Segovia-López and Romero-Rochín Reply:

Segovia-López, José G.; Romero-Rochı́n, Vı́ctor

doi:10.1103/physrevlett.87.209602

Cited by 10 publications

(23 citation statements)

References 2 publications

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“…The bending and Gaussian rigidity coefficients derived in this way are equal to those derived in the former approach, provided the fifth moment of attractive part of the potential exists. On the other hand in the case of van der Waals interactions the rigidity coefficients for cylindrical and spherical geometries turn into functions of the mean curvature of the interface [6,20,29,30]. This fact has been already noted in the literature.…”

Section: Bending and Gaussian Rigidity Coefficientsmentioning

confidence: 71%

“…Second, from considering the spherical interface (Section 3) one gets the expression for the sum of bending and Gaussian rigidity coefficients. Assuming the geometry independence of these coefficients, one can obtain also the expression for the Gaussian rigidity coefficient [28,29,30,31]. The bending and Gaussian rigidity coefficients derived in this way are equal to those derived in the former approach, provided the fifth moment of attractive part of the potential exists.…”

Section: Bending and Gaussian Rigidity Coefficientsmentioning

confidence: 99%

“…This fact has been already noted in the literature. However, the bending and Gaussian rigidity coefficient functions were derived within the second approach [29,30] by assuming that they depend on the interfacial curvature in a universal way, i.e. in the same way for the cylindrical and spherical geometry.…”

Section: Bending and Gaussian Rigidity Coefficientsmentioning

confidence: 99%

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Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Dutka

Napiórkowski

2009

Physica A: Statistical Mechanics and its Applications

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We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss implications of the structure of these functions on the effective Hamiltonian.

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Section: Bending and Gaussian Rigidity Coefficientsmentioning

confidence: 71%

Section: Bending and Gaussian Rigidity Coefficientsmentioning

confidence: 99%

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Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Dutka

Napiórkowski

2009

Physica A: Statistical Mechanics and its Applications

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“…In a recent Letter [1] a renormalization-group (RG) calculation of the gravity dependence of properties of a liquid-vapor interface is presented whose central point is the use of the (bare) capillary-wave-like Hamiltonian…”

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confidence: 99%

“…ζ 4 (1) to study the interface in the limit of vanishing gravitational acceleration g. Here ζ( R) is the local height of the interface configuration [ζ] at position R relative to the plane z = 0. Recognizing that (1) is just the usual ϕ 4 Hamiltonian and that a 0 (g) vanishes as g → 0, the authors followed the standard RG analysis for the critical Ising system, arrived at the fixed point Hamiltonian…”

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confidence: 99%

Comment on “Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface”

Diehl

Zia

2001

Phys. Rev. Lett.

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In a recent Letter [1] a renormalization-group (RG) calculation of the gravity dependence of properties of a liquid-vapor interface is presented whose central point is the use of the (bare) capillary-wave-like Hamiltonian2 |∇ζ| 2 + a 0 (g) 2 ζ 2 + λ 4! ζ 4 (1)to study the interface in the limit of vanishing gravitational acceleration g. Here ζ( R) is the local height of the interface configuration [ζ] at position R relative to the plane z = 0. Recognizing that (1) is just the usual ϕ 4 Hamiltonian and that a 0 (g) vanishes as g → 0, the authors followed the standard RG analysis for the critical Ising system, arrived at the fixed point Hamiltonianand reached a remarkable conclusion: interfacial properties (in d dimensions) for g = 0 should be identical to those in a critical, d − 1 dimensional bulk Ising system. In order for this analysis and its conclusions to be valid, the (renormalized) coupling constant λ must remain positive in this limit, i.e., lim g→0 λ(g) = λ (0) > 0. However, in the present interface case (in contrast to that of critical bulk systems), there are fundamental symmetry requirements that enforce λ (0) = 0. We believe that the authors' introduction of a nontrivial λ(g) is justifiable. But as we shall show in the sequel, their assumption of λ (0) > 0 is untenable, so that their subsequent analysis is irrelevant and the conclusion unreliable.Consider a simple liquid-vapor system in d dimensions, under the influence of a potential g z. Let (x i ) = (R α , x d ≡ z) ∈ R d be the coordinates of a point relative to a fixed frame with Euclidean unit vectors e i . In the absence of gravity, the system respects the Euclidean symmetries and hence is invariant under translations and rotationsis a rotation matrix. In the two-phase region (of the g = 0 system), these symmetries are broken spontaneously by the presence of an interface, so that nonlinear realizations of the Euclidean group are necessary. For g = 0, these symmetries are broken explicitly. Under a rotation, the system transforms into one with a rotated field: g e d → R id g e i .Let us write possible (bare) interface Hamiltonians aswhere ∂ζ, ∂ 2 ζ,. . . stand for first, second, and higher partial derivatives ∂ζ/∂R α etc. H (0) [ζ] must be invariant under the transformations discussed above. We consider separately the consequences of this trivial observation.(i) Translations along the z axis: This symmetry is realized by ζ → ζ ′ = ζ − A d . The invariance of H (0) means that the energy cost of such a translation vanishes as g → 0. Hence L (0) cannot depend explicitly on ζ: we must have L (g) → L (0) (∂ζ, ∂ 2 ζ, . . .). This rules out terms like λ ζ 4 , as well as (2), in the limit g → 0. Yet, λ (0) > 0 is crucial for the approach in [1], the presence of an upper critical dimension of 5, and the fixed point (2).(ii) Rotations about e α : As discussed in Ref.[2], H (0) must realize this symmetry in a nonlinear fashion. Specifically, if only first derivatives ∂ζ are taken into account, then H (0) is simply proportional to the surface area, i.e.,...

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Nucleon Viewed as a Borromean Bound-State

et al. 2018

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We explain how the emergent phenomenon of dynamical chiral symmetry breaking ensures that Poincaré covariant analyses of the three valencequark scattering problem in continuum quantum field theory yield a picture of the nucleon as a Borromean bound-state, in which binding arises primarily through the sum of two separate contributions. One involves aspects of the non-Abelian character of Quantum Chromodynamics that are expressed in the strong running coupling and generate tight, dynamical color-antitriplet quark-quark correlations in the scalar-isoscalar and pseudovector-isotriplet channels. This attraction is magnified by quark exchange associated with diquark breakup and reformation, which is required in order to ensure that each valence-quark participates in all diquark correlations to the complete extent allowed by its quantum numbers. Combining these effects, we arrive at a properly antisymmetrised Faddeev wave function for the nucleon and calculate, e.g. the flavor-separated versions of the Dirac and Pauli form factors and the proton's leading-twist parton distribution amplitude. We conclude that available data and planned experiments are capable of validating the proposed picture.

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Segovia-López and Romero-Rochín Reply:

Cited by 10 publications

References 2 publications

Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Comment on “Renormalization-Group Calculation of the Dependence on Gravity of the Surface Tension and Bending Rigidity of a Fluid Interface”

Nucleon Viewed as a Borromean Bound-State

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