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Non-abelian symmetries in tensor networks: a quantum symmetry space approachFeb 25 2012Nov 25 2012A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of orthonormal local as well as effective basis sets. The two crucial ingredients, the Clebsch-Gordan algebra for multiplet spaces ... More

Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum LimitApr 07 2016The description of interacting quantum impurity models in steady-state non-equilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing ... More

Local susceptibility and Kondo scaling in the presence of finite bandwidthSep 15 2013Feb 25 2014The Kondo scale TK for impurity systems is expected to guarantee universal scaling of physical quantities. However, in practice, not every definition of TK necessarily supports this notion away from the strict scaling limit. Specifically, this paper addresses ... More

Thermal Tensor Renormalization Group Simulations of Square-Lattice Quantum Spin ModelsApr 12 2019In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a thermal correlation length, ... More

Sum-rule Conserving Spectral Functions from the Numerical Renormalization GroupJul 19 2006Aug 20 2007We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of ``discarded'' numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously ... More

Incommensurate correlations in the anisotropic triangular Heisenberg latticeOct 06 2011We study the anisotropic spin-half antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings J (J') along (in between) chains, respectively. Our focus is on the incommensurate correlation that emerges in ... More

Matrix product state approach for a two-lead, multi-level Anderson impurity modelApr 03 2008Mar 16 2010We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity ... More

Identifying Symmetry-Protected Topological Order by Entanglement EntropyJun 24 2013Jan 08 2014According to the classification using projective representations of the SO(3) group, there exist two topologically distinct gapped phases in spin-1 chains. The symmetry-protected topological (SPT) phase possesses half-integer projective representations ... More

Adaptive broadening to improve spectral resolution in the numerical renormalization groupSep 05 2016We propose an adaptive scheme of broadening the discrete spectral data from numerical renormalization group (NRG) calculations to improve the resolution of dynamical properties at finite energies. While the conventional scheme overbroadens narrow features ... More

Aharonov-Bohm phase as quantum gate in two-electron charge qubitsMar 03 2004We analyze the singlet-triplet splitting on a planar array of quantum dots coupled capacitively to a set of external voltage gates. The system is modelled using an extended Hubbard Hamiltonian keeping two excess electrons on the array. The voltage dependence ... More

Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization groupApr 01 2008Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating quantum lattice ... More

Symmetric Minimally Entangled Typical Thermal StatesJun 10 2015Sep 05 2015We extend White's minimally entangled typically thermal states approach (METTS) to allow Abelian and non-Ablian symmetries to be exploited when computing finite-temperature response functions in one-dimensional (1D) quantum systems. Our approach, called ... More

Anderson Orthogonality and the Numerical Renormalization GroupApr 15 2011Anderson Orthogonality (AO) refers to the fact that the ground states of two Fermi seas that experience different local scattering potentials, say |G_I> and |G_F>, become orthogonal in the thermodynamic limit of large particle number N, in that |<G_I|G_F>| ... More

Hundness versus Mottness in a three-band Hubbard-Hund model: On the origin of strong correlations in Hund metalsAug 29 2018Dec 21 2018Hund metals are multi-orbital systems with moderate Coulomb interaction, $U$, and sizeable Hund's rule coupling, $J<U$, that aligns the spins in different orbitals. They show strong correlation effects, like very low Fermi-liquid coherence scales and ... More

Dynamic structure factor of the spin-1/2 XXZ chain in a transverse fieldJun 10 2016Aug 22 2016The spin-$\frac{1}{2}$ XXZ chain with easy-plane anisotropy in a transverse field describes well the thermodynamic properties of the material ${\rm Cs_2CoCl_4}$ in a wide range of temperatures and fields including the region close to the spin-flop Ising ... More

Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo modelMar 03 2014May 25 2014We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened $N$-channel Kondo model, namely $c_B$, $c_T$ and $c_\varepsilon$, characterizing the magnetic field and temperature dependence of the resisitivity, ... More

Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product StatesAug 21 2017Jan 03 2019The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome ... More

Interplay of mesoscopic and Kondo effects for transmission amplitude of few-level quantum dotsMay 20 2008The magnitude and phase of the transmission amplitude of a multi-level quantum dot is calculated for the mesoscopic regime of level spacing large compared to level width. The interplay between Kondo correlations and the influence by neighboring levels ... More

Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leadsMar 08 2008Jun 12 2008We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows, in contrast to previous belief, that NRG iterations can ... More

Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnetDec 22 2014Jun 25 2015We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially ... More

Critical and strong-coupling phases in one- and two-bath spin-boson modelsOct 28 2011Mar 06 2012For phase transitions in dissipative quantum impurity models, the existence of a quantum-to-classical correspondence has been discussed extensively. We introduce a variational matrix product state approach involving an optimized boson basis, rendering ... More

Chebyshev matrix product state approach for spectral functionsJan 31 2011We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main features of this ... More

Unified Phase Diagram of Antiferromagnetic SU(N) Spin LaddersMar 16 2018Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU($N$) spin ladders. Two-leg ladders provide a rich and highly non-trivial extension ... More

Non-Fermi liquid behaviour in non-equilibrium transport through Co doped Au chains connected to four-fold symmetric leadsMay 05 2014We calculate the differential conductance as a function of temperature and bias voltage, $G(T,V)$, through Au monoatomic chains with a substitutional Co atom as a magnetic impurity, connected to a four-fold symmetric lead. The system was recently proposed ... More

Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star latticeAug 14 2015We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We ... More

At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson modelSep 20 2016Jul 17 2018This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric ... More

Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum LimitApr 07 2016Nov 07 2016The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing ... More

Constrained optimization of sequentially generated entangled multiqubit statesOct 06 2008Sep 20 2009We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We consider a realistic ... More

Density matrix renormalization group study of a quantum impurity model with Landau-Zener time-dependent HamiltonianOct 16 2008Apr 01 2009We use the adaptive time-dependent density matrix renormalization group method (t-DMRG) to study the nonequilibrium dynamics of a benchmark quantum impurity system which has a time-dependent Hamiltonian. This model is a resonant-level model, obtained ... More

Signatures of Mottness and Hundness in archetypal correlated metalsAug 18 2017Jan 15 2019Physical properties of multi-orbital materials depend not only on the strength of the effective interactions among the valence electrons but also on their type. Strong correlations are caused by either Mott physics that captures the Coulomb repulsion ... More

Exponential Thermal Tensor Network Approach for Quantum Lattice ModelsDec 30 2017Oct 05 2018We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\hat\rho=e^{-\beta \hat{H}}$ onto itself. We refer to this scheme ... More

Anderson Orthogonality in the Dynamics After a Local Quantum QuenchAug 29 2011Sep 03 2011We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle ... More

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnetJun 23 2014Mar 19 2015We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site {$e_0=-1.41090(2)$ with $D^*=8$ multiplets retained (i.e., a bond dimension of $D=24$), and ... More

Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star latticeAug 14 2015Feb 26 2018We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We ... More

Two-bath spin-boson model: Phase diagram and critical propertiesOct 14 2014The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum phase transition. ... More

Spin-1/2 Kondo effect in an InAs nanowire quantum dot: the Unitary limit, conductance scaling and Zeeman splittingAug 08 2011Jan 16 2012We report on a comprehensive study of spin-1/2 Kondo effect in a strongly-coupled quantum dot realized in a high-quality InAs nanowire. The nanowire quantum dot is relatively symmetrically coupled to its two leads, so the Kondo effect reaches the Unitary ... More

Two-temperature scales in the triangular-lattice Heisenberg antiferromagnetNov 04 2018Apr 11 2019The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here we further the theoretical ... More

Two Temperature Scales in the Triangular Lattice Heisenberg AntiferromagnetNov 04 2018The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here we further the theoretical ... More

Quantum quench of Kondo correlations in optical absorptionFeb 19 2011The interaction between a single confined spin and the spins of a Fermionic reservoir leads to one of the most spectacular phenomena of many body physics -- the Kondo effect. Here we report the observation of Kondo correlations in optical absorption measurements ... More

Open Wilson chains for quantum impurity models: Keeping track of all bath modesNov 16 2016Apr 03 2017When constructing a Wilson chain to represent a quantum impurity model, the effects of truncated bath modes are neglected. We show that their influence can be kept track of systematically by constructing an "open Wilson chain" in which each site is coupled ... More

Open Wilson chains for quantum impurity models: Keeping track of all bath modesNov 16 2016When constructing a Wilson chain to represent a quantum impurity model, the effects of truncated bath modes are neglected. We show that their influence can be kept track of systematically by constructing an "open Wilson chain" in which each site is coupled ... More

Charge qubits and limitations of electrostatic quantum gatesJan 07 2004We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron{transistor ... More

Non-Topological Majorana Zero Modes in Inhomogeneous Spin LaddersJun 05 2018Dec 14 2018We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states ... More

Tunability of qubit Coulomb interaction: Numerical analysis of top gate depletion in two-dimensional electron systemsJul 28 2006We investigate the tunability of electrostatic coupling between solid state quantum dots as building blocks for quantum bits. Specifically, our analysis is based upon two-dimensional electron systems (2DEG) and depletion by top gates. We are interested ... More

Potential landscapes and induced charges near metallic islands in three dimensionsJun 24 2003We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known relaxation algorithm ... More

Thermalization and dynamics in the single impurity Anderson modelJul 13 2015We analyze the process of thermalization, dynamics and the eigenstate thermalization hypothesis (ETH) for the single impurity Anderson model, focusing on the Kondo regime. For this we construct the complete eigenbasis of the Hamiltonian using the numerical ... More

Equivariant characteristic forms in the Cartan model and Borel equivariant cohomologyAug 31 2015Nov 10 2015We show the compatibility of the differential geometric and the topological construction of equivariant characteristic classes for compact Lie groups. Our analysis motivates a differential geometric construction for equivariant characteristic classes ... More

Band-edge BCS-BEC crossover in a two-band superconductor: physical properties and detection parametersJul 11 2014Superconductivity in iron-based, magnesium diborides, and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity ... More

Imbalanced thee-component Fermi gas with attractive interactions: Multiple FFLO-pairing, Bose-Fermi and Fermi-Fermi mixtures versus collapse and phase separationJun 04 2009We present a detailed study of the population imbalanced three-component Hubbard chain with attractive interactions. Such a system can be realized experimentally with three different hyperfine states of ultra cold $^6$Li atoms in an optical lattice. We ... More

Domestic Corpuscular InflatonJun 28 2018The aim of this paper is to provide a more precise description of the paradigm of corpuscular slow-roll inflation, which was previously introduced by Casadio et al. in [1]. Specifically, we start by expanding the Starobinsky theory on a curved background ... More

Inverse wave scattering in the time domain: a factorization method approachMar 14 2019Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions assigned on the Lipschitz boundary of a bounded obstacle $\Omega$. Let $u^{\Lambda}_{f}$ and $u^{0}_{f}$ be the solutions ... More

Super-Poincare' algebras, space-times and supergravities (II)Aug 31 2011The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Kostant theory of supermanifolds. It is also shown that the equations of ... More

Classification of maximal transitive prolongations of super-Poincaré algebrasDec 08 2012Jul 22 2014Let $V$ be a complex vector space with a non-degenerate symmetric bilinear form and $\mathbb S$ an irreducible module over the Clifford algebra $Cl(V)$ determined by this form. A supertranslation algebra is a $\mathbb Z$-graded Lie superalgebra $\mathfrak ... More

Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficientsFeb 06 2019Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media, the parameters ... More

The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic fieldDec 17 2008Mar 16 2009We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and thus ... More

Solving DC programs with polyhedral component utilizing a multiple objective linear programming solverOct 18 2016A class of non-convex optimization problems with DC objective function and linear constraints is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case ... More

Formality of $\mathbb{P}$-objectsSep 19 2017We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. ... More

(a,b)-Koszul algebrasJul 20 2010Let $a$ and $b$ be two integers such that $2\le a<b$. In this article we define the notion of $(a,b)$-Koszul algebra as a generalization of $N$-Koszul algebras. We also exhibit examples and we provide a minimal graded projective resolution of the algebra ... More

PT-symmetrically deformed shock wavesJan 27 2012We investigate for a large class of nonlinear wave equations, which allow for shock wave formations, how these solutions behave when they are PT-symmetrically deformed. For real solutions we find that they are transformed into peaked solutions with a ... More

Numerical analysis of detection-mechanism models of SNSPDAug 27 2013Nov 12 2013The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. ... More

A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous CoefficientsFeb 06 2019Apr 18 2019The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly modeled by random ... More

Status of sub-GeV Hidden Particle SearchesAug 26 2010Hidden sector particles with sub-GeV masses like hidden U(1) gauge bosons, the NMSSM CP-odd Higgs, and other axion-like particles are experimentally little constrained as they interact only very weakly with the visible sector. For masses below the muon ... More

