A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons

We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phases, all having a regular or semiregular polyhedron as supporting frame for the clusters. The present results are relevant for the behavior of ultracold bosons weakly coupled to a Rydberg state.

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Computer Simulations and Statistical Theory of Normal Grain Growth in Two and Three Dimensions

Materials Science Forum ◽

10.4028/www.scientific.net/msf.467-470.1129 ◽

2004 ◽

Vol 467-470 ◽

pp. 1129-1136 ◽

Cited By ~ 11

Author(s):

Dana Zöllner ◽

Peter Streitenberger

Keyword(s):

Field Theory ◽

Grain Size ◽

Size Distribution ◽

Grain Growth ◽

Grain Size Distribution ◽

Mean Field Theory ◽

Mean Field ◽

Three Dimensions ◽

Monte Carlo Algorithm ◽

Geometric Properties

A modified Monte Carlo algorithm for single-phase normal grain growth is presented, which allows one to simulate the time development of the microstructure of very large grain ensembles in two and three dimensions. The emphasis of the present work lies on the investigation of the interrelation between the local geometric properties of the grain network and the grain size distribution in the quasi-stationary self-similar growth regime. It is found that the topological size correlations between neighbouring grains and the resulting average statistical growth law both in two and three dimensions deviate strongly from the assumptions underlying the classical Lifshitz- Sloyzov-Hillert theory. The average local geometric properties of the simulated grain structures are used in a statistical mean-field theory to calculate the grain size distribution functions analytically. By comparison of the theoretical results with the simulated grain size distributions it is shown how far normal grain growth in two and three dimensions can successfully be described by a mean-field theory and how stochastic fluctuations in the average growth law must be taken into account.

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Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

Materials Science Forum ◽

10.4028/www.scientific.net/msf.550.589 ◽

2007 ◽

Vol 550 ◽

pp. 589-594 ◽

Cited By ~ 1

Author(s):

Dana Zöllner ◽

Peter Streitenberger

Keyword(s):

Field Theory ◽

Grain Size ◽

Monte Carlo ◽

Distribution Function ◽

Grain Growth ◽

Mean Field Theory ◽

Mean Field ◽

Size Distribution Function ◽

Three Dimensions ◽

Self Similar

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

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Efficiently Generalizing Ultra-Cold Atomic Simulations via Inhomogeneous Dynamical Mean-Field Theory from Two- to Three-Dimensions

2010 DoD High Performance Computing Modernization Program Users Group Conference ◽

10.1109/hpcmp-ugc.2010.17 ◽

2010 ◽

Cited By ~ 1

Author(s):

J. K. Freericks ◽

H. R. Krishnamurthy ◽

P. Carrier ◽

Y. Saad

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Three Dimensions ◽

Dynamical Mean Field Theory ◽

Atomic Simulations

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Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

Materials Science Forum - Fundamentals of Deformation and Annealing ◽

10.4028/0-87849-434-0.589 ◽

2007 ◽

pp. 589-594

Author(s):

Dana Zöllner ◽

Peter Streitenberger

Keyword(s):

Field Theory ◽

Monte Carlo ◽

Grain Growth ◽

Potts Model ◽

Model Simulation ◽

Mean Field Theory ◽

Mean Field ◽

Three Dimensions

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ALLOY ANALOG APPROACH AND THE GUTZWILLER APPROXIMATION AS PARTICULAR CASES OF A MEAN-FIELD THEORY

International Journal of Modern Physics B ◽

10.1142/s021797929200147x ◽

1992 ◽

Vol 06 (20) ◽

pp. 3341-3352 ◽

Cited By ~ 3

Author(s):

A.A. ALIGIA ◽

M. AVIGNON

Keyword(s):

Field Theory ◽

Saddle Point ◽

Mean Field Theory ◽

Mean Field ◽

Functional Integral ◽

Three Dimensions ◽

Atomic Limit ◽

Analog Approach ◽

Metal To Insulator Transition ◽

Insulating Phase

We develop a new mean field-theory for systems with on-site correlations, like the Hubbard and Anderson models. It consists in a generalization of the saddle-point approximation to the functional integral representation proposed by Kotliar and Ruckenstein to more than one saddle point. It contains also the alloy analog approximation proposed by Hubbard as a particular case. For a half-filled Hubbard model and a model density of states appropriate for three dimensions, we obtain a metal to insulator transition as U increases. The effective Hamiltonian for the insulating phase contains two split bands (rather than only one with an extremely heavy mass) which reproduce correctly the Green’s functions of the atomic limit.

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Delays and weakly coupled neuronal oscillators

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2008.0259 ◽

2009 ◽

Vol 367 (1891) ◽

pp. 1097-1115 ◽

Cited By ~ 48

Author(s):

Bard Ermentrout ◽

Tae-Wook Ko

Keyword(s):

Travelling Waves ◽

Mean Field Theory ◽

Mean Field ◽

Coupled Systems ◽

State Variables ◽

Weakly Coupled ◽

Neuronal Oscillators ◽

Dendritic Branches ◽

Oscillator Theory

We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use mean field theory to show the emergence of travelling waves and the loss of synchronization. Next, we consider phase models with stronger coupling and delays in the state variables. We show that they have a richer dynamics but one that is still similar to the weakly coupled case.

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