Related papers: Decoupled molecules with binding polynomials of bi…
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…
A simple theory is proposed for the dispersive molecular binding of unusually high magnitude due to an enhanced polarizability. Two alternative ways have so far been considered in the literature leading to the polarizability enhancement:…
Multiparticle entangled states generated via interaction between narrow-band light and an ensemble of identical two-level atoms are considered. Depending on the initial photon statistics, correlation between atoms and photons can give rise…
We propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
Parametrized polynomial ordinary differential equation systems are broadly used for modeling, specially in the study of biochemical reaction networks under the assumption of mass-action kinetics. Understanding the qualitative behavior of…
We consider the ideal of inner $2$-minors $I_{\mathcal{P}}$ of a finite set of cells $\mathcal{P}$, which we call the cell ideal of $\mathcal{P}$. A nice interpretation for the height of an unmixed ideal $I_{\mathcal{P}}$, in terms of the…
The goal of structure-based drug discovery is to find small molecules that bind to a given target protein. Deep learning has been used to generate drug-like molecules with certain cheminformatic properties, but has not yet been applied to…
We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.
Understanding the binding dynamics of liquid molecules is of fundamental importance in physical and life sciences. However, nanoscale fast dynamics pose great challenges for experimental characterization. Conventionally, the binding…
Quantum entanglement cannot be unlimitedly shared among arbitrary number of qubits. Larger the number of entangled pairs in an N-qubit system, smaller the degree of bi-partite entanglement is. We analyze a system of N qubits in which an…
For certain polynomials we relate the number of roots inside the unit circle with the index of a non-degenerate isolated umbilic point on a real analytic surface in Euclidean 3-space. In particular, for $N>0$ we prove that for a certain…
Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops…
We study polynomial systems whose equations have as common support a set C of n+2 points in Z^n called a circuit. We find a bound on the number of real solutions to such systems which depends on n, the dimension of the affine span of the…
We reproduced the initial sticking probability of O$_{2}$/Al(111) by use of spin-polarized density functional theory and quantum dynamics calculations. We found a large activation barrier when the molecule is dissociatively adsorbed through…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
Like ordinary molecules are composed of atoms, colloidal molecules consist of several species of colloidal particles tightly bound together. If one of these components is self-propelled or swimming, novel "active colloidal molecules"…
This is a continuation of the early paper concerning matroid base polytope decomposition. Here, we will present sufficient conditions on $M$ so its base matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter yields to…
Coupled colloidal quantum dot molecules are an emerging class of nanomaterials, introducing new degrees of freedom for designing quantum dot-based technologies. The properties of multiply excited states in these materials are crucial to…
We review some results on the ionization conjecture, which says that a neutral atom can bind at most one or two extra electrons.
We discuss several aspects of multiparticle mixed state entanglement and its experimental detection. First we consider entanglement between two particles which is robust against disposals of other particles. To completely detect these kinds…