Related papers: Towards continuity: Universal frequency-preserving…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
We study the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, we show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical…
We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth…
We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…
This study deals with the Ulam stability of non-autonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional…
This paper is a sequel to "Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey…
In this paper we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems \begin{equation*} H=h(y)+f(x,y,t), \end{equation*} where $y\in D\subseteq\mathbb{R}^n$ with $D$ being a closed bounded domain,…
We introduce an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible Schr\"odinger systems. Using this KAM theorem together with partial Birkhoff normal form method, we find the existence of quasi-periodic…
A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
The coherence between quantum states with different particle numbers --- the Fock-space coherence --- qualitatively differs from the more common Hilbert-space coherence between states with equal particle numbers. For a quantum dot with…
By constructing an infinite dimensional KAM theorem of the normal frequencies being dense at finite-point, we show that some shallow water equations such as Benjamin-Bona-Mahony equation and the generalized $d$-Dim. Pochhammer-Chree…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…
We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…
We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that was developed recently in [BGK] to address the standard KAM…
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three paradigmatic 1D models, namely the…
We consider the possible concentration in phase space of a sequence of eigenfunctions (or, more generally, a quasimode) of an operator whose principal symbol has completely integrable Hamilton flow. The semiclassical wavefront set $WF_h$ of…
We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^{\kappa}\hat{K}$, where…
Unspeakable coherence is a key feature separating quantum and classical physics. Modelled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment,…
We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield…