Spectral Criterion for Stability of Mean-Field Stochastic Periodic Systems

2020 ◽  
pp. 562-570
Author(s):  
Yuechen Cui ◽  
Hongji Ma
Keyword(s):  
Mean Field ◽  
Periodic Systems ◽  
Spectral Criterion

Electronic Structure and Transport in Non Periodic Systems: New O(N) Methods

1997 ◽  
Vol 491 ◽  
Author(s):  
D. Mayou ◽  
P. E. A. Turchi ◽  
S. Roche ◽  
J. P. Julien
Keyword(s):  
Linear Response ◽  
Mathematical Theory ◽  
Tight Binding ◽  
Mean Field ◽  
Real Space ◽  
The Self ◽  
Field Theories ◽  
Periodic Systems ◽  
New Approach ◽  
Self Consistent

ABSTRACTThe mathematical theory of orthogonal polynomials and continued fractions provides efficient tools, via the recursion and related methods, for calculating diagonal elements of Green's function of tight-binding Hamiltonians. We present two recent generalizations of this formalism. The first one allows the calculation of conductivity and other linear response coefficients. The second one provides a new approach to the solution of mean-field theories of alloys. In particular it is shown that the self-consistent CPA equations can be easily solved, through a real-space calculation, for multi-component alloys based on periodic or non periodic lattices.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results
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