scholarly journals Ultracold Bosons on a Regular Spherical Mesh

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1289
Author(s):  
Santi Prestipino
Keyword(s):  
Phase Behavior ◽  
Quantum System ◽  
Mean Field ◽  
Ground States ◽  
Hard Core ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Hubbard Hamiltonian ◽  
The Mean ◽  
Theoretical Results

Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (“Platonic mesh”) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.

scholarly journals Особенности фазовой диаграммы полужестких бозонов на квадратной решетке

2021 ◽  
Vol 63 (9) ◽  
pp. 1361
Author(s):  
В.В. Конев ◽  
Ю.Д. Панов
Keyword(s):  
Mean Field ◽  
Hard Core ◽  
Field Approximation ◽  
Charge Ordering ◽  
Mean Field Approximation ◽  
New Order ◽  
Model Parameters ◽  
Local Correlation ◽  
The Mean ◽  
Limit Form

We investigated the phase diagrams of a system of charged semi-hardcore bosons in the mean-field approximation. It is shown that an increase in the local correlation parameter leads to the transformation of the phase diagram of the system from the form characteristic of hard-core bosons to the limit form with a parabolic dependence of the critical temperature of the charge ordering on the boson concentration. The evolution between these limiting cases depends on the ratio of the model parameters and is accompanied by various effects, including a change in the type of phase transition, the appearance of new order-order transitions, and the appearance of new critical points.

INTERACTING BOSONIC ATOMS WITH RANDOM POTENTIAL IN OPTICAL LATTICES

2009 ◽  
Vol 23 (11) ◽  
pp. 1391-1404
Author(s):  
WEI LIU ◽  
JIAN-YANG ZHU
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field Theory ◽  
Mean Field ◽  
Temperature Phase ◽  
Optical Parameters ◽  
Xxz Model ◽  
Bose Glass ◽  
The Mean ◽  
Bosonic Atoms

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder.

scholarly journals Degenerate approach to the mean field Bose-Hubbard Hamiltonian

2016 ◽  
Vol 89 (4) ◽  
Author(s):  
Alexander M. Belemuk ◽  
Valentin N. Ryzhov
Keyword(s):  
Mean Field ◽  
Hubbard Hamiltonian ◽  
The Mean

scholarly journals An analytical framework for consensus-based global optimization method

2018 ◽  
Vol 28 (06) ◽  
pp. 1037-1066 ◽  
Author(s):  
José A. Carrillo ◽  
Young-Pil Choi ◽  
Claudia Totzeck ◽  
Oliver Tse
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Mean Field ◽  
Optimization Method ◽  
Analytical Framework ◽  
Global Minimizer ◽  
Global Optimization Method ◽  
The Mean ◽  
Class Of Functions ◽  
Theoretical Results

In this paper, we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions. Theoretical results on consensus estimates are then illustrated by numerical simulations where variants of the method including nonlinear diffusion are introduced.

QUADRUPOLE DEFORMATION IN NUCLEI AT FINITE TEMPERATURE

1998 ◽  
Vol 13 (33) ◽  
pp. 2705-2713 ◽  
Author(s):  
B. J. COLE ◽  
H. G. MILLER ◽  
R. M. QUICK
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Quadrupole Deformation ◽  
Mean Field Approximation ◽  
Zero Temperature ◽  
Average Deformation ◽  
The Mean ◽  
Shape Changes

The intrinsic quadrupole deformation has been calculated at finite temperature in 20 Ne both in the mean-field approximation and using an exact shell model diagonalization. The results support the view that the phase transition seen at finite temperature in mean-field calculations is not due to the change in nuclear shape from deformed to spherical, but rather is a collective-to-non-collective transition. Both calculations indicate that the average deformation of 20 Ne changes from β rms ≈0.31 at zero temperature to just over β rms =0.2 at T=3.0 MeV. The calculations also suggest that, in the mean-field approximation, the square of the quadrupole operator, Q[2]·Q[2], is a better indicator of shape changes than Q[2] itself.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

scholarly journals Supersolids of Hard Core - Bosons on a Triangular Lattice

2011 ◽  
Vol 21 (4) ◽  
pp. 301
Author(s):  
Nguyen Toan Thang ◽  
Pham Thi Thanh Nga
Keyword(s):  
Long Range ◽  
Triangular Lattice ◽  
Mean Field Theory ◽  
Mean Field ◽  
Hard Core ◽  
Xxz Model ◽  
Supersolid Phase ◽  
The Mean ◽  
Boson Model ◽  
Broad Region

