MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language

The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.Comment: 37 pages, 10 figure

Grain Refinement in Iron-Based Materials

A process for manufacturing an iron-based alloy comprising forming targeted fine oxide and/or carbide dispersoids in a melt, and sequentially precipitating transition-metal nitrides on the dispersoids for heterogeneous nucleation of equiaxed grains. An iron-based cast alloy having a highly equiaxed fine grain structure

Physical Constraints and Functional Characteristics of Transcription Factor-DNA Interaction

We study theoretical ``design principles'' for transcription factor-DNA interaction in bacteria, focusing particularly on the statistical interaction of the transcription factors (TF's) with the genomic background (i.e., the genome without the target sites). We introduce and motivate the concept of `programmability', i.e. the ability to set the threshold concentration for TF binding over a wide range merely by mutating the binding sequence of a target site. This functional demand, together with physical constraints arising from the thermodynamics and kinetics of TF-DNA interaction, leads us to a narrow range of ``optimal'' interaction parameters. We find that this parameter set agrees well with experimental data for the interaction parameters of a few exemplary prokaryotic TF's. This indicates that TF-DNA interaction is indeed programmable. We suggest further experiments to test whether this is a general feature for a large class of TF's.Comment: 9 pages, 4 figures; revised version as published in PNA

On cardinal invariants and generators for von Neumann algebras

We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, "Is every separably-acting von Neumann algebra singly-generated?", with the formally stronger questions, "Is every countably-generated von Neumann algebra singly-generated?" and "Is the gen invariant monotone?" Modulo the generator problem, we determine the range of the invariant (gen(M), dec(M)), which is mostly governed by the inequality dec(M) leq c^{gen(M)}.Comment: 22 pages; the main additions are Theorem 3.8 and Section

Analytic continuation of multipoint correlation functions

Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well-known for two-point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism-independent partial spectral functions and formalism-specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. We use this representation to formally elucidate the connection between both formalisms. We show how a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart. The procedure is illustrated for various correlators of the Hubbard atom.Comment: 56 pages, 8 figure

Real-frequency quantum field theory applied to the single-impurity Anderson model

A major challenge in the field of correlated electrons is the computation of dynamical correlation functions. For comparisons with experiment, one is interested in their real-frequency dependence. This is difficult to compute, as imaginary-frequency data from the Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum field theory to the single-impurity Anderson model (AM), using the Keldysh instead of the Matsubara formalism with direct access to the self-energy and dynamical susceptibilities on the real-frequency axis. We present results from the functional renormalization group (fRG) at one-loop level and from solving the self-consistent parquet equations in the parquet approximation. In contrast to previous Keldysh fRG works, we employ a parametrization of the four-point vertex which captures its full dependence on three real-frequency arguments. We compare our results to benchmark data obtained with the numerical renormalization group and to second-order perturbation theory. We find that capturing the full frequency dependence of the four-point vertex significantly improves the fRG results compared to previous implementations, and that solving the parquet equations yields the best agreement with the NRG benchmark data, but is only feasible up to moderate interaction strengths. Our methodical advances pave the way for treating more complicated models in the future.Comment: 25 pages, 20 figure

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

Towards an Ontological Modelling of Preference Relations

Preference relations are intensively studied in Economics, but they are also approached in AI, Knowledge Representation, and Conceptual Modelling, as they provide a key concept in a variety of domains of application. In this paper, we propose an ontological foundation of preference relations to formalise their essential aspects across domains. Firstly, we shall discuss what is the ontological status of the relata of a preference relation. Secondly, we investigate the place of preference relations within a rich taxonomy of relations (e.g. we ask whether they are internal or external, essential or contingent, descriptive or nondescriptive relations). Finally, we provide an ontological modelling of preference relation as a module of a foundational (or upper) ontology (viz. OntoUML). The aim of this paper is to provide a sharable foundational theory of preference relation that foster interoperability across the heterogeneous domains of application of preference relations

Naive Pluripotent Stem Cells Derived Directly from Isolated Cells of the Human Inner Cell Mass.

Conventional generation of stem cells from human blastocysts produces a developmentally advanced, or primed, stage of pluripotency. In vitro resetting to a more naive phenotype has been reported. However, whether the reset culture conditions of selective kinase inhibition can enable capture of naive epiblast cells directly from the embryo has not been determined. Here, we show that in these specific conditions individual inner cell mass cells grow into colonies that may then be expanded over multiple passages while retaining a diploid karyotype and naive properties. The cells express hallmark naive pluripotency factors and additionally display features of mitochondrial respiration, global gene expression, and genome-wide hypomethylation distinct from primed cells. They transition through primed pluripotency into somatic lineage differentiation. Collectively these attributes suggest classification as human naive embryonic stem cells. Human counterparts of canonical mouse embryonic stem cells would argue for conservation in the phased progression of pluripotency in mammals.This work was supported by the Medical Research Council, Biotechnology and Biological Sciences Research Council, Swiss National Science Foundation (SNF)/Novartis SNF (F.v.M.) and core funding to the Cambridge Stem Cell Institute from the Wellcome Trust and Medical Research Council. AS is a Medical Research Council Professor.This is the final version of the article. It first appeared from Cell Press via http://dx.doi.org/10.1016/j.stemcr.2016.02.00

Integrated impedance bridge for absolute capacitance measurements at cryogenic temperatures and finite magnetic fields

We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4~aF$/\sqrt{\textrm{Hz}}$ at 77 K on a comb-drive actuator, while maintaining a small excitation amplitude of 15~$k_\text{B} T/e$. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60~mK with a probe signal of 12.8~$k_\text{B} T/e$.Comment: 7 pages, 5 figure