Related papers: Spectral Analysis for Gaussian Quantum Markov Semi…
We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with quasi-periodic twisted…
Let $T$ be the generator of a $C_0$-semigroup $e^{-Tt}$ which is of finite trace for all $t>0$ (a Gibbs semigroup). Let $A$ be another closed operator, $T$-bounded with $T$-bound equal to zero. In general $T+A$ might not be the generator of…
For a quantum Markov semigroup $\T$ on the algebra $\B$ with a faithful invariant state $\rho$, we can define an adjoint $\widetilde{\T}$ with respect to the scalar product determined by $\rho$. In this paper, we solve the open problems of…
For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in \cite{HiSeSu}. In this paper, as an application of the spectral mapping theorem, we investigate the spectrum of a one-dimensional…
We prove a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators…
The symplectic eigenvalues play a significant role in finite mode quantum information theory, and Williamson normal form proves to be a valuable tool in this area. Understanding the symplectic spectrum of a Gaussian Covariance Operator is a…
We study (quasi-)cohomological properties through an analysis of quantum Markov semi-groups. We construct higher order Hochschild cocycles using gradient forms associated with a quantum Markov semi-group. By using Schatten-$\mathcal{S}_p$…
In this paper we perform a numerical study of the spectra, eigenstates, and Lyapunov exponents of the skew-shift counterpart to Harper's equation. This study is motivated by various conjectures on the spectral theory of these…
We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed,…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schr\"odinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion…
We consider a collective quantum spin-$s$ in contact with Markovian spin-polarized baths. Using a conserved super-operator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigen-modes.…
We construct lower bounds to the spectral gap of a family of Lindblad generators known as Davies maps. These maps describe the thermalization of quantum systems weakly coupled to a heat bath. The steady state of these systems is given by…
We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
Suppose $(C_t)_{t\geq0}$ is the composition semigroup induced by a one-parameter semigroup $(\varphi_t)_{t\geq0}$ of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal…
Spectral inclusion and spectral pollution results are proved for sequences of linear operators of the form $T_0 + i \gamma s_n$ on a Hilbert space, where $s_n$ is strongly convergent to the identity operator and $\gamma > 0$. We work in…
The spectral theory of semigroup generators is a crucial tool for analysing the asymptotic properties of operator semigroups. Typically, Tauberian theorems, such as the ABLV theorem, demand extensive information about the spectrum to derive…
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…