We study the boson model on a triangular lattice interacting only via on-site hardcore repulsion by mapping to a system of spins $(S = 1/2)$. We investigate the supersolid phase of the systems which is a state matter displaying both diagonal long- range (solid) order as well as off-diagonal long-range (superfluidity) by utilizing a semionic representation for the spin-XXZ model. We show that the supersolid order is stable in the mean-field theory for a broad region of parameters. The inclusion of spin wave corrections modifies this picture, but the supersolid phase is still quite robust on the triangular lattices.

scholarly journals UNDERSCREENED KONDO NECKLACE

1992 ◽  
Vol 06 (26) ◽  
pp. 1681-1690 ◽  
Author(s):  
P. FAZEKAS ◽  
HAE-YOUNG KEE
Keyword(s):  
Mean Field ◽  
Magnetic Ordering ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Temperature Phase ◽  
Kondo Problem ◽  
Fermion Systems ◽  
Type Interaction ◽  
The Mean ◽  
Low Temperature Phase

It has been suggested recently by Gan, Coleman, and Andrei that studying the underscreened Kondo problem may help to understand the nature of magnetism in heavy fermion systems. Motivated by Doniach’s work on the S=1/2 Kondo necklace, we introduce the underscreened Kondo necklace models with S>1/2. The underscreened Kondo necklace is the simplest lattice model on which the competition between Kondo spin compensation, and magnetic ordering due to an RKKY-type interaction can be examined. We used the mean-field approximation to determine the phase diagram, and found that the low-temperature phase is always an x−y antiferromagnet. This contention is further supported by the derivation of the exact form of the effective Hamiltonian in the limit of very large Kondo coupling: it is found to be an antiferromagnetic x−y model for the residual S−1/2 spins. In general, the degree of moment compensation depends on both the Kondo coupling, and on S.

INTERACTIONS AND MOLECULAR ORIENTATIONS IN SOLID C60

1999 ◽  
Vol 13 (03) ◽  
pp. 253-281 ◽  
Author(s):  
P. LAUNOIS ◽  
S. RAVY ◽  
R. MORET
Keyword(s):  
Review Paper ◽  
Mean Field ◽  
High Temperature Phase ◽  
Scattering Data ◽  
Intermolecular Potential ◽  
Temperature Phase ◽  
Single Model ◽  
Molecular Dynamics Calculations ◽  
The Mean ◽  
Present Understanding

In spite of recent progress, our present understanding of the intermolecular interactions in solid C 60 is still imperfect and no single model is able to describe correctly its whole physical properties. These interactions induce elaborate orientational properties which have motivated thorough investigations. In this review paper we concentrate on the orientational properties in the high temperature phase. It is shown how the preferred orientations and the orientational correlations could be accessed through the analysis of the Bragg and diffuse scattering intensity data. The results obtained using either mean-field treatments or molecular dynamics calculations have brought information on the existence of competing local orientational orders. The scattering data have also been exploited to discriminate between different models of intermolecular potential. Within the mean-field treatment, necessary conditions for any model to satisfy scattering results are put forward.

Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations

2017 ◽  
Vol 10 (4) ◽  
pp. 798-828 ◽  
Author(s):  
Yabing Sun ◽  
Jie Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Taylor Expansion ◽  
Mean Field ◽  
Strong Convergence Theorem ◽  
The Mean ◽  
New Formula ◽  
Strong Order ◽  
Taylor Scheme ◽  
Theoretical Results

AbstractThis paper is devoted to numerical methods for mean-field stochastic differential equations (MSDEs). We first develop the mean-field Itô formula and mean-field Itô-Taylor expansion. Then based on the new formula and expansion, we propose the Itô-Taylor schemes of strong order γ and weak order η for MSDEs, and theoretically obtain the convergence rate γ of the strong Itô-Taylor scheme, which can be seen as an extension of the well-known fundamental strong convergence theorem to the mean-field SDE setting. Finally some numerical examples are given to verify our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document