Related papers: Doubly connected V-states for the planar Euler equ…
In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with $\alpha\in ]0,1[.$ They can be described by countable branches bifurcating from the annulus at some explicit "eigenvalues" related to…
In this paper, we prove the existence of doubly connected V-states (rotating patches) close to an annulus for active scalar equations with completely monotone kernels. This provides a unified framework for various results related to…
In this paper we study the existence of doubly-connected rotating patches for Euler equations when the classical non-degeneracy conditions are not satisfied. We prove the bifurcation of the V-states with two-fold symmetry, however for…
We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha\in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the trivial solution at some…
In this paper, we obtain families of two-fold doubly-connected uniformly rotating vortex patches of the 2-D incompressible Euler equations emanating from some specific annuli. The main difficulty comes from strong degeneracy of the problem,…
In the present contribution, we first prove the existence of $\mathbf{m}$-fold simply-connected V-states close to the unit disc for Euler-$\alpha$ equations. These solutions are implicitly obtained as bifurcation curves from the circular…
We consider the truncated equation for the centrally symmetric $V$-states in the 2d Euler dynamics of patches and prove the existence of solutions $y(x,\lambda),\, x\in [-1,1],\,\lambda\in (0,\lambda_0)$. These functions $y(x,\lambda)\in…
We present an analytically solvable model of $P$ colinear, two-dimensional quantum dots, each containing two electrons. Inter-dot coupling via the electron-electron interaction gives rise to sets of entangled ground states. These ground…
The work is intended to represent some interesting and apparently peculiar features of entangled system in both pure as well as mixed states level. In the pure state level, we are largely concerned about the existence and characteristics of…
We investigate the two-sided symmetric extendibility problem of Werner states. The interplay of the unitary symmetry of these states and the inherent bipartite permutation symmetry of the extendibility scenario allows us to map this problem…
We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown previously that there must be a global functional…
We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly…
We present an explicit family of two-qubit X states with entanglement-preserving unitary (EPU) equivalence to the set of general states; that is, for any spectrum-entanglement combination achievable by general states, this family contains…
Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and…
It is found that $15$ different types of two-qubit $X$-states split naturally into two sets (of cardinality $9$ and $6$) once their entanglement properties are taken into account. We {characterize both the validity and entangled nature of…
Multi-qubit quantum states corresponding to bipartite graphs $G(U,V,E)$ are examined. These states are constructed by applying $CNOT$ gates to an arbitrary separable multi-qubit quantum state. The entanglement distance of the resulting…
In this paper, we study the bipartite entanglement of spin coherent states in the case of pure and mixed states. By a proper choice of the subsystem spins, the entanglement for large class of quantum systems is investigated. We generalize…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
In this somewhat pedagogical paper we revisit complementarity relations in bipartite quantum systems. Focusing on continuous variable systems, we examine the influential class of EPR-like states through a generalization to Gaussian states…