Related papers: Stanley decompositions and localization
We show that the Stanley's conjecture holds for any multigraded $S$-module $M$ with $\sdepth(M)=0$, where $S=K[x_1,...,x_n]$. Also, we give some bounds for the Stanley depth of the powers of the maximal irrelevant ideal in $S$.
We compute the depth and Stanley depth for the quotient ring of the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv…
We give sharp bounds for the Stanley depth of a special class of ideals of Borel type.
We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the…
In this paper we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated to classes of graphs obtained by taking the strong product of two graphs. We consider the cases when either both graphs are…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a…
In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module $M$ over the polynomial ring $\mathbb{K}[X_1, \ldots, X_n]$. As an application, we give an example of a module whose Stanley…
It is reported a combined numerical approach to study the localization properties of the one-dimensional tight-binding model with potential modulated along the prime numbers. A localization-delocalization transition was found as function of…
We define and study a variant of the \emph{Stanley depth} which we call \emph{total depth} for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from $\llbracket S_k\rrbracket$ -- the poset of…
Let $J\subset I$ be monomial ideals. We show that the Stanley depth of $I/J$ can be computed in a finite number of steps. We also introduce the $\fdepth$ of a monomial ideal which is defined in terms of prime filtrations and show that it…
In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive…
We study a partially disordered one-dimensional system with interacting particles. Concretely, we impose a disorder potential to only every other site, followed by a clean site. Our numerical analysis of eigenstate properties is based on…
We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model,…
We consider isolated quantum systems with all of their many-body eigenstates localized. We define a sense in which such systems are integrable, and discuss a method for finding their localized conserved quantum numbers ("constants of…
In this paper we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial ring and the exterior algebra behave with respect to Alexander duality.
An alternative explanation of the physical nature of Anderson localization phenomenon and one of the most direct ways of its experimental study are discussed.
In this paper we show that the depth and the Stanley depth of the factor of two monomial ideals is invariant under taking a so called canonical form. It follows easily that the Stanley Conjecture holds for the factor if and only if it holds…
Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by four squarefree monomials of degrees $d$ and others of…