相关论文: The flux phase problem on the ring
We study the dynamics of pure phase decoherence for a particle hopping around an N-site ring, coupled both to a spin bath and to an Aharonov-Bohm flux which threads the ring. Analytic results are found for the dynamics of the influence…
We consider almost minimizers to the thin-one phase energy functional and we prove optimal regularity of the solution and partial regularity of the free boundary. We thus recover the theory for energy minimizers. Our methods are based on a…
The following problem, which stems from the ``flux phase'' problem in condensed matter physics, is analyzed and extended here: One is given a planar graph (or lattice) with prescribed vertices, edges and a weight $\vert t_{xy}\vert$ on each…
Diffusive operations, which mix the populations of different elements of phase space, can irreversibly transform a given initial state into any of a spectrum of different states from which no further energy can be extracted through…
This paper concerns the shape optimization problem of minimizing the ground state energy of the magnetic Dirichlet Laplacian with constant magnetic field among three-dimensional domains of fixed volume. In contrast to the two-dimensional…
The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
We consider the ground state energy of the Bose--Hubbard model on a graph with large and homogeneous coordination number. In the limit of infinite coordination number, we prove convergence of the ground state energy to the minimizer of a…
We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $\mathbb R^{n+1}_+$ plus the area of the positivity set of that function in $\mathbb R^n$. We establish full…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
A new numerical method to calculate exact ground states of multi-fluxline systems with quenched disorder is presented, which is based on the minimum cost flow algorithm from combinatorial optimization. We discuss several models that can be…
The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the $\mu-U$ plane, restricted to phases with no charge density modulation, extending the results presented in cond-mat/9511116. This allows…
The physical properties of striped Hall state in the presence of an external unidirectional periodic potential is investigated. The study of searching the optimal orientation of the state is reported for the state at filling factor…
According to the `folk knowledge', the Hartree-Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling $U$ (the smaller $|U|$, the better is the H-F approximation). In \cite{BP} Bach and Poelchau…
In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that…
Analytical models describing the motion of colloidal particles in given velocity fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker-Planck equations, a global…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
Phase separation may be driven by the minimization of a suitable free energy ${\cal F}$. This is the case, e.g., for diblock copolimer melts, where ${\cal F}$ is minimized by a steady periodic pattern whose wavelength $\lambda_{GS}$ depends…
A significant challenge in quantum annealing is to map a real-world problem onto a hardware graph of limited connectivity. If the maximum degree of the problem graph exceeds the maximum degree of the hardware graph, one employs minor…