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Chains of coupled two-level atoms behave as 1D quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered…
Decoherence-free subspaces (DFSs) provide a strategy for protecting the dynamics of an open system from decoherence induced by the system-environment interaction. So far, DFSs have been primarily studied in the framework of Markovian master…
An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of…
Mean-field systems provide a natural framework in which collective effects persist as the number of degrees of freedom N increases, raising fundamental questions about the emergence of integrability and the nature of chaos in large but…
Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes…
Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to…
A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the QE is partially stabilized in its excited state. We put forward a general approach for calculating the energy level shift at a…
The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate values of mass parameters. It is achieved by considering the…
We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{PT}$ symmetry under some specific conditions and…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
In the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this ever-lasting non-equilibrium evolution. A simple instance of such a behaviour is…