For Maxwell operators in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance Leontovich including the cases of singular, degenerate, randomized coefficients. To end construct Riesz bases trace spaces associated with curl-operator introduce a modified version triple adapted specifics equations, namely, mixed-order duality related sp...

We develop a novel numerical scheme for the simulation of dissipative quantum dynamics, following from two-body Lindblad master equations. It exactly preserves trace density matrix and shows only mild deviations hermiticity positivity, which are defining properties continuum dynamics. The central ingredient is new spatial difference operator, not fulfills summation by parts (SBP) property, but ...

In the Hilbert space ?2 ?(Z; E) (Z := {0,? 1, ? 2, ...}, dim E = N < ?), maximal dissipative singular second-order matrix difference operators that extensions of a minimal symmetric operator with deficiency indices (2N, 2N) (in limit-circle cases at ?) are considered. The general boundary conditions investigated. For operator, self-adjoint dilation and is its incoming outgoing spectral repre...

Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for Non-Equilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution ...

We study Krylov complexity $C_K$ and operator entropy $S_K$ in growth. find that for a variety of systems, including chaotic ones integrable theories, the two quantities always enjoy logarithmic relation $S_K\sim \log{C_K}$ at long times, where dissipative behavior emerges unitary evolution. Otherwise, does not hold any longer. Universality is deeply connected to irreversibility

Given γ ≥ 0, let us consider the following differential inclusion (S) ẍ(t) + γ ẋ(t) + ∂Φ(x(t)) 3 0, t ∈ R+, where Φ : Rd → R ∪ {+∞} is a lower semicontinuous convex function such that int(domΦ) 6= ∅. The operator ∂Φ denotes the subdifferential of Φ. When Φ = f + δK with f : Rd → R a smooth convex function and K ⊂ Rd a closed convex set, inclusion (S) describes the motion of a discrete mechanica...