Showing papers in "Annalen der Physik in 2003"
TL;DR: This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics, and the VO-Calculus formulation is compared to a CO- Calculus model to show the limitations of the latter in resolving the transition between the relevant dynamic regimes.
Abstract: This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics. A mathematical definition for the VO-differential operator that is suitable to mechanical modelling is proposed, and an example concerning the effect of nonuniform viscoelastic frictional forces is described. A numerical method for the solution of Variable Order Differential Equations (VODEs) is proposed. The physical model under study requires mathematical tools that lie beyond the traditional methods of Constant-Order (CO) differential equations. The VO-Calculus formulation is compared to a CO-Calculus model in order to show the limitations of the latter in resolving the transition between the relevant dynamic regimes.
427 citations
CERN1
TL;DR: The history of the universe after its first second is now tested by high quality observations of light element abundances and temperature anisotropies of the cosmic microwave background as mentioned in this paper, however, it is constrained by experiments at particle and heavy ion accelerators.
Abstract: The history of the Universe after its first second is now tested by high quality observations of light element abundances and temperature anisotropies of the cosmic microwave background The epoch of the first second itself has not been tested directly yet: however, it is constrained by experiments at particle and heavy ion accelerators Here I attempt to describe the epoch between the electroweak transition and the primordial nucleosynthesis The most dramatic event in that era is the quark--hadron transition at 10 $\mu$s Quarks and gluons condense to form a gas of nucleons and light mesons, the latter decay subsequently At the end of the first second, neutrinos and neutrons decouple from the radiation fluid The quark--hadron transition and dissipative processes during the first second prepare the initial conditions for the synthesis of the first nuclei As for the cold dark matter (CDM), WIMPs (weakly interacting massive particles) -- the most popular candidates for the CDM -- decouple from the presently known forms of matter, chemically (freeze-out) at 10 ns and kinetically at 1 ms The chemical decoupling fixes their present abundances and dissipative processes during and after thermal decoupling set the scale for the very first WIMP clouds
117 citations
TL;DR: In this paper, a relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers.
Abstract: Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.
85 citations
TL;DR: In this paper, the authors investigated Nb/Ni bilayers prepared by magnetron sputtering on glass subtrates and characterized the quality of the films by small-angle X-ray diffraction analysis.
Abstract: We investigated Nb/Ni bilayers prepared by magnetron sputtering on glass subtrates. The quality of the films was characterized by small-angle X-ray diffraction analysis. The thickness of the layers was determined by the Rutherford backscattering spectrometry (RBS). For specimens with constant Nb layer thickness we observed distinct oscillations of the superconducting critical temperature upon increasing the thickness of the Ni layer. The results are interpreted in terms of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like inhomogeneous superconducting pairing in the ferromagnetic Ni Layer.
63 citations
TL;DR: In this article, a supersymmetric technique for the solution of the effective mass Schrodinger equation is proposed, where the potentials are fully isospectral with the original potentials.
Abstract: A supersymmetric technique for the solution of the effective mass Schrodinger equation is proposed. Exact solutions of the Schrodinger equation corresponding to a number of potentials are obtained. The potentials are fully isospectral with the original potentials. The conditions for the shape invariance of the potentials are discussed.
52 citations
TL;DR: In this paper, the nonlocal electrodynamics of linearly accelerated systems are discussed in connection with the development of Lorentz-invariant nonlocal field equations.
Abstract: The nonlocal electrodynamics of accelerated systems is discussed in connection with the development of Lorentz-invariant nonlocal field equations. Nonlocal Maxwell’s equations are presented explicitly for certain linearly accelerated systems. In general, the field equations remain nonlocal even after accelerated motion has ceased.
44 citations
TL;DR: In this paper, a modified version of Nelson's seminal paper on the derivation of the time-dependent Schrodinger equation is presented, which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces.
Abstract: We present a modified version of Nelson's seminal paper on the derivation of the time-dependent Schrodinger equation which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces. The emphasis of our elaboration is focused on the implication of allowing stochastic forces to occur, viz. that the energy E of the particle is no longer conserved on its trajectory in a conservative force field. We correlate this departure Δ E from its classical energy with the energy/time uncertainty relation where Δ t is the average time for Δ E to persist. The stability of atoms, the zero-point energy of oscillators, the tunneling effect and the diffraction at slits are shown to be directly connected with the occurrence of such energy fluctuations. We discuss and rederive Nelson's theory entirely from this point of view and generalize his approach to systems of N particles which interact via pair forces. Achieving reversibility in a description of particle motion that is akin to Brownian motion, represents a salient point of the derivation. We demonstrate that certain objections raised against Nelson's theory are without substance. We also try to put the particular worldview of this version of stochastic quantum mechanics into perspective with regard to the established Copenhagen interpretation.
42 citations
TL;DR: In this paper, the probabilistic consequences of the choice of the basic number field in the quantum formalism were studied and it was shown that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena.
Abstract: We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p-adic representations.
37 citations
TL;DR: In this paper, it was shown that the Dirac current is the only conserved 4-vector implied by Dirac equation that is not a function of the quantum state, and the existence and properties of further conserved vectors that are not functions of just the state is examined.
Abstract: It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved currents implied by the coupled Maxwell-Dirac equations and the Klein-Gordon equation. The uniqueness of the usual Pauli and Schrodinger currents follows by regarding these as the non-relativistic limits of the Dirac and Klein-Gordon currents, respectively. The existence and properties of further conserved vectors that are not functions of just the state is examined.
33 citations
TL;DR: In this article, the authors discuss the electromagnetic measurements of rotating observers and study the propagation of electromagnetic waves in a uniformly rotating frame of reference, and some of the observational consequences of the coupling of the spin of a particle with the rotation of a gravitational source are briefly examined.
Abstract: We discuss the electromagnetic measurements of rotating observers and study the propagation of electromagnetic waves in a uniformly rotating frame of reference. The phenomenon of helicity-rotation coupling is elucidated and some of the observational consequences of the coupling of the spin of a particle with the rotation of a gravitational source are briefly examined.
31 citations
TL;DR: In this article, the SU(2,1) invariance of the stationary axisymmetric Einstein-Maxwell equations can be used to construct solutions for the electro-vacuum from solutions to the pure vacuum case via a so-called Harrison transformation.
Abstract: We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at the boundary of an electro-vacuum. The Einstein-Maxwell equations in the presence of one Killing vector are obtained by using a projection formalism. This leads to equations for three-dimensional gravity where the matter is given by a SU(2,1)/S[U(1,1)× U(1)] nonlinear sigma model. The SU(2,1) invariance of the stationary Einstein-Maxwell equations can be used to construct solutions for the electro-vacuum from solutions to the pure vacuum case via a so-called Harrison transformation. It is shown that the corresponding solutions will always have a non-vanishing total charge and a gyromagnetic ratio of 2. Since the vacuum and the electro-vacuum equations in the stationary axisymmetric case are completely integrable, large classes of solutions can be constructed with techniques from the theory of solitons. The richest class of physically interesting solutions to the pure vacuum case due to Korotkin is given in terms of hyperelliptic theta functions. Harrison transformed hyperelliptic solutions are discussed. As a concrete example we study the transformation of a family of counter-rotating dust disks. To obtain algebro-geometric solutions with vanishing total charge which are of astrophysical relevance, three-sheeted surfaces have to be considered. The matter in the disk is discussed following Bicak et al. We review the ‘cut and glue’ technique where a strip is removed from an explicitly known spacetime and where the remainder is glued together after displacement. The discontinuities of the normal derivatives of the metric at the glueing hypersurface lead to infinite disks. If the energy conditions are satisfied and if the pressure is positive, the disks can be interpreted in the vacuum case as made up of two components of counter-rotating dust moving on geodesics. In electro-vacuum the condition of geodesic movement is replaced by electro-geodesic movement. As an example we discuss a class of Harrison-transformed hyperelliptic solutions. The range of parameters is identified where an interpretation of the matter in the disk in terms of electro-dust can be given.
TL;DR: In this paper, a renormalization group formalism for weak coupling instabilities of a large class of interacting electron models is presented to the lowest (one-loop) order, connecting the idea of the ''parquet summation'' to the more modern concept of Wilson's effective action.
Abstract: We present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. As an example, we show the occurrence of d-wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one-loop) order on a most elementary level, connecting the idea of the ``parquet summation'' to the more modern concept of Wilson's effective action. The validity and restrictions of the one-loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two-dimensional Fermi system at Van Hove filling without nesting.
TL;DR: Theodor Kaluza (1885-1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions as discussed by the authors.
Abstract: Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space-time is followed by a discussion of the significance of Kaluza's five-dimensional unified theory in modern physics from the point of view of superstring and M-theory.
TL;DR: In this paper, a core-shell model was proposed to explain the abnormal increase of the saturation magnetization of γ-Fe2O3 nanoparticles dispersed in a silica matrix compared to bulk Fe2O 3 nanoparticles.
Abstract: The saturation magnetization of ferrimagnetic nanoparticles of γ-Fe2O3 that are isolated in an amorphous SiO2 matrix, has a high increase when the temperature decreases from 300 to 77K. In this case, the relative variation (69.7 magnetization corresponding to bulk ferrite (9.5 is attributed to the narrowing of the paramagnetic layer that exists at the surface of nanoparticles; with the decrease of temperature, the mean magnetic diameter, and implicitly the magnetic moment of the particles increases, which in turn leads to an increase of the saturation magnetization. The existence of the paramagnetic layer is a result of the modification of the superexchange interaction between iron ions at the nanoparticle surface, due to the distortion of the crystalline network in the presence of the silica matrix. Based on the experimental results we propose a core-shell model that explains the abnormal increase of the saturation magnetization of γ-Fe2O3 nanoparticles dispersed in a silica matrix compared to bulk γ-Fe2O3.
TL;DR: In this paper, a supersymmetric extension of quantum gauge theory based on a vector multiplet with spin 3/2 partners of spin 3 /2 for the vector fields is considered, and the constructions of the model follow closely the usual construction of gauge models for perturbative field theory.
Abstract: We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
TL;DR: In this article, the spectral characteristics of fluctuating electromagnetic fields generated by a half-space covered with a film of an arbitrary thickness are derived. But the spectral power densities of the field and all spatial derivatives expressed via Fresnel coefficients for both p and s waves were derived.
Abstract: We calculate the spectral characteristics of fluctuating electromagnetic fields generated by a half-space covered with a film of an arbitrary thickness. Materials of the half-space and the film are described by different complex permittivities. Expressions for spectral power densities of fluctuating fields and all spatial derivatives expressed via Fresnel coefficients for “p” and “s” waves are derived. Various limiting cases for propagating and evanescent waves in cases of different film thickness are considered. Possible contributions to spectral power densities from interface excitations and wave-guide modes are discussed by analyzing the Fresnel factors in the expressions. Using the results for spatial derivatives a closed analytical expression for a multipolar force acting on a small particle near a half-space is found for multipoles of all orders. The case for a dipole interaction follows directly from a general solution.
TL;DR: In this paper, the supersymmetric vector multiplet in a purely quantum framework is considered and it is shown that the super-propagator is consistent only for positive mass.
Abstract: We consider the supersymmetric vector multiplet in a purely quantum framework We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass The gauge structure is constructed purely deductive and leads to the introduction of scalar ghost superfields, in analogy to the usual gauge theories The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially on the definition of gauge invariance We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature
TL;DR: In this article, the local density of states (LDOS) for noninteracting electrons in a hard-wall ellipse in the presence of a single nonmagnetic scattering center was investigated.
Abstract: We investigate the local density of states (LDOS) for non-interacting electrons in a hard-wall ellipse in the presence of a single non-magnetic scattering center. Using a T-matrix analysis we calculate the local Green's function and observe a variety of quantum mirage effects for different impurity positions. Locating the impurity near positions with LDOS maxima for the impurity free corral can either lead to a reduction or an ehancement of the LDOS at the mirror image point, i.e. a mirage or anti-mirage effect, or even suppress LDOS maxima in the entire area of the corral.
TL;DR: In this paper, the authors considered the corrections to the Boltzmann theory of electrical transport arising from the Coulomb interaction in disordered conductors and formulated the theory in terms of quasiclassical Green's functions.
Abstract: We consider the corrections to the Boltzmann theory of electrical transport arising from the Coulomb interaction in disordered conductors. In this article the theory is formulated in terms of quasiclassical Green's functions. We demonstrate that the formalism is equivalent to the conventional diagrammatic technique by deriving the well-known Altshuler-Aronov corrections to the conductivity. Compared to the conventional approach, the quasiclassical theory has the advantage of being closer to the Boltzmann theory, and also allows description of interaction effects in the transport across interfaces, as well as non-equilibrium phenomena in the same theoretical framework. As an example, by applying the Zaitsev boundary conditions which were originally developed for superconductors, we obtain the P(E)-theory of the Coulomb blockade in tunnel junctions. Furthermore we summarize recent results obtained for the non-equilibrium transport in thin films, wires and fully coherent conductors.
Abstract: The present paper obtains the exact solutions to the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model and the Chiao-Wu model that describes the propagation of a photon inside an optical fiber. On the basis of the fact that the two-level multiphoton Jaynes-Cummings model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (i.e., the time-independent invariant). By constructing the effective Hamiltonian that describes the interaction of the photon with the medium of the optical fiber, it is further verified that the particular solution to the Schrodinger equation is the eigenfunction of the second-quantized momentum operator of photons field. This, therefore, means that the explicit expression (rather than the hidden form that involves the chronological product) for the time-evolution operator of wave function is obtained by means of the invariant theories.
TL;DR: The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a free model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques as mentioned in this paper.
Abstract: The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a “free” model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.
TL;DR: In this article, a supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analyzed from a quantum cosmological perspective, and it is shown that when the superpot potential is expanded in powers of a parameter λ≪1, the general class of solutions can be found at order λ0, which include in particular quantum states reported in the current literature.
Abstract: A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ≪1. At order λ0 we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ1, where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial ( = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time-reparametrization) can be relevant concerning the issue of supersymmetry breaking.
TL;DR: The nonperturbative approach presented in this paper can, in principle, be applied to clusters of any size, as well as, to another type of model Hamiltonians, and can be used for clustering.
Abstract: The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another type of model Hamiltonians.
TL;DR: In this paper, the theory and phenomenology of the interplay between the massless graviton and its massive Kaluza-Klein modes in the Randall-Sundrum two-brane model are discussed.
Abstract: We discuss the theory and phenomenology of the interplay between the massless graviton and its massive Kaluza-Klein modes in the Randall-Sundrum two-brane model. The equations of motion of the transverse traceless degrees of freedom are derived by means of a Green function approach as well as from an effective nonlocal action. The second procedure clarifies the extraction of the particle content from the nonlocal action and the issue of its diagonalization. The situation discussed is generic for the treatment of two-brane models if the on-brane fields are used as the dynamical degrees of freedom. The mixing of the effective graviton modes of the localized action can be interpreted as radion-induced gravitational-wave oscillations, a classical analogy to meson and neutrino oscillations. We show that these oscillations arising in M-theory-motivated braneworld setups could lead to effects detectable by gravitational-wave interferometers. The implications of this effect for models with ultra-light gravitons are discussed.
TL;DR: In this paper, it was shown that the Reeh-Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition.
Abstract: Recently it has been shown that the Reeh–Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.
TL;DR: In this article, the authors considered the motion of an electric charge in a medium over a finite spatial distance and showed that the intensity of the radiation is proportional to the frequency in some angular region and decreases exponentially outside of it.
Abstract: We study the motion of an electric charge in a medium over a finite spatial distance. We consider at first the motion described by continuous functions of time, that is, its velocity and all its time derivatives are continuous. If the velocity v of the charge is greater than the velocity cn of light in the medium, then the intensity of the radiation is proportional to the frequency in some angular region and decreases exponentially outside of it. If the motion has no jumps in the velocity but jumps in the acceleration, the exponential decrease changes to a reciprocal one with 1/ω. For a purely decelerated motion, when both the initial and the final velocities are greater than cn, the intensity of the radiation contains a plateau. For practical application, the case with a vanishing final charge velocity is important: the intensity of the radiation is then maximal at the Cherenkov angle θc that corresponds to the initial charge velocity whereas it decreases sharply for θ>θc. For this case, provided the velocity of the charge exceeds cn, the total intensity (obtained by integrating the angular intensity of the radiation over the solid angle) is a linear function of the frequency, even though the Tamm condition is strongly violated.
TL;DR: The bulk quantization method was used for regularizing a conventional four dimensional theory of massless fermions coupled to an external non-Abelian gauge field and for subsequently evaluating the associated Ward identity as mentioned in this paper.
Abstract: The bulk quantization method is used for regularizing a conventional four dimensional theory of massless fermions coupled to an external non-Abelian gauge field and for subsequently evaluating the associated Ward identity As a result one obtains the well-known chiral anomaly