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We present an expansion of a many-body correlation function in a sum of pseudomodes - exponents with complex frequencies that encompass both decay and oscillations. We demonstrate that, typically, it is enough to take a few first terms of this infinite sum to obtain an excellent approximation to the correlation function at any time, with the large time behavior being determined solely by the first pseudomode. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we apply the pseudomode expansion to calculate infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice.

We address dissipative dynamics of the one-dimensional nearest-neighbour $XX$ spin-$1/2$ chain governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the absence of dissipation the model is integrable. We identify a broad class of dissipative terms that generically destroy integrability but leave the operator space of the model fragmented into an extensive number of dynamically disjoint subspaces of varying dimensions. In sufficiently small subspaces the GKSL equation in the Heisenberg representation can be easily solved, sometimes in a closed analytical form. We provide an example of such an exact solution for a specific choice of dissipative terms. It is found that observables experience the Wannier-Stark localization in the corresponding operator subspace. As a result, the expectation values of the observables are linear combinations of essentially a few discrete decay modes, the long time dynamics being governed by the slowest mode. We examine the complex Liouvillian eigenvalue corresponding to this latter mode as a function of the dissipation strength. We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace. Finally, we point out that our exact solutions of the GKSL equation entail exact solutions of the Schr\"odinger equation describing the quench dynamics in closed spin ladders dual to the dissipative spin chains., Comment: Originally this work appeared as a part of arXiv:2304.03155v1. Later this preprint was split into two separate papers. The first one retained the original arXiv identifier. The second one is presented here

The formation of Schrodinger cat-like states during the spontaneous parametric down-conversion process (SPDC) is studied when the pump mode is considered quantum and depleted. The Schrodinger cat-like state is formed in the fundamental and second harmonic modes, and the negativity in both modes is studied for certain initial state conditions and interaction lengths. The Wigner function is used to visualize qualitatively Schrodinger cat-like states.

We establish a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation and satisfying the detailed balance condition on the one side, and closed bilayer systems with a self-adjoint Hamiltonian on the other side. Under this duality, the identity operator on the open system side maps to the thermofield double state which turns out to be a quantum many-body scar of the dual Hamiltonian $\mathcal H$. A remarkable feature of this thermofield scar is a tunable entanglement entropy controlled by the reservoir temperature on the open system side. Further, we identify broad classes of many-body open systems with nontrivial explicit eigen operators $Q$ of the Lindbladian superoperator. The expectation values of the corresponding observables exhibit a simple exponential decay, $\langle Q\rangle_t=e^{-\Gamma t} \langle Q \rangle_0$, irrespectively of the initial state. Under the above duality, these eigen operators give rise to additional (towers of) scars. Finally, we point out that more general superoperators (not necessarily of the GKSL form) can be mapped to self-adjoint Hamiltonians of bilayer systems harbouring scars, and provide an example thereof., Comment: Comment on v2: v1 of this manuscript was split in two pieces. The first piece was posted separately as arXiv 2405.17310 and published as Phys. Rev. B 109, L140302 (2024). The second piece is presented in v2

Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in this article, we derive a new model of dissipative time evolution based on unitary Lindblad operators which, while does not preserve the set of Gaussian states, preserves the set of their convex combinations, i.e. so-called quantum Gaussian states. As we demonstrate, the considered evolution proves useful both as a description for random scattering and as a tool in dissipator engineering., Comment: 12 pages