相关论文: Global Optimization by Adiabatic Switching
Minimum energy conical intersections can be used to rationalize photochemical processes. In this Letter, we examine an algorithm to locate these structures that does not require the evaluation of nonadiabatic coupling vectors, showing that…
Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within N-soliton train of the nonlinear Schrodinger equation (NLS). Perturbations induced by weak quadratic and periodic external…
The degenerate Landau-Zener-Majorana-St\"uckelberg model consists of two degenerate energy levels whose energies vary with time and in the presence of an interaction which couples the states of the two levels. In the adiabatic limit, it…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1/\beta\in(0,\infty)$. The ground state is a periodic lattice. We show that when the…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…
We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the…
We study the local and global well-posedness for the coupled system of Schr\"odinger and Kawahara equations on the real line. The Sobolev space $L^{2} \times H^{-2}$ is the space where the lowest regularity local solutions are obtained. The…
This paper addresses the computation of ground states of multicomponent Bose-Einstein condensates, defined as the global minimiser of an energy functional on an infinite-dimensional generalised oblique manifold. We establish the existence…
We present a genetic algorithm for the atomistic design and global optimisation of substitutionally disordered bulk materials and surfaces. Premature convergence which hamper conventional genetic algorithms due to problems with…
We have located the global minimum for all lead clusters with up to 160 atoms using a glue potential to model the interatomic interactions. The lowest-energy structures are not face-centred cubic as suggested previously. Rather, for N<40…
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states…
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…
We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schr{\"o}dinger equation under partial harmonic confinement. We establish a necessary and sufficient condition on the initial data below…
Many-body ground states can be prepared via unitary evolution in cold atomic systems. Given the initial state and a fixed time for the evolution, how close can we get to a desired ground state if we can tune the Hamiltonian in time? Here we…
The ground state properties of the Shastry-Sutherland model in the presence of an external field are investigated by means of variational states built up from unpaired spins (monomers) and singlet pairs of spins (dimers). The minimum of the…
We propose the Adaptive Levenberg-Marquardt Third-Order Newton Method (ALMTON) for unconstrained nonconvex optimization, providing the first globally convergent realization of the unregularized third-order Newton method. Unlike the standard…
Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze a particular method to explain its success in locating global minima…
Hysteretic optimization is a heuristic optimization method based on the observation that magnetic samples are driven into a low energy state when demagnetized by an oscillating magnetic field of decreasing amplitude. We show that hysteretic…
Statistical mechanics is widely applied to solve hard optimization problem, the optimal strategy related to ground state energy that depends on low temperature. Common thermodynamic process is expected to approach the ground state energy if…