The electroweak chiral Lagrangian reanalyzedJul 09 1999Oct 26 2000In this paper we reanalyze the electroweak chiral Lagrangian with particular focus on two issues related to gauge invariance. Our analysis is based on a manifestly gauge-invariant approach that we introduced recently. It deals with gauge-invariant Green's ... More

A universal ionization threshold for strongly driven Rydberg statesApr 21 2004We observe a universal ionization threshold for microwave driven one-electron Rydberg states of H, Li, Na, and Rb, in an {\em ab initio} numerical treatment without adjustable parameters. This sheds new light on old experimental data, and widens the scene ... More

Residual Symmetries in the Spectrum of Periodically Driven Alkali Rydberg StatesNov 25 1999We identify a fundamental structure in the spectrum of microwave driven alkali Rydberg states, which highlights the remnants of the Coulomb symmetry in the presence of a non-hydrogenic core. Core-induced corrections with respect to the hydrogen spectrum ... More

Lipschitz functions with prescribed blowups at many pointsDec 15 2016In this paper we prove generalizations of Lusin-type theorems for gradients due to Giovanni Alberti, where we replace the Lebesgue measure with any Radon measure $\mu$. We apply this to go beyond the known result on the existence of Lipschitz functions ... More

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theoryMar 13 2019We investigate the basis-set convergence of coupled cluster electronic correlation energies using a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed ... More

Inverse Scattering for the Laplace operator with boundary conditions on Lipschitz surfacesJan 26 2019Feb 17 2019We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators $(\widetilde\Delta,\Delta)$, where $\Delta$ is the free Laplacian in $L^{2}({\mathbb ... More

A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous CoefficientsFeb 06 2019The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly modeled by random ... More

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theoryMar 13 2019Mar 14 2019We investigate the basis-set convergence of coupled cluster electronic correlation energies using a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and is based on a diagrammatically decomposed ... More

Tanaka structures modeled on extended Poincaré algebrasJan 03 2012Oct 04 2012Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive ... More

Gauge-invariant Green's functions for the bosonic sector of the standard modelDec 18 1998Jun 21 2000There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we present a manifestly ... More

Equivariant Differential CohomologyOct 21 2015Nov 10 2015The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action ... More

A Grothendieck-type inequality for local maximaMar 13 2016A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few hundreds variables ... More

Graphical Models Concepts in Compressed SensingNov 18 2010Mar 15 2011This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via ell_1 penalized least-squares ... More

Two Lectures on Iterative Coding and Statistical MechanicsDec 14 2005These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects, such as, iterative ... More

Turbo codes: the phase transitionMar 13 2000Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning ... More

Cooper-Mesons in the Color-Flavor-Locked Superconducting Phase of Dense QCDSep 01 2000QCD superconductors in the color-flavor-locked (CFL) phase sustain excitations (``Cooper'' mesons) that can be described as pairs of particles or holes around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy the masses, decay ... More

A note on normal generation and generation of groupsFeb 03 2014In this note we study sets of normal generators of finitely presented residually $p$-finite groups. We show that if an infinite, finitely presented, residually $p$-finite group $G$ is normally generated by $g_1,\dots,g_k$ with order $n_1,\dots,n_k \in ... More

The origin of the Frey elliptic curve in a too narrow marginApr 13 2016May 27 2016It is shown that an appropriate use of so-called double equations by Diophantus provides the origin of the Frey elliptic curve and from it we can deduce an elementary proof of Fermat's Last Theorem.

The Parton Structure of Real PhotonsSep 15 1997The QCD treatment of the photon structure is recalled. Emphasis is given to the recently derived momentum sum rule, and to the proper choice of the factorization scheme and/or boundary conditions for the evolution equations beyond the leading order. Parametrizations ... More

Spectral Invariance of Besov-Bessel SubalgebrasDec 15 2010Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular we obtain the inverse-closedness ... More

Spherical Casimir effect for a massive scalar field on the three dimensional ballOct 28 2014The zeta function regularization technique is used to study the Casimir effect for a scalar field of mass $m$ satisfying Dirichlet boundary conditions on a spherical surface of radius $a$. In the case of large scalar mass, $ma\gg1$, simple analytic expressions ... More

Neutrino self-energy in external magnetic fieldAug 28 2009Nov 23 2009Using the exact propagators in a constant magnetic field, the neutrino self-energy has been calculated to all orders in the field strength B within the minimal extension of the Weinberg-Salam model with massive Dirac neutrinos. A simple and very accurate ... More

Noise induced stability in fluctuating, bistable potentialsDec 14 1999The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model ... More

Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground statesOct 25 1999A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. It is shown rigorously that the local stability of ferromagnetism in such a model implies global ... More

Similarity renormalization of the electron--phonon couplingSep 06 1996Dec 17 1996We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. ... More

Calculating critical temperatures of superconductivity from a renormalized HamiltonianSep 16 1997It is shown that one can obtain quantitatively accurate values for the superconducting critical temperature within a Hamiltonian framework. This is possible if one uses a renormalized Hamiltonian that contains an attractive electron-electron interaction ... More

Pion photoproduction in a nonrelativistic theorySep 16 2009The pion and nucleon mass differences generate a very pronounced cusp in the photoproduction reaction of a single pion on the nucleon. A nonrelativistic effective field theory to describe this reaction is constructed. The approach is rigorous in the sense ... More

Measuring Dark Matter at CollidersSep 20 2005Sep 26 2005We investigate the need and prospects for measuring dark matter properties at particle collider experiments. We discuss the connections between the inferred properties of particle dark matter and the physics that is expected to be uncovered by the Large ... More

The geometry and origin of ultra-diffuse ghost galaxiesAug 31 2016Sep 02 2016The geometry and intrinsic ellipticity distribution of ultra diffuse galaxies (UDGs) is determined from the line-of-sight distribution of axial ratios q of a large sample of UDGs, detected by Koda et al. (2015) in the Coma cluster. With high significance ... More

Point kinetic model of the early phase of a spherically symmetric nuclear explosionJun 06 2016A concise point kinetic model of the explosion of a prompt supercritical sphere driven by a nuclear fission chain reaction is presented. The findings are in good agreement with the data available for Trinity, the first detonation of a nuclear weapon conducted ... More

On the precision of a data-driven estimate of hadronic light-by-light scattering in the muon g-2: pseudoscalar-pole contributionFeb 10 2016The evaluation of the numerically dominant pseudoscalar-pole contribution to hadronic light-by-light scattering in the muon g-2 involves the pseudoscalar-photon transition form factor F_{P gamma^* gamma^*}(-Q_1^2, -Q_2^2) with P = pi^0, eta, eta^\prime ... More

Star products on graded manifolds and $α'$-corrections to double field theoryNov 12 2015Originally proposed as an $O(d,d)$-invariant formulation of classical closed string theory, double field theory (DFT) offers a rich source of mathematical structures. Most prominently, its gauge algebra is determined by the so-called C-bracket, a generalization ... More

Thermodynamics of Deconfined QCD at Small and Large Chemical PotentialAug 31 2004We present large $N_f$ QCD/QED as a test bed for improved pressure calculations, show how to apply the hints obtained on optimized renormalization scales at large $N_f$ to finite $N_f=2$, and compare the results to recent lattice data.

Quantum Corrections to Thermodynamic Properties in the Large $N_f$ Limit of the Quark Gluon PlasmaMay 13 2004In this doctoral thesis we present the exact large $N_f$ calculation at next-to-leading order of the thermal interaction pressure of deconfined QCD for small and large quark chemical potential where the presence of the Landau pole is negligible numerically. ... More

Correspondence Theorems via Tropicalizations of Moduli SpacesJun 08 2014We show that the moduli spaces of irreducible labeled parametrized marked rational curves in toric varieties can be embedded into algebraic tori such that their tropicalizations are the analogous tropical moduli spaces. These embeddings are shown to respect ... More

Correlation of internal representations in feed-forward neural networksApr 11 1996Feed-forward multilayer neural networks implementing random input-output mappings develop characteristic correlations between the activity of their hidden nodes which are important for the understanding of the storage and generalization performance of ... More

Laboratory Studies of Astrophysical JetsMar 02 2009Jets and outflows produced during star-formation are observed on many scales: from the "micro-jets" extending a few hundred Astronomical Units to the "super-jets" propagating to parsecs distances. Recently, a new "class" of short-lived (hundreds of nano-seconds) ... More

Status of the global electroweak fit of the Standard ModelSep 07 2009Sep 09 2009Results from the global Standard Model fit to electroweak precision data, including newest Tevatron measurements, are reviewed and discussed. The complete fit using also the constraints from the direct Higgs boson searches yields an upper limit on the ... More