2,105 research outputs found
Multiloop functional renormalization group for general models
We present multiloop flow equations in the functional renormalization group
(fRG) framework for the four-point vertex and self-energy, formulated for a
general fermionic many-body problem. This generalizes the previously introduced
vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403
(2018)] and provides the necessary corrections to the self-energy flow in order
to complete the derivative of all diagrams involved in the truncated fRG flow.
Due to its iterative one-loop structure, the multiloop flow is well-suited for
numerical algorithms, enabling improvement of many fRG computations. We
demonstrate its equivalence to a solution of the (first-order) parquet
equations in conjunction with the Schwinger-Dyson equation for the self-energy
When Is it Wrong to Trade Stocks on the Basis of Non-Public Information?: Public Views of the Morality of Insider Trading
Fermi-edge singularity and the functional renormalization group
We study the Fermi-edge singularity, describing the response of a degenerate
electron system to optical excitation, in the framework of the functional
renormalization group (fRG). Results for the (interband) particle-hole
susceptibility from various implementations of fRG (one- and two-
particle-irreducible, multi-channel Hubbard-Stratonovich, flowing
susceptibility) are compared to the summation of all leading logarithmic (log)
diagrams, achieved by a (first-order) solution of the parquet equations. For
the (zero-dimensional) special case of the X-ray-edge singularity, we show that
the leading log formula can be analytically reproduced in a consistent way from
a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic
structure, we show that this derivation relies on fortuitous partial
cancellations special to the form of and accuracy applied to the X-ray-edge
singularity and does not generalize
Multiloop functional renormalization group that sums up all parquet diagrams
We present a multiloop flow equation for the four-point vertex in the
functional renormalization group (fRG) framework. The multiloop flow consists
of successive one-loop calculations and sums up all parquet diagrams to
arbitrary order. This provides substantial improvement of fRG computations for
the four-point vertex and, consequently, the self-energy. Using the X-ray-edge
singularity as an example, we show that solving the multiloop fRG flow is
equivalent to solving the (first-order) parquet equations and illustrate this
with numerical results
Counting Feynman diagrams via many-body relations
We present an iterative algorithm to count Feynman diagrams via many-body
relations. The algorithm allows us to count the number of diagrams of the exact
solution for the general fermionic many-body problem at each order in the
interaction. Further, we apply it to different parquet-type approximations and
consider spin-resolved diagrams in the Hubbard model. Low-order results and
asymptotics are explicitly discussed for various vertex functions and different
two-particle channels. The algorithm can easily be implemented and generalized
to many-body relations of different forms and levels of approximation
RG transport theory for open quantum systems: Charge fluctuations in multilevel quantum dots in and out of equilibrium
We present the real-time renormalization group (RTRG) method as a method to
describe the stationary state current through generic multi-level quantum dots
with a complex setup in nonequilibrium. The employed approach consists of a
very rudiment approximation for the RG equations which neglects all vertex
corrections while it provides a means to compute the effective dot Liouvillian
self-consistently. Being based on a weak-coupling expansion in the tunneling
between dot and reservoirs, the RTRG approach turns out to reliably describe
charge fluctuations in and out of equilibrium for arbitrary coupling strength,
even at zero temperature. We confirm this in the linear response regime with a
benchmark against highly-accurate numerically renormalization group data in the
exemplary case of three-level quantum dots. For small to intermediate bias
voltages and weak Coulomb interactions, we find an excellent agreement between
RTRG and functional renormalization group data, which can be expected to be
accurate in this regime. As a consequence, we advertise the presented RTRG
approach as an efficient and versatile tool to describe charge fluctuations
theoretically in quantum dot systems
From Identification to Identity Theft: Public Perceptions of Biometric Privacy Harms
Central to understanding biometric privacy is the question of biometric privacy harms. How much do people value biometric privacy, and what evils should biometric privacy laws seek to avert? This Article addresses these questions by surveying two nationally representative samples to determine what does, and does not, worry people in the context of biometrics. The results show that many people are deeply concerned about biometric privacy in the consumer context, that they are willing to sacrifice real benefits to preserve biometric privacy, and that those who are concerned with biometric privacy attribute their concern to many factors that are not directly related to data security, particularly public tracking. Further, people’s level of comfort with biometric data collection differs sharply depending on the uses to which the data will be put and not just on the type of data collected. These nuanced attitudes about biometric privacy are in sharp conflict with a purely data security approach to biometric harms, and therefore have substantial implications both for future legislative consideration as well as current standing litigation
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