相关论文: The Stability of Free Fermi Hamiltonians

We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial…

Recently, several spin chain models have been discovered that admit solutions in terms of "free fermions in disguise." A graph-theoretical treatment of such models was also established, giving sufficient conditions for free fermionic…

We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the drift of the system. The main assumption is the strong…

We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured, it fully suffices to observe spectral shifts induced by fields applied to local `markers'.…

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and…

We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…

We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal…

We revisit the problem of characterizing band topology in dynamically-stable quadratic bosonic Hamiltonians that do not conserve particle number. We show this problem can be rigorously addressed by a smooth and local adiabatic mapping…

The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…

We study a diagonalizable Hamiltonian that is not at first hermitian. Requirement that a measurement shall not change one Hamiltonian eigenstate into another one with a different eigenvalue imposes that an inner product must be defined so…

In this note, we prove the Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons which are either asymptotically locally flat (ALF) and Ricci-flat, or compact and Einstein with positive…

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…

In this paper we investigate a class of natural Hamiltonian systems with two degrees of freedom. The kinetic energy depends on coordinates but the system is homogeneous. Thanks to this property it admits, in a general case, a particular…

For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…

In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field games. The considered Hamiltonians are non-separable and $local$…

It is known that inhomogeneous second-order macroscopic traffic models can reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic condition is violated, uniform traffic flow is unstable, and small perturbations grow…

Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral…

We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, named the perturbing and dissipative parameters, and it…

This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL…