Showing papers in "Annalen der Physik in 2008"

On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics

Abstract: The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the eld of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl’s attempt to extend General Relativity, the slow rise of

Entanglement in a periodic quench

Abstract: We consider a chain of free electrons with periodically switched dimerization and study the entanglement entropy of a segment with the remainder of the system. We show that it evolves in a stepwise manner towards a value proportional to the length of the segment and displays in general slow oscillations. For particular quench periods and full dimerization an explicit solution is given. Relations to equilibrium lattice models are pointed out.

Waiting times and noise in single particle transport

Abstract: The waiting time distribution w(τ), i.e. the probability for a delay τ between two subsequent transition (‘jumps’) of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled to external particle reservoirs, one can establish relations between w(τ) and other statistical transport quantities such as the noise spectrum and the Full Counting Statistics. It turns out that w(τ) usually contains additional information on system parameters and properties such as quantum coherence, the number of internal states, or the entropy of the current channels that participate in transport.

Special relativity in the 21st century

Abstract: This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the limiting situation in which the effects of gravity can be neglected, leads to a formulation of special relativity based on the appearance of two universal constants: a limiting speed c and a cosmological constant Λ which measures a residual curvature of the universe, which is not ascribable to the distribution of matter-energy. That these constants should exist is an outcome of the underlying symmetries and is confirmed by experiments and observations, which furnish their actual values. Specifically, it turns out on these foundations that the kinematical group of special relativity is the de Sitter group dS(c, Λ) = SO(1,4). On this basis, we develop at an elementary classical and, hopefully, sufficiently didactical level the main aspects of the theory of special relativity based on SO(1,4) (de Sitter relativity). As an application, we apply the formalism to an intrinsic formulation of point particle kinematics describing both inertial motion and particle collisions and decays.

Nonlocal special relativity

Abstract: In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always pointwise inertial. A critical examination of the locality assumption reveals its domain of validity: it is true for pointwise coincidences, but is in conflict with wave-particle duality. To remedy this situation, a nonlocal theory of accelerated systems is presented that reduces to the standard theory in the limit of small accelerations. Some of the main consequences of nonlocal special relativity are briefly outlined.

Electromagnetic energy and momentum in moving media

Abstract: The problem of the electromagnetic energy-momentum tensor is among the oldest and the most controversial in macroscopic electrodynamics. In the center of the issue is a dispute about the Minkowski and the Abraham tensors for moving media. An overview of the current situation is presented. After putting the discussion into a general Lagrange-Noether framework, the Minkowski tensor is recovered as a canonical energy-momentum. It is shown that the balance equations of energy, momentum, and angular momentum are always satisfied for an open electromagnetic system despite the lack of the symmetry of the canonical tensor. On the other hand, although the Abraham tensor is not defined from first principles, one can formulate a general symmetrization prescription provided a time-like vector is available. We analyze in detail the variational model of a relativistic ideal fluid with isotropic electric and magnetic properties interacting with the electromagnetic field. The relation between the Minkowski energy-momentum tensor, the canonical energy-momentum of the medium and the Abraham tensor is clarified. It is demonstrated that the Abraham energy-momentum is relevant when the 4-velocity of matter is the only covariant variable that enters the constitutive tensor. (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Perfect electromagnetic conductor medium

Abstract: This article presents a review of a novel concept in electromagnetics, the Perfect Electromagnetic Conductor (PEMC). In the Minkowskian representation of the material response to electromagnetic fields, PEMC corresponds to the axion part of the constitutive tensor. From the electrical engineering point of view, PEMC is a generalization of the perfect electric conductor (PEC) and perfect magnetic conductor (PMC) materials which are useful concepts as ideal boundaries in the modeling of electromagnetic problems. PEMC is characterized by a pseudoscalar, admittance-type parameter M, with limits 1/M (PEC) and M (PMC). This paper discusses how the PECM medium as a boundary or in particulate form generalizes earlier known electromagnetic problems (reflection, scattering, materials modeling, waveguides, resonators, image principles). The main effect of PEMC boundary is to rotate the polarization plane of the reflected electric field vector. Also practical realization aspects of a PEMC medium are discussed in the paper.

Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential

Abstract: The Schrodinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers n and l with three different values of the potential parameter α. It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional system from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation (n,l,D) (n,l ± 1,D ∓ 2). This solution reduces to the Hulthen potential case.

Electrodynamics of spin currents in superconductors

Abstract: In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the prediction that a spontaneous spin current exists near the surface of superconductors (spin Meissner effect). In this paper we extend the electrodynamic equations proposed earlier for the charge density and charge current to describe also the space and time dependence of the spin density and spin current. This allows us to determine the magnitude of the expelled negative charge and interior electric field as well as of the spin current in terms of other measurable properties of superconductors. We also provide a `geometric' interpretation of the difference between type I and type II superconductors, discuss how superconductors manage to conserve angular momentum, discuss the relationship between our model and Slater's seminal work on superconductivity, and discuss the magnitude of the expected novel effects for elemental and other superconductors.

History of the Kohlrausch (stretched exponential) function: Pioneering work in luminescence

Abstract: M. Berberan-Santos1,∗, E. N. Bodunov2, and B. Valeur3 1 Centro de Quimica-Fisica Molecular, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, 1049-001 Lisboa, Portugal 2 Department of Physics, Petersburg State Transport University, St. Petersburg, 190031, Russia 3 CNRS UMR 8531, Laboratoire de Chimie Generale, CNAM, 292 rue Saint-Martin, 75141 Paris cedex 03, and Laboratoire PPSM, ENS-Cachan, 61 avenue du President Wilson, 94235 Cachan cedex, France

DMRG studies of critical SU(N) spin chains

Abstract: The DMRG method is applied to integrable models of antiferromagnetic spin chains for fundamental and higher representations of SU(2), SU(3), and SU(4). From the low energy spectrum and the entanglement entropy, we compute the central charge and the primary field scaling dimensions. These parameters allow us to identify uniquely the Wess–Zumino–Witten models capturing the low energy sectors of the models we consider.

The Weinberg-Witten theorem on massless particles: An Essay

Abstract: In this essay we deal with the Weinberg-Witten theorem [1] which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincar´e group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincar´e covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories.

Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy‐momentum tensor

Abstract: In December 1907, Minkowski expressed the Maxwell equations in the very beautiful and compact 4-dimensional form: lor f = -s, lor F*= 0. Here ‘lor’, an abbreviation of Lorentz, represents the 4-dimensional differential operator. We study Minkowski's derivation and show how these equations generalize to their modern premetric form in the framework of tensor and exterior calculus (valid also in general relativity). After mentioning some applications of premetric electrodynamics, we turn to Minkowski's discovery of the energy-momentum tensor of the electromagnetic field. We discuss how he arrived at it and how its premetric formulation looks like.

Feedback control in flashing ratchets

Abstract: A flashing ratchet uses a time-dependent, spatially periodic, asymmetric potential to rectify thermal motion of Brownian particles. Here we review approaches to improve the particle flux in this type of Brownian motor by feedback strategies that switch the potential based on the instantaneous particle distribution. We review strategies that are based on the force experienced by the particles, and introduce a new feedback strategy that is based on the expected displacement that can be achieved. Langevin dynamics simulations show that this maximum net displacement strategy performs better than force-based strategies in the limit of very small particle numbers and not too high temperatures. We also review the effects of time delay and noisy channels on feedback control, and perform a feasibility analysis of an experimental system that can realize feedback control using a computer-controlled, scanning-line optical trap and suspended microspheres.

Universal tunneling time for all fields

Abstract: Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrodinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

On the construction of Fermi‐Walker transported frames

Abstract: We consider tetrad fields as reference frames adapted to observers that move along arbitrary timelike trajectories in spacetime. By means of a local Lorentz transformation we can transform these frames into Fermi-Walker transported frames, which define a standard of non-rotation for accelerated observers. Here we present a simple prescription for the construction of Fermi-Walker transported frames out of an arbitrary set of tetrad fields.

Symanzik's method applied to fractional quantum Hall edge states

Abstract: The method of separability, introduced by Symanzik, is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern-Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga-Luttinger commutation relation.

The Fokker‐Planck equation, and its application in plasma physics

Abstract: In a classic paper Max Planck derived an equation, now known as the Fokker-Planck equation, which plays a central role in the statistics description of many body problems. The equation is used in many branches of physics as well as chemistry and biology to describe a variety of different processes. In plasma physics, on which this paper concentrates, it forms the corner stone for the description of the Coulomb collisions. Furthermore, it is pointed out that also the so-called quasi-linear theory is closely related to the Fokker-Planck equation. (c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interacting bosons in an optical lattice

Abstract: A strongly interacting Bose gas in an optical lattice is studied using a hard-core interaction. Two different approaches are introduced, one is based on a spin-1/2 Fermi gas with attractive interaction, the other one on a functional integral with an additional constraint (slave-boson approach). The relation between fermions and hard-core bosons is briefly discussed for the case of a one-dimensional Bose gas. For a three-dimensional gas we identify the order parameter of the Bose-Einstein condensate through a Hubbard-Stratonovich transformation and treat the corresponding theories within a mean-field approximation and with Gaussian fluctuations. This allows us to evaluate the phase diagram, including the Bose-Einstein condensate and the Mott insulator, the density-density correlation function, the static structure factor, and the quasiparticle excitation spectrum. The role of quantum and thermal fluctuations are studied in detail for both approaches, where we find good agreement with the Gross-Pitaevskii equation and with the Bogoliubov approach in the dilute regime. In the dense regime, which is characterized by the phase transition between the Bose-Einstein condensate and the Mott insulator, we discuss a renormalized Gross-Pitaevskii equation. This equation can describe the macroscopic wave function of the Bose-Einstein condensate in the dilute regime as well as close to the transition to the Mott insulator. Finally, we compare the results of the attractive spin-1/2 Fermi gas and those of the slave-boson approach and find good agreement for all physical quantities.

Influence of light waves on the thermoelectric power under large magnetic field in III‐V, ternary and quaternary materials

Abstract: We study theoretically the influence of light waves on the thermoelectric power under large magnetic field (TPM) for III-V, ternary and quaternary materials, whose unperturbed energy-band structures, are defined by the three-band model of Kane. The solution of the Boltzmann transport equation on the basis of this newly formulated electron dispersion law will introduce new physical ideas and experimental findings in the presence of external photoexcitation. It has been found by taking n-InAs, n-InSb, n-Hg1-xCdxTe and n-In1-xGaxAsyP1-y lattice matched to InP as examples that the TPM decreases with increase in electron concentration, and increases with increase in intensity and wavelength, respectively in various manners. The strong dependence of the TPM on both light intensity and wavelength reflects the direct signature of light waves that is in direct contrast as compared with the corresponding bulk specimens of the said materials in the absence of external photoexcitation. The rate of change is totally band-structure dependent and is significantly influenced by the presence of the different energy-band constants. The well-known result for the TPM for nondegenerate wide-gap materials in the absence of light waves has been obtained as a special case of the present analysis under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. Besides, we have also suggested the experimental methods of determining the Einstein relation for the diffusivity:mobility ratio, the Debye screening length and the electronic contribution to the elastic constants for materials having arbitrary dispersion laws.

Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature

Abstract: In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses – beside the Hodge decomposition for one-forms – an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss’ theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations.

What is missing from Minkowski's “Raum und Zeit” lecture

Abstract: This contribution tries to highlight the importance of Minkowski's “Raum und Zeit” lecture in a “negative” way, where negative is taken in the photographic sense of reversing lights and shades. Indeed, we focus on the “shades” of Minkowski's text, i.e. what is missing, or misunderstood. In particular, we focus on two issues: (i) why are Poincare's pioneering contributions to four-dimensional geometry not quoted by Minkowski (while he abundantly quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski fully grasp the physical (and existential) meaning of “time” within spacetime? We think that this “negative” approach (and the contrast between Poincare's and Minkowski's attitudes towards physics) allows one to better grasp the boldness of the revolutionary step taken by Minkowski in his Cologne lecture.

Approximate record length constraints for experimental identification of dynamical fractals

Abstract: The ambiguity that can exist, for short datasets, between the observational power spectra of dynamical fractals and low-order linear memory processes is demonstrated and explained. It is argued that it could be broadly useful to have a highly practical rule-of-thumb for assessing whether a data record is sufficiently long to permit distinguishing the two types of processes, and if it is not, to produce an approximate estimate of the amount of additional data that would be required to do so. Such an expression is developed using the AR(1) process as a loose benchmark. Various aspects of the technique are successfully tested using synthetic time series generated by a range of prescribed models, and its application and relevance to observational datasets is then demonstrated using examples from mathematical ecology (wild steelhead population size), geophysics (river flow volume), and econophysics (stock price volatility).

Ettore Majorana and his heritage seventy years later

Abstract: The physicists working in several areas of research know quite well the name of Ettore Majorana, since it is currently associated to fundamental concepts like Majorana neutrinos in particle physics and cosmology or Majorana fermions in condensed matter physics. But, probably, very few is known about other substantial contributions of that ingenious scholar, and even less about his personal background. For non specialists, instead, the name of Ettore Majorana is usually intimately related to the fact that he disappeared rather mysteriously on March 26, 1938, just seventy years ago, and was never seen again. The life and the work of this Italian scientist is the object of the present review, which will also offer a summary of the main results achieved in recent times by the historical and scientific researches on his work.

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

Abstract: Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of the covariant four-dimensional form unique? How do the different sign assumptions of electrodynamics emerge from this decomposition? Which of these assumptions are fundamental and which of them may be modified? How does the Minkowski space-time metric emerge from this preliminary metric-free construction? In this paper we are looking for answers to the problems mentioned. Our main result is the derivation of four different possible sets of electrodynamic equations which may occur in different types of isotropic electromagnetic media. The wave propagation in each of these media is described by the Minkowskian optical metrics. Moreover, the electric and magnetic energies are nonnegative in all cases. We also show that the correct directions of the Lorentz force (as a consequence of the Dufay and the Lenz rules) hold true for all these cases. However, the differences between these four types of media must have a physical meaning. In particular, the signs of the three electromagnetic invariants are different.

Vacuum driven accelerated expansion

Abstract: It has been shown that an improved estimation of the quantum vacuum energy can yield not only theoretically acceptable but also experimentally realistic results. Our idea consists in a straightforward extraction of the gravitationally interacting part of the full quantum vacuum energy by means of gauge transformations. The implementation of this idea has been performed, in the background of a Friedmann-Lemaitre-Robertson-Walker geometry, by means of the euclidean version of the effective action formalism, in the language of Schwinger's proper time and Seeley-DeWitt's heat kernel expansion.

On the nature of thermodynamic extremum principles: The case of maximum efficiency and maximum work†

Abstract: Extremum principles are at the heart of theoretical physics. For a complete definition one does not only need to specify the variable to be extremized but also the respective functional space and its parametrization. Here we use a control-theoretical approach to clarify the meaning of two maximum principles in the context of cyclic thermodynamic processes.

Recent developments in quantum key distribution: Theory and practice

Abstract: Quantum key distribution is among the foremost applications of quantum mechanics, both in terms of fundamental physics and as a technology on the brink of commercial deployment. Starting from principal schemes and initial proofs of unconditional security for perfect systems, much effort has gone into providing secure schemes which can cope with numerous experimental imperfections unavoidable in real world implementations. In this paper, we provide a comparison of various schemes and protocols. We analyse their efficiency and performance when implemented with imperfect physical components. We consider how experimental faults are accounted for using effective parameters. We compare various recent protocols and provide guidelines as to which components propose best advances when being improved.

Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and isotropic exchange interaction on a triangle and tetrahedron

Abstract: The Hubbard model extended by both nearest-neighbour (nn) Coulomb correlation and nearest-neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak-interacting clusters is considered. The grand-canonical potential Ω (μ, T, h) and the electron occupation N (μ, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N (μ, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the μ-U ground-state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field hc. The dependence of hc on U shows a maximum for strong on-site correlation. The influence of nn-exchange and nn-Coulomb correlation on the ground-state phase diagrams is calculated. Whereas antiferromagnetic nn-exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn-Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn-exchange and attractive nn-Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed.

Pressure driven transport of glassy solid helium in cylindrical nanopores at very low temperature regime

Abstract: By using the glassy helium model and boundary perturbation method, we can obtain the velocity fields (as well as the flow rate up to the second order) at very low temperature regime inside the wavy-rough cylindrical nanopores. Our results show that the velocities of solid helium reported before by many groups could be reproduced by carefully selecting relevant physical parameters.