second moments as (rho ). In this paper, we contribute to resolving the problem of finding the optimal rate of convergence for this quantum central limit theorem. We first show that if an m-mode quantum state has a finite moment of order (max {3, 2m}), then we have (Vert rho ^{boxplus n} - rho _textrm{G}Vert _1={mathcal {O}}(n^{-1/2})). We also introduce a notion of Poincaré inequality for quantum states and show that if (rho ) satisfies this Poincaré inequality, then (D(rho ^{boxplus n}Vert rho _textrm{G})= {mathcal {O}}(n^{-1})). By giving an explicit example, we verify that both these convergence rates are optimal.

Quantum information processing and computing tasks can be understood as quantum networks, comprising quantum states and channels and possible physical transformations on them. It is hence pertinent to estimate the change in informational content of quantum processes due to physical transformations they undergo. The physical transformations of quantum states are described by quantum channels, while the transformations of quantum channels are described by quantum superchannels. In this work, we determine fundamental limitations on how well the physical transformation on quantum channels can be undone or reversed, which are of crucial interest to design and benchmark quantum information and computation devices. In particular, we refine (strengthen) the quantum data processing inequality for quantum channels under the action of quantum superchannels. We identify a class of quantum superchannels, which appears to be the superchannel analog of subunital quantum channels, under the action of which the entropy of an arbitrary quantum channel is nondecreasing. We also provide a refined inequality for the entropy change of quantum channels under the action of an arbitrary quantum superchannel.

We propose a mirror derivation of the quiver description of open topological strings known as the knots-quivers correspondence, based on enumerative invariants of augmentation curves encoded by exponential networks. Quivers are obtained by studying M2 branes wrapping holomorphic disks with Lagrangian boundary conditions on an M5 brane, through their identification with a distinguished sector of BPS kinky vortices in the 3d-3d dual QFT. Our proposal suggests that holomorphic disks with Lagrangian boundary conditions are mirror to calibrated 1-chains on the associated augmentation curve, whose intersections encode the linking of boundaries.

In previous papers, it has been shown that the coefficients of terms in the large-N expansion of a certain integrated four-point correlator of superconformal primary operators in (mathcal {N}=4) supersymmetric Yang–Mills theory are rational sums of real-analytic Eisenstein series and “generalised Eisenstein series”. The latter are novel modular functions first encountered in the context of graviton amplitudes in type IIB superstring theory. Similar modular functions, known as two-loop modular graph functions, are also encountered in the low-energy expansion of the integrand of genus-one closed superstring amplitudes. In this paper, we further develop the mathematical structure of such generalised Eisenstein series emphasising, in particular, the occurrence of L-values of holomorphic cusp forms in their Fourier mode decomposition. We show that both the coefficients in the large-N expansion of this integrated correlator and two-loop modular graph functions admit a unifying description in terms of four-dimensional lattice sums generated by theta lifts of certain local Maass functions, which generalise the structure of real-analytic Eisenstein series. Through the theta lift representation, we demonstrate that elements belonging to these two families of non-holomorphic modular functions can be expressed as rational linear combinations of generalised Eisenstein series for which all the L-values of holomorphic cusp forms precisely cancel.