bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bosonization for beginners — refermionization for experts
Authors: von Delft Jan , Schoeller Herbert 
Published: April 2022

AbstractThis tutorial review gives an elementary and self‐contained derivation of the standard identities (ψη(x) ∼ Fη e, etc.) for abelian bosonization in 1 dimension in a system of finite size L, following and simplifying Haldane's constructive approach. As a non‐trivial application, we rigorously resolve (following Furusaki) a recent controversy regarding the tunneling density of states, ρdos(ω), at the site of an impurity in a Tomonaga‐Luttinger liquid: we use finite‐size refermionization to show exactly that for g = 1/2 its asymptotic low‐energy behavior is ρdos(ω) ∼ ω. This agrees with the results of Fabrizio & Gogolin and of Furusaki, but not with those of Oreg and Finkel'stein (probably because we capture effects not included in their mean‐field treatment of the Coulomb gas that they obtained by an exact mapping; their treatment of anti‐commutation relations in this mapping is correct, however, contrary to recent suggestions in the literature). — The tutorial is addressed to readers with little or no prior knowledge of bosonization, who are interested in seeing “all the details” explicitly; it is written at the level of beginning graduate students, requiring only knowledge of second quantization, but not of field theory (which is not needed here). At the same time, we hope that experts too might find useful our explicit treatment of certain subtleties that can often be swept under the rug, but are crucial for some applications, such as the calculation of ρdos(ω) — these include the proper treatment of the so‐called Klein factors that act as fermion‐number ladder operators (and also ensure the anti‐commutation of different species of fermion fields), the retention of terms of order 1/L, and a novel, rigorous formulation of finite‐size refermionization of both F e—iΦ(x) and the boson field Φ(x) itself.
Localization behavior of vibrational modes
Authors: Bunde Armin , Kantelhardt Jan W. , Schweitzer Ludwig 
Published: April 2022

AbstractAfter a short introduction into percolation theory we discuss the localization behavior of vibrational modes of infinite percolation clusters above the critical concentration in two and three dimensions. Results from level statistics show that all eigenstates are localized in d = 2, including the low frequency phonon states. In d = 3 there is evidence for a localization‐delocalization transition. But contrary to the common view this transition occurs for frequencies above the phonon‐fracton crossover giving rise to a new regime of extended fracton states.
Low temperature behavior of the thermopower in disordered systems near the Anderson transition
Authors: Villagonzalo C. , Römer R.A. 
Published: April 2022

AbstractWe investigate the behavior of the thermoelectric power S in disordered systems close to the Anderson‐type metal‐insulator transition (MIT) at low temperatures. In the literature, we find contradictory results for S. It is either argued to diverge or to remain a constant as the MIT is approached. To resolve this dilemma, we calculate the number density of electrons at the MIT in disordered systems using an averaged density of states obtained by diagonalizing the three‐dimensional Anderson model of localization. From the number density we obtain the temperature dependence of the chemical potential necessary to solve for S. Without any additional approximation, we use the Chester‐Thellung‐Kubo‐Greenwood formulation and numerically obtain the behavior of S at low T as the Anderson transition is approached from the metallic side. We show that indeed S does not diverge.
Critical level statistics at the Anderson transition in four‐dimensional disordered systems
Authors: Zharekeshev I.Kh. , Kramer B. 
Published: April 2022

AbstractThe level spacing distribution is numerically calculated at the disorder‐induced metal–insulator transition for dimensionality d = 4 by applying the Lanczos diagonalisation. The critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d = 3 and to become closer to the Poisson limit of uncorrelated spectra. Using the finite size scaling analysis for the probability distribution Qn(E) of having n levels in a given energy interval E we find the critical disorder Wc = 34.5 ± 0.5, the correlation length exponent ν = 1.1 ± 0.2 and the critical spectral compressibility κc ≈︂ 0.5.
Energy level statistics at the metal‐insulator transition in the Anderson model of localization with anisotropic hopping
Authors: Milde F. , Römer R.A. 
Published: April 2022

AbstractRecently, a metal‐insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer‐matrix methods. This MIT has been also investigated by multifractal analysis and the same critical disorders Wc have been obtained within the accuracy of the data. We now employ energy level statistics to further characterize the MIT. We find a crossover of the nearest‐neighbor level spacing distribution from the Gaussian orthogonal ensemble at small disorder indicating metallic behavior to the Poisson distribution at large disorder characteristic for localized states. An analysis of the system size dependence of the spectral rigidity confirms the values of Wc found previously.
Luttinger‐liquid features in the resonant Raman spectra of quantum wires
Authors: Sassetti M. , Kramer B. 
Published: April 2022

AbstractUsing the bosonization technique, we develop a theory for the Raman scattering of the interacting electrons in quantum wires. The energy spectra of the collective excitations in a two‐subband model are given. The density correlation functions for the Raman cross section are calculated. The charge and spin density excitations observed in recent Raman experiments are identified. Hitherto unexplained “single particle excitations” which appear near resonance and are independent of the relative polarization of incoming and scattered light are shown to originate in higher order spin density excitations, which can be evaluated due to the bosonization. For the intraband excitations, the peak strengths in the Raman cross section as a function of the frequency of the incoming light is explicitely calculated. Power law behaviors depending on the strength of the interaction are predicted.
Exciton dispersion in quantum wells
Authors: Siarkos A. , Runge E. , Zimmermann R. 
Published: April 2022

AbstractWe present for the first time numerical calculations of the center‐of‐mass (c.o.m.) dispersion of an exciton in a quantum well using a finite‐differences method. The coupling of heavy‐ and light‐hole bands is accounted for in →k · →p‐theory, while the conduction band dispersion is assumed parabolic. We motivate a suitable choice of the c.o.m. coordinate system, which increases remarkably the numerical accuracy for finite c.o.m. wavevector. The desired eigenvalues and eigenfunctions of the involved huge matrices are calculated with modern iterative sparse matrix solvers. Results are shown for the example case of a GaAs/Ga7Al3As 〈100〉 quantum well.
Critical and off‐critical singularities in disordered quantum magnets
Authors: Rieger H. 
Published: April 2022

AbstractWe study disordered systems at and near quantum phase transitions, which are transitions at zero temperature that are driven by quantum instead of thermal fluctuations. Special emphasis is put on the so‐called Griffiths‐McCoy regions surrounding these transitions in magnetic systems, where various susceptibilities are found to be divergent for T → 0 without the system being critical. We present a phenomenological picture for uncorrelated and weakly or strongly correlated disorder and check it for various models. In higher dimensions the phenomena seem to be connected to a percolation transition.
Numerical tests of conjectures of conformal field theory for three‐dimensional systems
Authors: Weigel Martin , Janke Wolfhard 
Published: April 2022

AbstractThe concept of conformal field theory provides a general classification of statistical systems on two‐dimensional geometries at the point of a continuous phase transition. Considering the finite‐size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three‐dimensional manifolds.Using Monte Carlo simulations based on the Wolff single‐cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three‐dimensional, hyper‐cylindrical geometry with a toroidal cross‐section considering both periodic and antiperiodic boundary conditions. Studying the correlation lengths of the Ising, the XY, and the Heisenberg model, we find strong evidence for a scaling relation analogous to the two‐dimensional case, but in contrast here for the systems with antiperiodic boundary conditions.
Quantile motion of electromagnetic waves in wave guides of varying cross section and dispersive media
Authors: Dahmen H.D. , Gjonaj E. , Stroh T. 
Published: April 2022

AbstractWe discuss applications of the quantile concept of trajectories and velocities to the propagation of electromagnetic signals in wave guides of varying cross section. Quantile motion is a general description of the transport properties of measurable quantities in quantum mechanics as well as in classical electrodynamics. In the latter case we consider the quantile motion of electromagnetic energy as the direct result of a physical measurement. In this sense the quantile velocity corresponds to the electromagnetic signal velocity. We show that this signal velocity is always smaller than the speed of light in vacuum.
Are predicted superluminal tunneling times an artifact of using the nonrelativistic Schrödinger equation?
Authors: Leavans C.R. , Sala Mayato R. 
Published: April 2022

AbstractFor many approaches to timing electrons scattering from an electrostatic potential barrier there are simple realistic situations, involving barrier heights and incident electron kinetic energies both many orders of magnitude less than the rest energy mc2, for which the calculated mean transmission times imply superluminal velocities. The question of whether or not this is an artifact of using the nonrelativistic Schrödinger equation is investigated for the Bohm trajectory and Salecker‐Wigner quantum clock approaches.
Minimum tunneling time in quantum motion
Authors: Bracher C. , Kleber M. 
Published: April 2022

AbstractStarting out with the dwell time approach by Smith for stationary one‐dimensional tunneling problems, we introduce the notion of the minimum tunneling time required for traversal through an arbitrary potential barrier. The newly devised time scale is based on a simple variational principle and presents a strictly local quantity not depending on the asymptotics of the potential distribution. Its properties are illustrated using the customary square barrier as an example. The minimum tunneling time approach cannot support the existence of superluminal velocities in barrier penetration.
The velocities of light in modified QED vacua
Authors: Scharnhorst K. 
Published: April 2022

AbstractQED vacua under the influence of external conditions (background fields, finite temperature, boundary conditions) can be considered as dispersive media whose complex behaviour can no longer be described in terms of a single universal vacuum velocity of lightc. Beginning in the early 1950's (J.S. Toll), quantum field theoretic investigations have led to considerable insight into the relation between the vacuum structure and the propagation of light. Recent years have witnessed a significant growth of activity in this field of research. After a short overview, two characteristic situations are discussed: the propagation of light in a constant homogeneous magnetic field and in a Casimir vacuum. The latter appears to be particularly interesting because the Casimir vacuum has been found to exhibit modes of the propagation of light with phase and group velocities larger thancin the low frequency domain ω ≪mwheremis the electron mass. The impact of this result on the front velocity of light in a Casimir vacuum is discussed by means of the Kramers‐Kronig relations.
On the application of the Kramers‐Kronig relations to the interaction time problem
Authors: Gasparian V. , Schön G. , Ruiz J. , Ortuño M. 
Published: April 2022

AbstractIt is shown that the two components of the complex characteristic interaction time τ(ω) = τ1(ω) — iτ2(ω) for classical electromagnetic waves with an arbitrary shaped barrier are not entirely independent quantities, but are connected by the Kramers‐Kronig relations. The corresponding macroscopic sum rule for the complex time is also derived. An analogy between the interaction time problem and an electrical circuit with capacitive and conducting components is established from which we propose that the effective crossing time should be the maximum of the two components.
Quantizing gravity and spacetime: Where do we stand ?
Authors: Ne'eman Yuval 
Published: April 2022

AbstractWe review five possible solutions to the riddle posed by Quantum Gravity: (1) Gravity should stay as a classical theory (L. Rosenfeld); (2) Quantum Gravity requires a formalism which will take the human mind (or the intelligent observer) into account, resolving at the same time the riddle of the collapse of the wave function/state vector in Quantum Mechanics in general (Penrose); (3) Perturbative Quantization; (4) Hamiltonian Quantization (Dirac, Ashtekar); (5) String Theory. We also discuss the quantization of spacetime.
Nonuniqueness of memories
Authors: Čápek V. 
Published: April 2022

AbstractNature prefers infinite to finite order perturbation theories. That is why we studied the exciton dynamics in a simple model of the interacting exciton‐phonon system again, by a tricky form of the Tokuyama‐Mori method yielding a natural way of including higher‐order terms and avoiding the problem of memories. Physically reasonable solution for site‐occupation probabilities corresponding to previous results is then used in an inverse manner to deduce the exciton memories able to reproduce them. We found that: 1. Thus determined memories are not unique. 2. Their different forms reconcile different conjectures about structure of the exciton memory functions. 3. The markovian approximation to the resulting Generalized master equations fails even when the memories decay much faster than the solution. 4. In connection with that, the Förster transfer rate formula together with the current Markov understanding of the exciton transfer becomes dubious.
Scattering of neutrons on a Bose condensate
Authors: Baranov D.B. , Kozlov Z.A. , Siurakshina L.A. , Yarunin V.S. 
Published: April 2022

AbstractThe spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path‐integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time‐independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron‐boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi‐elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.
Quantum motion of electrons in topologically distorted crystals
Authors: Bausch Richard , Schmitz Rudi , Turski Łukasz A. 
Published: April 2022

AbstractFor the description of the long‐wavelength quantum states of electrons in crystals with topological defects we establish a general framework on the basis of the continuum theory of defects. The resulting one‐particle Schrödinger equation lives on a Riemann‐Cartan manifold, representing the distorted crystal, and consists of two parts. All effects due to the topology of the defects are contained in the first part which has a covariant form and describes the purely geometric particle motion. The second part is non‐covariant and derives from deformation‐dependent tunneling rates of the particle which e.g. are responsible for the existence of bound states to edge dislocations.
New concepts for molecular magnets
Authors: Pilawa Bernd 
Published: April 2022

AbstractMiller and Epstein (1994) define molecular magnets as magnetic materials which are prepared by the low‐temperature methods of the preparative chemistry. This definition includes molecular crystals of neutral radicals, radical salts and charge transfer complexes as well as metal complexes and polymers with unpaired spins (Dormann 1995). The challenge of molecular magnets consists in tailoring magnetic properties by specific modifications of the molecular units. The combination of magnetism with mechanical or electrical properties of molecular compounds promise materials of high technical interest (Gatteschi 1994a and 1994b, Möhwald 1996) and both the chemical synthesis of new molecular materials with magnetic properties as well as the physical investigation and explanation of these properties is important, in order to achieve any progress. This work deals with the physical characterization of the magnetic properties of molecular materials. It is organized as follows. In the first part molecular crystals of neutral radicals are studied. After briefly discussing the general magnetic properties of these materials and after an overview over the physical principles of exchange interaction between organic radicals I focus on the interplay between the crystallographic structure and the magnetic properties of various derivatives of the verdazyl and nitronyl nitroxide radicals. The magnetic properties of metal complexes are the subject of the second part. After an overview over the experimental and theoretical tools which are used for the investigation of the magnetic properties I shortly discuss the exchange coupling of transition metal ions and the magnetic properties of complexes of two and three metal ions. Special emphasis is given to spin cluster compounds. Spin cluster denote complexes of many magnetic ions. They are attractive as building blocks of molecular magnets as well as magnetic model compounds for the study of spin frustration, molecular super‐paramagnetism and quasi one‐dimensional magnets.
Perturbative gauge invariance: the electroweak theory
Authors: Dütsch Michael , Schaf Günter 
Published: April 2022

AbstractThe concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.
Perturbative gauge invariance: electroweak theory II
Authors: Aste Andreas , Schaf Günter , Dütsch Michael 
Published: April 2022

AbstractA recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction.
Numerical study on Anderson transitions in three‐dimensional disordered systems in random magnetic fields
Authors: Kawarabayashi Tohru , Kramer Bernhard , Ohtsuki Tomi 
Published: April 2022

AbstractThe Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent ν for the localization length to be 1.45 ± 0.09 with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation‐of‐motion method.
Theoretical approaches to the metal‐insulator transition in 2D
Authors: Abrahams Elihu 
Published: April 2022

AbstractRecent experiments on the two‐dimensional electron gas in various semiconductor structures have revealed the existence of what appears to be a continuous low‐temperature metal‐insulator transition as the electron density is varied, although it was previously commonly accepted that all electronic states will be localized in a two‐dimensional disordered medium. Theoretical proposals for the explanation of various aspects of the experiments will be reviewed and implications for the scaling theory of localization will be discussed.
Disorder induced ferromagnetism
Authors: Eisenberg E. , Berkovits R. 
Published: April 2022

AbstractWe study the in uence of on‐site disorder on the magnetic properties of the ground state for restricted geometries. We find that for two dimensional systems disorder enhances the spin polarization of the system. The tendency of disorder to enhance magnetism in the ground state may be relevant to recent experimental observations of spin polarized ground states in quantum dots.
Does a magnetic field suppress the Coulomb gap?
Authors: Sandow B. , Gloos K. , Rentzsch R. , Ionov A.N. , Schirmacher W. 
Published: April 2022

AbstractWe used electron‐tunnelling spectroscopy to investigate the Coulomb correlation in n ‐ type Germanium. The dopant concentration was smaller than the critical concentration for the metal‐insulator (Anderson) transition. The tunnelling conductance, which probes the electronic density of states, was found to depend strongly on both voltage and temperature. At low temperatures it shows a conductance minimum at the Fermi energy as expected for the Coulomb correlation gap. Applying a magnetic field up to B = 4T at T = 0.1 K reduces the magnitude of the tunneling conductance, but does not significantly change the shape of the spectra. At higher fields, the conductance minimum disappears, suggesting a suppression of the Coulomb gap. This could be due to the field‐induced confinement of the electron wave functions, that strongly reduces the overlap between the localized electron states.