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In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this…
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the…
The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly…
Based on a relationship with continuous-time random walks discovered by Igl\'oi, Turban, and Rieger [Phys. Rev. E {\bf 59}, 1465 (1999)], we derive exact lower and upper bounds on the lowest energy gap of open transverse-field Ising chains,…
In 1996, Hatano and Nelson proposed a non-Hermitian lattice model containing an imaginary Peierls phase [Phys. Rev. Lett. 77 570-573 (1996)], which subsequent analyses revealed to be an instance of a new class of topological systems. Here,…
Topological phase transitions are typically associated with the formation of gapless states. Spontaneous symmetry breaking can lead to a gap opening thereby obliterating the topological nature of the system. Here we highlight a completely…
A novel quantum dynamical model based on the dissipative quantum dynamics of open quantum systems is presented. It allows the treatment of both deep-inelastic processes and quantum tunneling (fusion) within a fully quantum mechanical…
We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles…
We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven…
Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter…
It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching.…
In this paper, we review our novel information geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy (IGE) as an indicator of chaoticity in a…
The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium…
Open quantum systems interacting with an environment exhibit dynamics described by the combination of dissipation and coherent Hamiltonian evolution. Taken together, these effects are captured by a Liouvillian superoperator. The…
The non-Hermitian skin effect, by which the eigenstates of Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a…
Non-Hermitian topological edge states have many intriguing properties, but have so far mainly been discussed in terms of bulk-boundary correspondence. Here we propose to use a bulk property of diffusion coefficients for probing the…
Model calculations that include the effects of irreversible, environmental couplings on top of a coupled-channels dynamical description of the collision of two complex nuclei are presented. The Liouville-von Neumann equation for the…
We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator ${\cal L}$. The eigenvalues…