Related papers: Null bootstrap for non-Hermitian Hamiltonians
Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…
Determining the solvability of a given quantum mechanical system is generally challenging. We discuss that the numerical bootstrap method can help us to solve this question in one-dimensional quantum mechanics. We show that the bootstrap…
Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. Identifying systems where at least some eigenstates are non-thermal is an outstanding question. In this work we…
High control in the preparation and manipulation of states is an experimental and theoretical important task in many quantum protocols. Shortcuts to adiabaticity methods allow to obtain desirable states of a adiabatic dynamics but in short…
The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet…
Passive states are special configurations of a quantum system which exhibit no energy decrement at the end of an arbitrary cyclic driving of the model Hamiltonian. When applied to an increasing number of copies of the initial density…
A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…
Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with…
We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be…
Zero indirect gaps in band models are typically viewed as unstable and achievable only through fine-tuning. Recent works, however, have revealed robust semimetallic phases in Hermitian systems where the indirect gap remains pinned at zero…
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of…
Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case, affection of…
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive…
Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low…
Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(\gamma,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$ and $\gamma \to v$, as…
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
In this paper we demonstrate that the inevitable action of the environment can be substantially weakened when considering appropriate nonstationary quantum systems. Beyond protecting quantum states against decoherence, an oscillating…