711 research outputs found
The momentum map for nonholonomic field theories with symmetry
In this note, we introduce a suitable generalization of the momentum map for
nonholonomic field theories and prove a covariant form of the nonholonomic
momentum equation. We show that these covariant objects coincide with their
counterparts in mechanics by making the transition to the Cauchy formalism
On the irredundant part of the first Piola-Kirchhoff stress tensor
Let us assume a given medium moves and deforms in an ambient smooth and oriented Riemannian manifold N with metric (, ). This medium at hand is supposed to maintain the shape of a compact smooth orientable and connected manifold M with boundary. Clearly dim M ≤ dim N. By a configuration j of the medium we mean a smooth embedding of M into N. The configuration space is E(M, N), the collection of all smooth embeddings of M into N endowed with the C∞-topology. [...] The main purpose of this notes is to exhibit (in absence of exterior force densities) the irredundant part of a(j) that determines the force densities mentioned and the virtual work caused by any infinitesimal distortion at j.[...
Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase
We study the electronic instabilities in a 2D Hubbard model where one of the
dimensions has a finite width, so that it can be considered as a large array of
coupled chains. The finite transverse size of the system gives rise to a
discrete string of Fermi points, with respective electron fields that, due to
their mutual interaction, acquire anomalous scaling dimensions depending on the
point of the string. Using bosonization methods, we show that the anomalous
scaling dimensions vanish when the number of coupled chains goes to infinity,
implying the Fermi liquid behavior of a 2D system in that limit. However, when
the Fermi level is at the Van Hove singularity arising from the saddle points
of the 2D dispersion, backscattering and Cooper-pair scattering lead to the
breakdown of the metallic behavior at low energies. These interactions are
taken into account through their renormalization group scaling, studying in
turn their influence on the nonperturbative bosonization of the model. We show
that, at a certain low-energy scale, the anomalous electron dimension diverges
at the Fermi points closer to the saddle points of the 2D dispersion. The
d-wave superconducting correlations become also large at low energies, but
their growth is cut off as the suppression of fermion excitations takes place
first, extending progressively along the Fermi points towards the diagonals of
the 2D Brillouin zone. We stress that this effect arises from the vanishing of
the charge stiffness at the Fermi points, characterizing a critical behavior
that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure
On the Evolution of Simple Material Structures
The evolution of a distribution of material inhomogeneities is investigated by analyzing the evolution of the corresponding material connections. Some general geometric relations governing such evolutions are derived. These relations are then analyzed by looking at the restrictions imposed by the material symmetry group
Breakdown of the Fermi-liquid regime in the 2D Hubbard model from a two-loop field-theoretical renormalization group approach
We analyze the particle-hole symmetric two-dimensional Hubbard model on a
square lattice starting from weak-to-moderate couplings by means of the
field-theoretical renormalization group (RG) approach up to two-loop order.
This method is essential in order to evaluate the effect of the
momentum-resolved anomalous dimension which arises in the
normal phase of this model on the corresponding low-energy single-particle
excitations. As a result, we find important indications pointing to the
existence of a non-Fermi liquid (NFL) regime at temperature displaying
a truncated Fermi surface (FS) for a doping range exactly in between the
well-known antiferromagnetic insulating and the -wave singlet
superconducting phases. This NFL evolves as a function of doping into a
correlated metal with a large FS before the -wave pairing
susceptibility finally produces the dominant instability in the low-energy
limit.Comment: 9 pages, 9 figures; published in Phys. Rev.
On a global differential geometric approach to the rational mechanics of deformable media
In the past the rational mechanics of deformable media was largely concerned with materials governed by linear constitutive equations. In recent years, the theory has expanded considerably towards covering materials for which the constitutive equations are inherently nonlinear, and/or whose mechanical properties resemble in some respects those of a fluid and in others those of a solid. In the present article we formulate a satisfactory global mathematical theory of moving deformable media, which includes all these aspects
The Most Severe Test for Hydrophobicity Scales: Two Proteins with 88% Sequence Identity but Different Structure and Function
Protein-protein interactions (protein functionalities) are mediated by water,
which compacts individual proteins and promotes close and temporarily stable
large-area protein-protein interfaces. In their classic paper Kyte and
Doolittle (KD) concluded that the "simplicity and graphic nature of
hydrophobicity scales make them very useful tools for the evaluation of protein
structures". In practice, however, attempts to develop hydrophobicity scales
(for example, compatible with classical force fields (CFF) in calculating the
energetics of protein folding) have encountered many difficulties. Here we
suggest an entirely different approach, based on the idea that proteins are
self-organized networks, subject to finite-scale criticality (like some network
glasses). We test this proposal against two small proteins that are delicately
balanced between alpha and alpha/beta structures, with different functions
encoded with only 12% of their amino acids. This example explains why protein
structure prediction is so challenging, and it provides a severe test for the
accuracy and content of hydrophobicity scales. The new method confirms KD's
evaluation, and at the same time suggests that protein structure, dynamics and
function can be best discussed without using CFF
The Reconstruction Problem and Weak Quantum Values
Quantum Mechanical weak values are an interference effect measured by the
cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states,
leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase
space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of
the two functions {\phi},{\psi} unambiguously determines the other, thus
generalizing a recent reconstruction result of Lundeen and his collaborators.Comment: To appear in J.Phys.: Math. Theo
Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
We develop a new formulation of the functional renormalization group (RG) for
interacting fermions. Our approach unifies the purely fermionic formulation
based on the Grassmannian functional integral, which has been used in recent
years by many authors, with the traditional Wilsonian RG approach to quantum
systems pioneered by Hertz [Phys. Rev. B 14, 1165 (1976)], which attempts to
describe the infrared behavior of the system in terms of an effective bosonic
theory associated with the soft modes of the underlying fermionic problem. In
our approach, we decouple the interaction by means of a suitable
Hubbard-Stratonovich transformation (following the Hertz-approach), but do not
eliminate the fermions; instead, we derive an exact hierarchy of RG flow
equations for the irreducible vertices of the resulting coupled field theory
involving both fermionic and bosonic fields. The freedom of choosing a momentum
transfer cutoff for the bosonic soft modes in addition to the usual band cutoff
for the fermions opens the possibility of new RG schemes. In particular, we
show how the exact solution of the Tomonaga-Luttinger model emerges from the
functional RG if one works with a momentum transfer cutoff. Then the Ward
identities associated with the local particle conservation at each Fermi point
are valid at every stage of the RG flow and provide a solution of an infinite
hierarchy of flow equations for the irreducible vertices. The RG flow equation
for the irreducible single-particle self-energy can then be closed and can be
reduced to a linear integro-differential equation, the solution of which yields
the result familiar from bosonization. We suggest new truncation schemes of the
exact hierarchy of flow equations, which might be useful even outside the weak
coupling regime.Comment: 27 pages, 15 figures; published version, some typos correcte
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