Related papers: Liouvillian exceptional points in continuous varia…
I consider the problem of self-oscillatory systems undergoing a homogeneous Hopf bifurcation when they are submitted to an external forcing that is periodic in time, at a frequency close to the system's natural frequency (1:1 resonance),…
We study a quantum Ising chain with tailored bulk dissipation, which can be mapped onto a non-Hermitian Ashkin-Teller model. By exploiting the Kohmoto-den Nijs-Kadanoff transformation, we further map it to a staggered XXZ spin chain with…
Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector…
Exceptional points (EPs) are central to non-Hermitian physics because of their unique properties and broad application prospects. While extensively studied in parity-time ($\mathcal{P}\mathcal{T}$)-symmetric systems and under Markovian…
We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator generating the dissipative dynamics of the standard optomechanical system. The corresponding Lindblad master equation describes the dynamics of…
A rigorous theory of liquid-crystal transitions is developed starting from the Liouville equation. The starting point is an all-atom description and a set of order parameter field variables that are shown to evolve slowly via Newton's…
If a quantum system interacts with the environment, then the Hamiltonian acquires a correction known as the Lamb-shift term. There are two other corrections to the Hamiltonian, related to the stationary state. Namely, the stationary state…
We investigate the impact of quantum noise on non-Hermitian resonators at an exceptional point (EP). The system's irreversible Markovian dynamics is modeled using the Lindblad master equation, which accounts for the incoherent pump,…
Relaxation in open quantum systems is fundamental to quantum science and technologies. Yet, the influence of the initial state on relaxation remains a central, largely unanswered question. Here, by systematically characterizing the…
We reformulate the Generalized Proudman--Johnson (GPJ) equation with parameter a in Lagrangian variables, where it takes the form of an inhomogeneous Liouville equation. This allows us to provide an explicitformula for the flow map, up to…
The dynamical phase diagram of the fractional Langevin equation is investigated for harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents…
We study the symmetries of the Liouville superoperator of one dimensional parametric oscillators, especially the so-called squeeze-driven Kerr oscillator, and discover a remarkable quasi-spin symmetry $su(2)$ at integer values of the ratio…
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems…
We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the…
Based on a Liouville-space formulation of open systems, we present two methods to solve the quantum dynamics of coupled harmonic oscillators experiencing Markovian loss. Starting point is the quantum master equation in Liouville space which…
We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch…
The paper deals with the Neumann spectral problem for a singularly perturbed second order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue…
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in $\dim$-dimensional space. As alternative to the established approach of averaging Hamiltonian dynamics by reformulating the system as…
We calculate analytically the geometric phases that the eigenvectors of a parametric dissipative two-state system described by a complex symmetric Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a parameter setting…
Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is…