In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dYt = −AYtdt−f0(t, Yt)dt−f1(t, Yt, Zt)dt+ZtdWt, 0 ≤ t ≤ T ; YT = ξ in an infinite dimensional Hilbert space H , where the unbounded operator A is sectorial and dissipative and the nonlinearity f0(t, y) is dissipative and defined for y only taking values in a subspace of H . A typical example is prov...

In the context of non-critical Liouville strings, we clarify why we expect non-quantum-mechanical dissipative effects to be O(E2/M P), where E is a typical energy scale of the probe, and M P is the Planck scale. In Liouville strings, energy is conserved at best only as a statistical average, as distinct from Lindblad systems, where it is strictly conserved at an operator level, and the magnitud...

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group method...

We present a new variational method based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus, allowing for a faster convergence ...

Abstract In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces L p (ℝ n ), Hardy H ) general mixed norm spaces, which implies almost everywhere convergence of such operator. this paper, we study rate some sobolev type spaces.

The two-dimensional (2D) quasi-geostrophic (QG) equation is a 2D model of the 3D incompressible Euler equations, and its dissipative version includes an extra term bearing the operator (−∆)α with α ∈ [0, 1]. Existing research appears to indicate the criticality of α = 1 2 in the sense that the issue of global existence for the 2D dissipative QG equation becomes extremely difficult when α ≤ 1 2 ...

We study a quantumharmonic oscillator linearly coupled through the position operator q̂ to a first bath and through themomentumoperator p̂ to a second bath yielding anOhmic–Drude dissipation. We analyse the oscillator’sfluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation inwhich the two dissipative interactions are comparable. ...

A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad’s angular cut-off condition. Two proofs are given: a non-constructive one, based on the decomposition of the collision operator into a compact and a coercive part, and a constructiv...

We introduce the notion of a symmetrizable finite difference operator and prove that such operators are stable. We then present some sufficient conditions for symmetrizability. One of these extends H.-O. Kreiss' theorem on dissipative difference schemes for hyperbolic equations to a more general case with full (jc , invariable coefficients.

For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.