Related papers: Non-Hermitian physics and master equations
This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a…
We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different,…
The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The…
Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised…
Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach…
A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…
This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for quantum open systems. On the classical side, we consider…
The mathematically sound theory of quantum open systems, formulated in the 70-ties of XX century and highlighted by the discovery of Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation, found a wide range of applications in various…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $\mathcal{PT}$-symmetric superintegrable models over an $n$-dimensional sphere $S^n$. The mechanism is illustrated with…
Intrinsic noise in pre-fault-tolerant quantum devices poses a major challenge to the reliable realization of unitary dynamics in quantum algorithms and simulations. To address this, we present a method for simulating open quantum system…
The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr\"odinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of…
Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings…
The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The…
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…
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…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
Despite acute interest in the dynamics of non-Hermitian systems, there is a lack of consensus in the mathematical formulation of non-Hermitian quantum mechanics in the community. Different methodologies are used in the literature to study…
Gorini-Kossakowski-Sudarshan-Lindblad equation of Poisson-type for the density matrix is considered. The Poisson jumps are assumed to be unitary operators with generators, which are quadratic in fermionic creation and annihilation…