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By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in ${\Cb}^{K_1} \otimes {\Cb}^{K_2} \otimes ... \otimes {\Cb}^{K_m} \otimes {\Cb}^N$…
Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
We study how measures with finite lower density are distributed around $(n-m)$-planes in small balls in $\mathbb{R}^n$. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
The studies of the generalized Einstein Lagrangian densities without torsion are extended to those of the more generalized Lagrangian densities with torsion. The properties of the more generalized Lagrangian densities are studied…
We resolve a problem posed by Mattila, Serapioni and Serra Cassano concerning the role of density assumptions in the characterization of rectifiable sets of low codimension in Heisenberg groups. Specifically, we prove that the positive…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e inequality, we show that every set satisfying a suitable capacitary density condition is removable for Newton-Sobolev functions.
A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
It is shown that when the initial particles probability density is discontinuous the emerging currents appear instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value.…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…