Related papers: Characteristic dynamics near two coalescing eigenv…
This paper summarises an investigation of the statistical properties of orbits escaping from three different two-degree-of-freedom Hamiltonian systems which exhibit global stochasticity. Each H=H_{0}+eH', with H_{0} integrable and eH' a…
Diagonalization of the effective Hamiltonian describing an open quantum system is the usual method of tracking its exceptional points. Although, such a method is successful for tracking EPs in Markovian systems, it may be problematic in…
Exceptional points (EPs), as an exclusive feature of a non-Hermitian system, support coalescing states to be alternative stable state beyond the ground state. In this work, we explore the influence of non-Hermitian impurities on the dynamic…
The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as $A$ and $B$, is computed analytically using a Coulomb gas method. It is shown that this probability, for large…
A macroscopic effect can be induced by a local non-Hermitian term in a many-body system, when it manifests simultaneously level coalescence of a full real degeneracy spectrum, leading to exceptional spectrum. In this paper, we propose a…
Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…
Exceptional points are the branch-point singularities of non-Hermitian Hamiltonians, and have rich consequences in open-system dynamics. While the exceptional points and their critical phenomena are widely studied in the non-Hermitian…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
So far, the well known two branches of real discrete spectrum of complex PT-symmetric Scarf II potential are kept isolated. Here, we suggest that these two need to be brought together as doublets: $E^n_{\pm}(\lambda)$ with $n=0,1,2...$.…
We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This Pairwise Coalescence (PC) is an…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
Exceptional points (EPs) in non-Hermitian photonics offer singular sensitivity enhancements but have thus far been realized almost exclusively in spatially engineered platforms with fixed geometries and limited tunability. Here we extend EP…
In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by…
The non-Hermitian dynamics of open systems deal with how intricate coherent effects of a closed system intertwine with the impact of coupling to an environment. The system-environment dynamics can then lead to so-called exceptional points,…
Non-Hermitian systems have been at the center of intense research for over a decade, partly due to their nontrivial energy topology formed by intersecting Riemann manifolds with branch points known as exceptional points (EPs). This spectral…
Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of…
We discuss the emulation of non-Hermitian dynamics during a given time window by a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an…
The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite…
The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase…