Is the dynamics of open quantum systems always linear?

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.Comment: 19 pages, 3 figures, minor changes to improve readability, discussion on Mori's linear regime and references adde

An intrusion layer in stationary incompressible fluids Part 2: A solitary wave

The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg-de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces

An intrusion layer in stationary incompressible fluids Part 2: A solitary wave

The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg-de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces

Optical Limiting and Theoretical Modelling of Layered Transition Metal Dichalcogenide Nanosheets

Nonlinear optical property of transition metal dichalcogenide (TMDC) nanosheet dispersions, including MoS2, MoSe2, WS2, and WSe2, was performed by using Z-scan technique with ns pulsed laser at 1064 nm and 532 nm. The results demonstrate that the TMDC dispersions exhibit significant optical limiting response at 1064 nm due to nonlinear scattering, in contrast to the combined effect of both saturable absorption and nonlinear scattering at 532 nm. Selenium compounds show better optical limiting performance than that of the sulfides in the near infrared. A liquid dispersion system based theoretical modelling is proposed to estimate the number density of the nanosheet dispersions, the relationship between incident laser fluence and the size of the laser generated micro-bubbles, and hence the Mie scattering-induced broadband optical limiting behavior in the TMDC dispersions

Existence of global weak solutions to compressible isentropic finitely extensible nonlinear bead-spring chain models for dilute polymers

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier-Stokes system in a bounded domain $\Omega$ in $\mathbb{R}^d$, $d = 2$ or $3$, for the density, the velocity and the pressure of the fluid. The right-hand side of the Navier-Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. The elastic extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a nonnegative initial density for the continuity equation; a square-integrable initial velocity datum for the Navier-Stokes momentum equation; and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian associated with the spring potential in the model, we prove, via a limiting procedure on certain discretization and regularization parameters, the existence of a global-in-time bounded-energy weak solution to the coupled Navier-Stokes-Fokker-Planck system, satisfying the prescribed initial condition.Comment: 83 pages, 1 figure. arXiv admin note: text overlap with arXiv:1112.4781, arXiv:1004.143

Mixed convection dissipative viscous fluid flow over a rotating cone by way of variable viscosity and thermal conductivity

AbstractThe effects of temperature-dependent viscosity and thermal conductivity on the flow and heat transfer characteristics of a viscous fluid over a rotating vertical cone are premeditated. The properties of the fluid are assumed to be constant except for the density difference with the temperature. Also, the effect of viscous dissipation is considered in the energy equation. The highly nonlinear unsteady equations are converted into a system of nonlinear ordinary differential equations which is solved by using Homotopy analysis method. The interesting findings for different pertinent parameters on momentum, energy, skin friction coefficient and local Nusselt number are demonstrated in the form of graphs and tables. A comparison has been made with literature as a limiting case of the well-chosen unsteady problem