Structure of uniform estimates in partial phase deformation

1990 ◽  
pp. 247-250
Author(s):  
V. Karpushkin
Keyword(s):  
Partial Phase ◽  
Uniform Estimates ◽  
Phase Deformation

scholarly journals Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

2021 ◽  
Vol 182 (2) ◽  
Author(s):  
Li Chen ◽  
Jinyeop Lee ◽  
Matthew Liew
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Weak Limit ◽  
Weak Compactness ◽  
Three Dimensions ◽  
Uniform Estimates ◽  
Fermionic Systems ◽  
Semiclassical Limits ◽  
Semiclassical Regime

AbstractWe study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

2021 ◽  
pp. 1-29
Author(s):  
ALEXANDER BRUDNYI
Keyword(s):  
Disjoint Union ◽  
A Priori ◽  
Holomorphic Functions ◽  
Stable Rank ◽  
Open Unit ◽  
Uniform Estimates ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Similar Approximation ◽  
Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

Uniform Estimates on the Tsallis Entropies

2007 ◽  
Vol 80 (2) ◽  
pp. 171-181 ◽  
Author(s):  
Zhengmin Zhang
Keyword(s):  
Uniform Estimates

scholarly journals Uniform Estimates of Nonlinear Spectral Gaps

2014 ◽  
Vol 31 (5) ◽  
pp. 1517-1530
Author(s):  
Takefumi Kondo ◽  
Tetsu Toyoda
Keyword(s):  
Spectral Gaps ◽  
Uniform Estimates

Stepwise conductance control of niobium nanocontacts by partial phase transformation

2021 ◽  
pp. 110247
Author(s):  
Yusuke Ochiai ◽  
Takuya Obi ◽  
Yuuki Tsuruoka ◽  
Tokushi Kizuka
Keyword(s):  
Phase Transformation ◽  
Partial Phase

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

Partial Phase Diagram of BaO-TeO2 System

2014 ◽  
Vol 35 (2) ◽  
pp. 127-136 ◽  
Author(s):  
R. Mishra ◽  
S. Phapale ◽  
P. Samui ◽  
A. Nagaraj ◽  
S. R. Dharwadkar
Keyword(s):  
Phase Diagram ◽  
Partial Phase Diagram ◽  
Partial Phase
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