scholarly journals Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling

1972 ◽  
Vol 24 (2) ◽  
pp. 133-150 ◽  
Author(s):  
E. Prugovečki ◽  
E. B. Manoukian
Keyword(s):  
Asymptotic Behaviour ◽  
Momentum Distribution ◽  
Fermion Fields ◽  
Spin Momentum

ASYMPTOTIC BEHAVIOUR OF THE VACUUM ENERGY FOR SMALL SKYRMIONS

1990 ◽  
Vol 05 (18) ◽  
pp. 3549-3597 ◽  
Author(s):  
JOSEF A. ZUK
Keyword(s):  
Field Theory ◽  
Asymptotic Behaviour ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Functional Dependence ◽  
Analytical Approximation ◽  
Low Energy ◽  
Fermion Fields ◽  
Self Consistent ◽  
Vacuum Instability

Various schemes for deriving effective Lagrangians, involving both quark and meson degrees of freedom, which are intermediate between QCD and low-energy pion dynamics have been proposed. While integration over the fermion fields within the framework of renormalized field theory leads to a vacuum instability, physically reasonable results are obtained for the theory taken with finite cut-off. In principle, properties of the nucleon, such as its mass, can be obtained from a self-consistent calculation in the Skyrmion sector. This procedure can be simplified by implementing an analytical approximation for the fermion vacuum energy which plays a central role. We discuss such an approximation, and use it to calculate exactly the asymptotic behaviour of the vacuum energy for small Skyrmions. It is found that, unlike in the renormalized theory, its functional dependence on the Skymion radius in this limit depends on the characteristics of the Skyrmion profile and choice of regularization scheme; however, the cut-off field theory exhibits no vacuum instability.

Prediction of momentum distribution of supercooled atoms in optical lattice using convolutional-recurrent network

2020 ◽  
Vol 28 (7) ◽  
pp. 1480-1484
Author(s):  
Yun-hong LI ◽  
◽  
Hong-hao LI ◽  
Da WEN ◽  
Fan-su WEI ◽  
...  
Keyword(s):  
Momentum Distribution ◽  
Optical Lattice ◽  
Recurrent Network

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

scholarly journals Spin–valley Hall phenomena driven by Van Hove singularities in blistered graphene

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
M. Umar Farooq ◽  
Arqum Hashmi ◽  
Tomoya Ono ◽  
Li Huang
Keyword(s):  
First Principles ◽  
Opposite Sign ◽  
Spin Splitting ◽  
First Principles Calculations ◽  
Van Hove Singularities ◽  
Spin Degree ◽  
Hall Effects ◽  
Back Scattering ◽  
Structural Deformations ◽  
Spin Momentum

AbstractUsing first-principles calculations, we investigate the possibility of realizing valley Hall effects (VHE) in blistered graphene sheets. We show that the Van Hove singularities (VHS) induced by structural deformations can give rise to interesting spin–valley Hall phenomena. The broken degeneracy of spin degree of freedom results in spin-filtered VH states and the valley conductivity have a Hall plateau of ±e2/2h, while the blistered structures with time-reversal symmetry show the VHE with the opposite sign of $$\sigma _{xy}^{K/K^{\prime}}$$ σ x y K / K ′ (e2/2h) in the two valleys. Remarkably, these results show that the distinguishable chiral valley pseudospin state can occur even in the presence of VHS induced spin splitting. The robust chiral spin–momentum textures in both massless and massive Dirac cones of the blistered systems indicate significant suppression of carrier back-scattering. Our study provides a different approach to realize spin-filtered and spin-valley contrasting Hall effects in graphene-based devices without any external field.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

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