相关论文: Bloch Equations and Completely Positive Maps

We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…

The concept of weak invariants has recently been introduced in the context of conserved quantities in finite-time processes in nonequilibrium quantum thermodynamics. A weak invariant itself has a time-dependent spectrum, but its expectation…

We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of (or less) completely positive maps, where d is the dimension of the system. Only one such map is required…

We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…

A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum…

We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…

A proof using the theory of completely positive maps is given to the fact that if $A \in M_2$, or $A \in M_3$ has a reducing eigenvalue, then every bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the form $I \otimes…

A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate…

The Vlasov equation embodies the smooth field approximation of the self-consistent equation of motion for charged particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual…

We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…

We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…

We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…

In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…

We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a…

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents…

We present an analysis of complete positivity (CP) constraints on qutrit quantum channels that have a form of affine transformations of generalized Bloch vector. For diagonal (damping) channels we derive conditions analogous to the ones…

What is the probability that all the gas in a box accumulates in the same half of this box? Though amusing, this question underlies the fundamental problem of density fluctuations at equilibrium, which has profound implementations in many…

The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case…