29,172 research outputs found
Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
We consider a general class of approximations which guarantees the
conservation of particle number in many-body perturbation theory. To do this we
extend the concept of -derivability for the self-energy to a
larger class of diagrammatic terms in which only some of the Green's function
lines contain the fully dressed Green's function . We call the corresponding
approximations for partially -derivable. A special subclass of
such approximations, which are gauge-invariant, is obtained by dressing loops
in the diagrammatic expansion of consistently with . These
approximations are number conserving but do not have to fulfill other
conservation laws, such as the conservation of energy and momentum. From our
formalism we can easily deduce if commonly used approximations will fulfill the
continuity equation, which implies particle number conservation. We further
show how the concept of partial -derivability plays an important role in
the derivation of a generalized sum rule for the particle number, which reduces
to the Luttinger-Ward theorem in the case of a homogeneous electron gas, and
the Friedel sum rule in the case of the Anderson model. To do this we need to
ensure that the Green's function has certain complex analytic properties, which
can be guaranteed if the spectral function is positive semi-definite.The latter
property can be ensured for a subset of partially -derivable
approximations for the self-energy, namely those that can be constructed from
squares of so-called half-diagrams. In case the analytic requirements are not
fulfilled we highlight a number of subtle issues related to branch cuts, pole
structure and multi-valuedness. We also show that various schemes of computing
the particle number are consistent for particle number conserving
approximations.Comment: Minor changes, corrected typo
Certified lattice reduction
Quadratic form reduction and lattice reduction are fundamental tools in
computational number theory and in computer science, especially in
cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm
(so-called LLL) has been improved in many ways through the past decades and
remains one of the central methods used for reducing integral lattice basis. In
particular, its floating-point variants-where the rational arithmetic required
by Gram-Schmidt orthogonalization is replaced by floating-point arithmetic-are
now the fastest known. However, the systematic study of the reduction theory of
real quadratic forms or, more generally, of real lattices is not widely
represented in the literature. When the problem arises, the lattice is usually
replaced by an integral approximation of (a multiple of) the original lattice,
which is then reduced. While practically useful and proven in some special
cases, this method doesn't offer any guarantee of success in general. In this
work, we present an adaptive-precision version of a generalized LLL algorithm
that covers this case in all generality. In particular, we replace
floating-point arithmetic by Interval Arithmetic to certify the behavior of the
algorithm. We conclude by giving a typical application of the result in
algebraic number theory for the reduction of ideal lattices in number fields.Comment: 23 page
Self-energy Effects in the Superfluidity of Neutron Matter
The superfluidity of neutron matter in the channel is studied by
taking into account the effect of the ground-state correlations in the
self-energy. To this purpose the gap equation has been solved within the
generalized Gorkov approach. A sizeable suppression of the energy gap is driven
by the quasi-particle strength around the Fermi surface.Comment: 8 pages and 3 figure
Bootstrapping Vector Models with Four Supercharges in
We analyze the conformal bootstrap constraints in theories with four
supercharges and a global flavor symmetry in dimensions. In particular, we consider the 4-point function of
-fundamental chiral operators that have no chiral primary in the
-singlet sector of their OPE. We find features in our numerical bounds
that nearly coincide with the theory of chiral super-fields with
superpotential , as well as general bounds on SCFTs
where vanishes in the chiral ring.Comment: 25 pages, 8 figure
The two-fluid model with superfluid entropy
The two-fluid model of liquid helium is generalized to the case that the
superfluid fraction has a small entropy content. We present theoretical
arguments in favour of such a small superfluid entropy. In the generalized
two-fluid model various sound modes of HeII are investigated. In a
superleak carrying a persistent current the superfluid entropy leads to a new
sound mode which we call sixth sound. The relation between the sixth sound and
the superfluid entropy is discussed in detail.Comment: 22 pages, latex, published in Nuovo Cimento 16 D (1994) 37
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