Related papers: Weakly regular Floquet Hamiltonians with pure poin…

We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + \beta V(\omega t)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a…

We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a…

The spectral analysis of the unitary monodromy operator, associated with a time-periodically (paramatrically) forced Schrodinger equation, is a question of longstanding interest. Here, we consider this question for Hamiltonians of the form…

We compute the Floquet Hamiltonian $H_F$ for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to…

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that…

Open systems with gain, loss, or both, described by non-Hermitian Hamiltonians, have been a research frontier for the past decade. In particular, such Hamiltonians which possess parity-time ($\mathcal{PT}$) symmetry feature dynamically…

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians,…

We develop a theory to derive effective Floquet Hamiltonians in the weak drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially-periodic and weak potential, such as occurs in some…

We prove that the $1-d$ quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their…

Non-Hermitian Hamiltonians provide a simple picture for analyzing systems with natural or induced gain and loss; however, in general, such Hamiltonians feature complex energies and a corresponding non-orthonormal eigenbasis. Provided that…

We prove that a dense subset of limit periodic operators have spectra which are homogeneous Cantor sets in the sense of Carleson. Moreover, by using work of Egorova, our examples have purely absolutely continuous spectrum. The construction…

We consider the twisted waveguide $\Omega_\theta$, i.e. the domain obtained by the rotation of the bounded cross section $\omega \subset {\mathbb R}^{2}$ of the straight tube $\Omega : = \omega \times {\mathbb R}$ at angle $\theta$ which…

We prove a localization theorem for continuous ergodic Schr\"odinger operators $ H_\omega := H_0 + V_\omega $, where the random potential $ V_\omega $ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$. We consider…

We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third…

We study a non-Hermitian two-level system with square-wave modulated dissipation and coupling. Based on the Floquet theory, we achieve an effective Hamiltonian from which the boundaries of the $\mathcal{PT}$ phase diagram are captured…

We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a…

Consider the Dirichlet Laplacian operator $-\Delta^D$ in a periodic waveguide $\Omega$. On the condition that $\Omega$ is sufficiently thin, we show that its spectrum $\sigma(-\Delta^D)$ is absolutely continuous (in each finite region). In…

We consider a class of Hermitian Hamiltonians with position-dependent mass $H=((m^alpha)p(m^beta)p(m^alpha))/2+\V$ with $2(alpha)+\beta=-1$. We apply these Hamiltonians to different piecewise flat potentials and masses (step, barrier, well…

Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…

We investigate the continuous function $f$ defined by $$x\mapsto \sum_{\sigma\le_L x }2^{-K(\sigma)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we…