Temperature phase transitions associated with local minima of energy

We develop an alternative version of the theory of contour models adapted to continuous spins located in sites of a ($d⩾2$)-dimensional lattice. The spins interacting via nearest-neighbor ferromagnetic interactions are embedded in a single spin potential $V$ similar to that already introduced by Dobrushin and Shlosman. The potential $V$ has a finite-ordered sequence of local minima and satisfy certain conditions. For all finite-reciprocal temperatures less than one, we prove the Peierls condition and we show that there exists a sequence of first-order phase transition temperature points.     

Networks of local minima in optical system optimization

We discuss a surprising new feature of the merit function landscape in optical system design. When certain conditions are satisfied, the local minima form a network in which all nodes are connected. Each link between two neighboring minima contains a saddle point with a Morse index of 1. For a simple global optimization search (the symmetric Cooke triplet), the network of the corresponding set of local minima is presented.     

Phase transitions and local minima of the action

We present evidence that non-trivial, non-degenerate local minima of the one-plaquette action in 4-dimensional lattice gauge theories with continuous gauge groups, give rise to a line of first-order “discreteness” phase transitions, persisting down to the region where the non-trivial minima become unstable. We illustrate this mechanism by analysing an extended model, involving the traces in the fundamental and six representation of SU(3), in which neither the topology, nor the group theoretic properties of the centre seem to play any role.     

Effect of local minima on adiabatic quantum optimization

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.     

Communities of minima in local optima networks of combinatorial spaces

In this work, we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.     

Method for creating hollow light beams with local intensity minima and possibilities for their application

We propose and experimentally realize methods for forming light beams with local spatial intensity minima of different types (hollow light beams), based on application of specially shaped linear optics phase elements. The fields with local intensity minima, obtained as a result of phase conversion, are comparable with respect to transverse dimensions, power, and intensity gradient to the initial gaussian beam focused by means of a spherical lens. The optical layouts were assembled using photostable optical elements and therefore make it possible to create high-power laser fields suitable not only for manipulation of microparticles but also for laser machining of materials, in particular laser welding of metals. Using a phase element with planar symmetry, we can select the optimal laser beam profile that will ensure no burning on the line of contact between the ends of the parts to be welded for high penetration and will make it possible to achieve the maximum possible strength of the weld joint for a specified laser radiation power.     

Nature of interacting electron states of Coulomb glass in local energy minima

Non-equilibrium relaxation of Coulomb glass in disordered thin films is investigated by kinetic Monte Carlo simulation. We numerically confirm aging phenomena in the autocorrelation function C(t, t_W ) in a quasi-two-dimensional system with finite thickness and clarify the effect of an external electric field on the elongated relaxation time due to aging. We also study the statistical properties of electron states belonging to local energy minima in random site models. Our results highlight the difference in the properties of energy landscape between two different models to describe Coulomb glass, called the random site model and the lattice model.     

Judd—Ofelt parametrizations for lanthanides: sensitivity analysis of multiple local minima

For most symmetries the standard parametrization of one-photon electric-dipole transitions between crystal-field levels of the 4f^N configuration of lanthanide ions gives the same predictions for several quite different parameter sets. An alternative parametrization scheme which provides separate parameters for each of the different polarization directions has been shown to remove this anomaly. A second problem arises due to the fact that multiple local minima may fit the data nearly equally well. Through a detailed re-examination of the previously well-studied lanthanide oxydiacetate (LnODA) systems, where Ln = Nd, Sm, Eu, Dy, Ho and Er, we examine the multiple local minima problem. Parameter robustness is determined by means of an analysis of the sensitivity of the local minima with respect to perturbation of experimental intensities and rotatory strengths. Inclusion of circular dichroism rotatory strengths in the calculation is shown to greatly reduce the total number of local minima which must be considered, resulting in much better determination of the overall intensity parameter values.     

Minimal potentials with very many minima

We demonstrate, by construction, that simple renormalizable matrix potentials with S(N), as opposed to O(N), symmetry can exhibit an exponentially large number of inequivalent deep local minima.     

Mutated and converged damping factors in lens system optimization to find new local minima

In this paper, we proposed a strategy to find new local minima based on mutated damping factors and converged damping factor (conventional damping factor). In this proposed strategy, the converged damping factor is used to make the algorithm converge to a certain local minimum, and the mutated damping factors are used to make the trapped solution jump out of present convergence area. We study the behavior of the two kinds of factors in lens system optimization. The proposed strategy is successfully applied in lens system optimization. The result shows that the proposed strategy is reliable to make a further improvement especially when the solution is approaching target design.     

Magnetohydrodynamics computations with lattice gas automata

Lattice gas automata have received considerable interest for the last several years and possibly may become a powerful numerical method for solving various partial differential equations and modeling different physical phenomena, because of their discrete and parallel nature and the capability of handling complicated boundaries. In this paper, we present recent studies on the lattice gas model for magnetohydrodynamics. The FHP-type lattice gas model has been extended to include a bidirectional random walk process, which allows well-defined statistical quantities, such as velocity and magnetic field, to be computed from the microscopic particle representation. The model incorporates a new sequential particle collision method to increase the range of useful Reynolds numbers in the model, an improvement that may also be of use in other lattice gas models. In the context of a Chapman-Enskog expansion, the model approximates the incompressible magnetic hydrodynamic equations in the limit of low Mach number and high. Simulation results presented here demonstrate the validity of the model for several basic problems, including sound wave and Alfvén wave propagation, and diffusive Kolmogoroff-type flows.     

The global minimum of energy is not always a sum of local minima—A note on frustration

A classical lattice gas model with translation-invariant, finite-range competing interactions, for which there does not exist an equivalent translation-invariant, finite-range nonfrustrated potential, is constructed. The construction uses the structure of nonperiodic ground-state configurations of the model. In fact, the model does not have any periodic ground-state configurations. However, its ground-state—a translation-invariant probability measure supported by ground-state configurations—is unique.     

Simulated quantum computation of global minima

Finding the optimal solution to a complex optimisation problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations N reduced from O(N) in classical simulation to O(N ^1/2) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimisation to treat larger systems.     

Resistance minima in amorphous PdSi alloy

The resistivity minimum in amorphous PdSi containing transition metals is magnetic in origin. For high purity samples a weak minimum, possibly associated with residual Fe impurity, is removed by a mild heat-treatment known to reduce the density of localized “tunneling” states.     

Resistivity minima in quench-condensed films of palladium

We have found a shallow low temperature minimum in the electrical resistivity of thin quench-condensed Pd-films. The depth and temperature of this minimum depends upon the residual resistivity of the film.