相关论文: The flux phase problem on the ring
We study the evolution of nearest-neighbor entanglement in the one dimensional Ising model with an external transverse field. The system is initialized as the so called "thermal ground state" of the pure Ising model. We analyze properties…
We study a two-dimensional cylindrically-symmetric electron droplet separated from a surrounding electron ring by a tunable barrier using the exact diagonalization method. The magnetic field is assumed strong so that the electrons become…
We consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein,…
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
In any dimension $N \geq 1$, for given mass $m > 0$ and for the $C^1$ energy functional \begin{equation*} I(u):=\frac{1}{2}\int_{\mathbb{R}^N}|\nabla u|^2dx-\int_{\mathbb{R}^N}F(u)dx, \end{equation*} we revisit the classical problem of…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
According to energy band theory, ground states of a normal conductor and insulator can be obtained by filling electrons individually into energy levels, without any restrictions. It fails when the electron-electron correlation is taken into…
We present a new method that accurately approximates the shell-model ground-state by products of suitable states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional…
We derive an upper bound on the ground state energy of the three-dimensional (3D) repulsive Hubbard model on the cubic lattice agreeing in the low density limit with the known asymptotic expression of the ground state energy of the dilute…
The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy…
An elementary proof of Robinson's Energy Delay Theorem on minimum-phase functions is presented. The proof is generalized to the matrix case as well.
Under certain simplifying conditions we detect monotonicity properties of the ground-state energy and the canonical-equilibrium density matrix of a spinless charged particle in the Euclidean plane subject to a perpendicular, possibly…
We call \emph{Alphabet model} a generalization to N types of particles of the classic ABC model. We have particles of different types stochastically evolving on a one dimensional lattice with an exchange dynamics. The rates of exchange are…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
We establish the phase diagram of the Hubbard model on a cubic lattice for a wide range of temperatures, dopings and interaction strengths, considering both commensurate and incommensurate magnetic orders. We use the dynamical mean-field…
We present a set of {\em optimum ground states} for a large class of spin-$\frac{3}{2}$ chains. Such global ground states are simultaneously ground states of the local Hamiltonian, i.e. the nearest neighbour interaction in the present case.…
We study the closest disentangled state to a given entangled state in any system (multi-party with any dimension). We obtain the set of equations the closest disentangled state must satisfy, and show that its reduction is strongly related…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani, our result proves that in the low density limit, the leading…