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Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
A property of dynamical correlation functions for nonequilibrium states is discussed. We consider arbitrary dimensional quantum spin systems with local interaction and translationally invariant states with nonvanishing current over them. A…
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the…
Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by the competition between unitary dynamics and dissipation. In this work, we reveal the fundamental role of conservation laws in shaping this…
We develop a manifest non-Hermitian approach of spectral and transport properties of two- dimensional mesoscopic systems in strong magnetic field. The finite system to which several ter- minals are attached constitutes an open system that…
We report on a remarkable spectral phenomenon in a generic type of quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize and lead to plateaus of the interaction energy, with gaps opening akin…
Time crystals are a nonequilibrium phase of matter that extend fundamental spontaneous symmetry breaking into the temporal dimension, typically requiring external driving for their realization. Here, we explore the nonequilibrium phase…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…
Understanding how microscopic few-body interactions give rise to thermal behavior in isolated quantum many-body systems remains a central challenge in nonequilibrium statistical mechanics. While individual energy eigenstates are expected to…
We consider fully many-body localized systems, i.e. isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators.…
This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians…
In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an…
Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
New emergent states of matter in quantum systems may be created under non-equilibrium conditions if - through many body interactions - its constituents order on a timescale which is shorter than the time required for the system to reach…
In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov…
It was at the dawn of the historical developments of quantum mechanics when Schr\"odinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave…
The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by…