We study the operator growth in open quantum systems with dephasing dissipation terms, extending Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by Markovian dynamics. introduce a notion ''operator size concentration'' which allows diagrammatic and combinatorial proof asymptotic linear behavior two ...

The aim of this short note is to reconsider and to extend a former result of K. Mochizuki [Moc76], [MN96] on the existence of the scattering operator for wave equations with small dissipative terms. Contrary to the approach used by Mochizuki we construct the wave operator explicitly in terms of the parametrix construction obtained by a (simplified) diagonalization procedure, cf. [Yag97]. The me...

The effect of the numerical dissipation level of implicit operators on the stability and convergence characteristics of the upwind point Gauss-Seidel (GS) method for solving the Euler equations was studied through the von Neumann stability analysis and numerical experiments. The stability analysis for linear model equations showed that the point GS method is unstable even for very small CFL num...

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev’s non-equilibrium statistical-operator formalism. This is achieved by systematic expansion the energy–momentum tensor and charge current to second order in deviations from equilibrium. As concrete example, we obtain relaxation equations shear-stress tensor, bulk-viscous pressure,...

This paper is concerned with time reversal in photoacoustic tomography of dissipative media that are similar to water. Under an appropriate condition, it is shown that the time reversal method in [A. Wahab, Modeling and Imaging of Attenuation in Biological Media, Ph.D. dissertation, Ecole Polytechnique Palaiseau, Paris, 2011; H. Ammari et al., in Mathematical and Statistical Methods for Imaging...

We consider a second order linear equation with a time-dependent coefficient c(t) in front of the “elastic” operator. For these equations it is well-known that a higher spaceregularity of initial data compensates a lower time-regularity of c(t). In this paper we investigate the influence of a strong dissipation, namely a friction term which depends on a power of the elastic operator. What we di...

The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissipative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this operator based on Padé approximants is the...

In the framework of the Lindblad theory for open quantum systems, a master equation for the quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived for the case when the interaction is based on deformed algebra. The equations of motion for observables strongly depend on the deformation function. The expectation values of the number o...

We construct the symmetric functional model for an arbitrary closed operator with a non-empty resolvent set acting on a separable Hilbert space. The main techniques of the study are based on the explicit form of the Sz.-Nagy-Foiaş model for a closed dissipative operator, the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried ...