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Showing papers in "Annalen der Physik in 1998"


Journal ArticleDOI
TL;DR: In this article, the authors give an elementary and self-contained derivation of the standard identities for abelian bosonization in 1 dimension in a system of finite size L, following and simplifying Haldane's constructive approach.
Abstract: This tutorial review gives an elementary and self-contained derivation of the standard identities OwhOxUFh eif hOxU , 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, r dos OwU, at the site of an impurity in a Tomonaga-Luttinger liquid: we use finite-size refer- mionization to show exactly that for ga 1 its asymptotic low-energy behavior is r dos OwUw. 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 rela- tions 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 inter- ested 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 rdosOwU - 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 eiFOxU and the boson field FOxU itself.

464 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the same instantaneous spreading can occur in relativistic quantum theory and that transition probabilities in widely separated systems may instantaneously become nonzero, and how this affects Einstein causality.
Abstract: In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous spreading can occur in relativistic quantum theory and that transition probabilities in widely separated systems may instantaneously become nonzero. We discuss how this affects Einstein causality.

96 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered the propagation of light in a constant homogeneous magnetic field and in a Casimir vacuum and found that the latter exhibits modes of light with phase and group velocities larger than c in the low frequency domain ω ≪ m where m is the electron mass.
Abstract: QED 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 light c. 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 than c in the low frequency domain ω ≪ m where m is 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.

48 citations


Journal ArticleDOI
TL;DR: In this article, Monte Carlo simulations in two to seven dimensions at the percolation threshold depend on the number N of clusters trading within one time step, and the changes follow a power law; for 1 ≪ n ≪ Nt they are bell-shaped with power-law tails; for N ∼ nt they crossover to a Gaussian.
Abstract: The fluctuations of the stock market — the price changes per unit time — seem to deviate from Gaussians for short time steps. Power laws, exponentials, and multifractal descriptions have been offered to explain this short-time behavior. Microscopic models dealing with the decisions of single traders on the market have tried to reproduce this behavior. Possibly the simplest of these models is the herding approach of Cont and Bouchaud. Here a total of Nt traders cluster together randomly as in percolation theory. Each cluster randomly decides by buy or sell an amount proportional to its size, or not to trade. Monte Carlo simulations in two to seven dimensions at the percolation threshold depend on the number N of clusters trading within one time step. For N ∼ 1, the changes follow a power law; for 1 ≪ N ≪ Nt they are bell-shaped with power-law tails; for N ∼ Nt they crossover to a Gaussian. The correlations in the absolute value of the change decay slowly with time. Thus percolation not only describes the origin of life or the boiling of your breakfast egg, but also explains why we are not rich.

45 citations


Journal ArticleDOI
TL;DR: In this paper, it has been demonstrated that signals conveyed by evanescent modes can travel faster than light, and it has also been shown that the superluminal signal velocity of these modes can be measured by quantum mechanics.
Abstract: It recently has been demonstrated that signals conveyed by evanescent modes can travel faster than light. In this report some special features of signals are introduced and investigated, for instance the fundamental property that signals are frequency band limited. Evanescent modes are characterized by extraordinary properties: Their energy is negative, they are not directly measurable, and the evanescent region is not causal since the modes traverse this region instantaneously. The study demonstrates the necessity of quantum mechanics in order to understand the superluminal signal velocity of classical evanescent modes.

42 citations


Journal ArticleDOI
TL;DR: In this article, the authors clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties, and discuss the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.
Abstract: We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the problem of time-of-arrivals in the nonrelativistic quantum mechanics of a single particle, where the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum.
Abstract: In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

27 citations


Journal ArticleDOI
TL;DR: In this article, the Lanczos diagonalization of the level spacing distribution is applied to the disorder-induced metal-insulator transition for dimensionality d = 4 and the critical level statistics are shown to deviate stronger from the result of the random matrix theory compared to those of d = 3 and become closer to the Poisson limit of uncorrelated spectra.
Abstract: The 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 Q_n(E) of having n levels in a given energy interval E we find the critical disorder W_c = 34.5 \pm 0.5, the correlation length exponent u = 1.1 \pm 0.2 and the critical spectral compressibility k_c \approx 0.5.

27 citations



Journal ArticleDOI
TL;DR: In this article, the authors consider several arguments which were put forward in recent years in order to show that these nonlocal effects cannot be used for superluminal communication and show that the question in the title of this paper is still open.
Abstract: In a compound quantum system with EPR–like correlations a measurement of one subsystem induces instantaneously changes of the other subsystem, irrespective of the relative distance of the two subsystems. We consider several arguments which were put forward in recent years in order to show that these nonlocal effects cannot be used for superluminal communication. It turns out that the arguments mentioned above are merely plausible but not really stringent and convincing. This means that the question in the title of this paper is still open.

16 citations



Journal ArticleDOI
TL;DR: In this paper, the authors present the theory of how to generate UPW solutions of the Maxwell equation and discuss the particular case of the superluminal electromagnetic X-wave (SEXW), clarifying its extraordinary properties.
Abstract: Recently it has been shown that all relativistic wave equations possess families of undistorted progressive waves (UPWs) which can travel with arbitrary speeds 0 ≤ v < ∞. In this paper we present the theory of how to generate UPW solutions of the Maxwell equation and discuss the particular case of the superluminal electromagnetic X-wave (SEXW), clarifying its extraordinary properties. The theory of how it is possible to launch finite aperture approximations for the SEXW in free space is also discussed in detail. The theory is illustrated by computer simulations showing the birth of a finite aperture approximation for a SEXW and its superluminal propagation without appreciable distortion up to a 100 km. We discuss also the experimental evidence available and discuss if SEXWs can be used to transmit information.

Journal ArticleDOI
TL;DR: In this paper, the effects of random coordination on the statistical properties of energy spectra were analyzed for planar topologically disordered systems generated from Voronoi tessellations of space.
Abstract: Networks generated from Voronoi tessellations of space are prototypes for topologically disordered systems. In order to assess the effects of random coordination on the statistical properties of energy spectra, we analyze tight-binding models for planar topologically disordered systems. To this end, the networks are generated by a simple topological model covering a wide range of naturally observed random structures. We find that the energy-level-spacing distributions exhibit level repulsion, similar to the spacings in the energetically disordered Anderson model of localization in the metallic regime.

Journal ArticleDOI
TL;DR: In this paper, a thorough understanding of the excitonic spectra from quantum wells with rough interfaces or alloy disorder requires large-scale numerical simulations with detailed modeling of the underlying quantum mechanics of exciton localization and relaxation.
Abstract: A thorough understanding of the excitonic spectra from quantum wells with rough interfaces or alloy disorder requires large-scale numerical simulations with detailed modeling of the underlying quantum mechanics of exciton localization and relaxation. We discuss various numerical aspects of the calculation of wave functions, phonon transition rates and radiative lifetimes, as well as absorption and luminescence spectra. We argue, that spatially and energetically resolved spectra yield information on wave function size and localization character and discuss phonon scattering between disorder eigenstates for the limit of small energy transfer which is relevant at low temperatures.

Journal ArticleDOI
TL;DR: In this article, the asymptotic behavior of the critical coupling Ut (t′) at small t′ is calculated in dimensions d = 2,3, ∞ using Hartree theory; this yields the exact result at least in d >> 2.
Abstract: The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t′. The asymptotic behavior of the critical coupling Ut (t′) at small t′ is calculated in dimensions d = 2,3, ∞ using Hartree theory; this yields the exact result at least in d >> 2. The order of the transition is also determined. A region of stability of a metallic antiferromagnetic phase in d = 3 is identified.

Journal ArticleDOI
TL;DR: In this article, total energy pseudopotential calculations on neutral and negatively charged Snn and Pbn (n = 3 − 10) clusters were performed and the lowest energy structures have been determined for all clusters, and the stabilities of neutral clusters were investigated by comparing their evaporation energies and stability functions.
Abstract: We have performed ab initio total-energy pseudopotential calculations on neutral and negatively charged Snn and Pbn (n = 3 − 10) clusters. The lowest energy structures have been determined for all clusters, and the stabilities of neutral clusters were investigated by comparing their evaporation energies and stability functions. Clusters with n = 7, 10 were found to be most stable while the clusters with n = 8 and Pb5 were much less stable, in agreement with features of the observed mass spectra. Calculations on Sn−n and Pb−n show that both atomic and electronic structures of a neutral cluster change substantially upon charging. The densities of states of Sn−n clusters reproduce the main features of the experimental photoelectron spectra. The agreement is poorer for Pb−n clusters where the calculations underestimate the separation between energy levels which we think is due to the larger spin-orbit splitting in Pb, which was neglected in the calculations. We found that the differences between Sn and Pb clusters cannot be completely addressed without a more complete accounting of relativistic effects. The electron affinities of Snn and Pbn clusters have also been calculated and the results agree fairly well with experimental values. Finally we considered Sn2−4 and Pb2−4 clusters and related the results to the formation of Zintl anions in liquid alkali-Sn and alkali-Pb alloys.

Journal ArticleDOI
TL;DR: An example of anomalous negative time delay in resonance scattering is provided in this paper, where the effect is due to an absorbing, negative imaginary part in the interaction potential, and it is assumed that the absorbing part is a function of the resonance frequency.
Abstract: Quantum scattering resonances are generally associated with a positive time delay. An example of anomalous negative time delay in resonance scattering is provided. The effect is due to an absorbing, negative imaginary part in the interaction potential.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source.
Abstract: We investigate the time evolution of waves in evanescent media generated by a source within this medium and observed at some distance away from the location of the source. The aim is to find a velocity which describes a causal process and is thus, for a medium with relativistic dispersion, limited by the velocity of light. For a source with a sharp onset in time, the wave function consists of a forerunner generated by the onset of the source, and of a monochromatic front. The forerunner is dominated by a frequency which decreases with time, and the monochromatic front carries the oscillation frequency of the source into the evanescent medium. For a medium with Schrodinger-like dispersion the velocity of the front is infinite and the monochromatic front propagates with a velocity which is in agreement with the traversal time for tunneling. In the relativistic case the forerunners travel with the velocity of light and the velocity the monochromatic front is smaller than the velocity of light and only for special energies equal to the velocity of light. For sources with a sharp onset, the forerunners are not attenuated and in magnitude far exceed the monochromatic front. This renders the detection of the monochromatic front difficult. To avoid the different behavior of forerunners and monochromatic fronts, sources which are frequency-band limited can be considered or a short-time Fourier transform of the field at the observation point can be taken. Both discussions suggest that the traversal time can be determined only up to a factor of (1).

Journal ArticleDOI
TL;DR: In this paper, the correlation of eigenvectors in Ginibre's and Girko's ensembles of Gaussian, non-Hermitian random N × N matrices J is analyzed.
Abstract: We analyse correlations of eigenvectors in Ginibre's and Girko's ensembles of Gaussian, non-Hermitian random N × N matrices J. We study the ensemble average of 〈Lα|Lβ〉 〈Rβ|Rα〉, where 〈Lα| and |Rβ〉 are the left and right eigenvectors of J. The case of Ginibre's ensemble, in which the real and imaginary parts of each element of J are independent random variables, is sufficiently symmetric to allow for an exact solution. In the more general case of Girko's ensemble, we rely on approximations which become exact in the limit of N ∞.

Journal ArticleDOI
TL;DR: In this article, the authors describe a series of atom optics experiments underway at Toronto for investigating tunnelling interaction times of various sorts and argue that atom optics is an arena ideally suited for addressing a variety of remaining questions about how, where, and for how long a particle interacts with a tunnel barrier.
Abstract: We describe a series of atom optics experiments underway at Toronto for investigating tunnelling interaction times of various sorts. We begin by discussing some outstanding issues and confusions related to the question of whether or not superluminal tunnelling can be construed as true faster-than-light ``signal propagation,'' a question which we answer in the negative. We then argue that atom optics is an arena ideally suited for addressing a variety of remaining questions about how, where, and for how long a particle interacts with a tunnel barrier. We present recent results on a modified ``delta-kick cooling'' scheme which we have used to prepare Rubidium atoms with one-dimensional de Broglie wavelengths on the order of an optical wavelength, along with simulations showing that from these temperatures, we will be able to use acousto-optically modulated dipole-force barriers to velocity-select ultracold atom samples ideal for future tunnelling experiments.

Journal ArticleDOI
TL;DR: In this article, the authors compare numerically the localization behavior of electronic eigenfunctions in the Anderson model and on self-similar percolation clusters at criticality, and find that the distributions of the local wave function amplitudes at fixed distances from the localization center are very similar for both models.
Abstract: We compare numerically the localization behavior of electronic eigenfunctions in the Anderson model and on self-similar percolation clusters at criticality. We find that the distributions of the local wave function amplitudes |ψ| at fixed distances from the localization center are very similar for both models. The amplitude distributions are well approximated by log-normal fits, which seem to become exact at large distances. From the distributions, we can calculate analytically the behavior of the averages at sufficiently large distances. We observe two different localization regimes. In the first regime, at intermediate distances from the localization center, we find stretched exponential localization (‘sublocalization’), ln 〈|ψ|〉 ∼ —r, with effective localization exponents dψ 1) is observed, converging to simple exponential behavior asymptotically as expected. The crossover from the intermediate to the asymptotic regime depends logarithmically on the number of configurations.

Journal ArticleDOI
TL;DR: In this article, the integrable small-polaron model with general open boundary conditions was constructed using a fermionic version of the Lax pair formulation, which provides a direct proof of integrability of the model.
Abstract: Using a fermionic version of the Lax pair formulation, we construct an integrable small-polaron model with general open boundary conditions. The Lax pair and the boundary supermatrices for the model are obtained. This provides a direct proof of the integrability of the model.


Journal ArticleDOI
TL;DR: In this paper, a numerical decimation method for the study of transport properties of disordered tight-binding systems is presented, where two interacting particles (TIPs) in a quasi-one dimensional random potential and disordered normal -superconducting structures are considered.
Abstract: We present a numerical decimation method for the study of transport properties of disordered tight-binding systems. We demonstrate this method by considering two situations: 1) the problem of two interacting particles (TIP) in a quasi-one dimensional random potential and 2) the conductance of disordered normal - superconducting structures. For case 1) we compute the two particle localisation length lambda(2) presenting results for its dependence on disorder, interaction strength and system width. For case 2) we illustrate the method by presenting results for the sub-gap conductance of a normal wire connected to one normal and one superconducting reservoir and the case of a normal region in contact with two superconductors.

Journal ArticleDOI
TL;DR: In this paper, the shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet, and the maximum of a tunneled wavepacket exhibits a shift which can be interpreted as an enhanced velocity during tunneling.
Abstract: The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schrodinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier width, height and initial width of the wave packet. Compared to the case of free propagation, the maximum of a tunneled wavepacket exhibits a shift, which can be interpreted as an enhanced velocity during tunneling.

Journal ArticleDOI
TL;DR: In this article, the localization behavior of vibrational modes of infinite percolation clusters above the critical concentration in two and three dimensions is discussed, including the low frequency phonon states.
Abstract: After 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.

Journal ArticleDOI
TL;DR: In this paper, the averaged dynamics of a class of random quantum-dynamical systems in continuous space are derived, where each member of the class is characterized by a Hamiltonian which is the sum of two parts.
Abstract: Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the other part is a homogeneous Gaussian random field which is delta correlated in time, but smoothly correlated in position and momentum. The averaged dynamics of the resulting white-noise system is shown to be a monotone mixing increasing quantum-dynamical semigroup. Its generator is computed explicitly. Typically, in the course of time the mean energy of such a system grows linearly to infinity. In the second part of the paper an extended model is studied, which, in addition, accounts for dissipation by coupling the white-noise system linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that, under suitable assumptions on the spectral density of the heat bath, the mean energy then saturates for long times.

Journal ArticleDOI
TL;DR: In this paper, the influence of structural and dynamical properties of a polymer membrane on the gas transport through this matrix is considered. But the authors only consider the case of a glassy polymer, and they only interact through repulsive interactions.
Abstract: We consider the influence of structural and dynamical properties of a polymer membrane on the gas transport through this matrix. The diffusant and the polymer only interact through repulsive interactions. In the case of a glassy polymer, when one can consider the matrix as frozen, the gas particle diffusion is determined by the free volume structure of the system. We show how the percolation properties of the free volume show up in a subdiffusive behavior of the diffusant. When one takes matrix mobility into account the ideal percolation transition vanishes but its trace can still be found in a subdiffusive regime in the gas particle mean square displacement. In the statically non-percolating regime gas transport is enabled and dominated through matrix mobility, whereas in the percolating regime it is determined by matrix structure.

Journal ArticleDOI
TL;DR: In this paper, the uniqueness theorem of Gelfand-Levitan and Marchenko for the one-dimensional inverse spectral and scattering problems has been proved for the class L1,1, obtained by the Marchenko reconstruction procedure.
Abstract: New proofs of the known uniqueness theorems for the one-dimensional inverse spectral and scattering problems are given. Proof of the invertibility of all of the steps in the inversion procedures of Gelfand-Levitan and Marchenko is given. The proposed method of investigation yields some new results, for example, a Marchenko-type equation at x = 0 which holds on the whole axis, rather than on a half-axis, as usual for the scattering theory on half-axis. It also yields a new method, shorter and simpler than earlier published, for proving that the potential in the class L1,1, obtained by the Marchenko reconstruction procedure, generates the scattering data from which it was reconstructed.

Journal ArticleDOI
TL;DR: In this article, the authors employ energy level statistics (ELS) to further characterize the metal-insulator transition in the anisotropic Anderson model of localization by transfer-matrix methods and find a crossover of the nearest-neighbor level spacing distribution from GOE statistics at small disorder indicating metallic behavior to the Poisson distribution at large disorder characteristic for localized states.
Abstract: Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders $W_c$ have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution $P(s)$ from GOE statistics 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 $\Delta_3(L)$ confirms the values of $W_c$ from TMM and MFA.