Vacuum Wave Research Articles

Proton-neutron self-consistent quasiparticle random phase approximation within the O(5) model

The self-consistent quasiparticle random phase approximation (SCQRPA) within the O(5) model in the coupled proton-neutron representation is analyzed. The exact vacuum wave function is used to compute all involved matrix elements. A stability analysis of the stationary points is performed. A phase transition from the uncoupled to the coupled stable proton-neutron regime beyond the QRPA breakdown value of the particle-particle strength is evidenced. The excitation energies are close to the lowest stable exact eigenvalues given by the diagonalization procedure for all cases. The conditions for which the Ikeda sum rule is fulfilled for all values of the particle-particle strength are pointed out.

Approximated fourth order calculation of the vacuum wave function of(2+1)dimensional SU(3) lattice gauge theory

We propose a scheme to improve the coupled cluster expansion in lattice gauge theory (LGT), based on the application of the random phase approximation, in order to approximate a wave function in terms of a linear combination of Wilson loops. Using this method, we study the vacuum energy and vacuum wave function in $(2+1)\mathrm{D}$ SU(3) LGT up to fourth order. The vacuum energy is lower than that obtained by the unimproved approach. The coefficients ${\ensuremath{\mu}}_{0},{\ensuremath{\mu}}_{2}$ of the vacuum wave function show good scaling behavior and convergence.

Simple wave solutions for the Maxwell equations in bianisotropic, nonlinear media, with application to oblique incidence

We analyze the propagation of electromagnetic waves in nonlinear, bianisotropic, nondispersive, homogeneous media using simple waves and six-vector formalism. The Maxwell equations are formulated as an eigenvalue problem, whose solutions are equivalent to the characteristic propagation directions. We solve the oblique incidence of plane waves in vacuum on a half space of nonlinear material, and present a method to calculate the reflected and transmitted fields for all angles of incidence and all polarizations of the incident field. Numerical examples for reflection and transmission illustrate the field dependence of the Brewster angle, and the birefringence of an anisotropic material.

Reflection amplitudes in non-simply laced Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in non-simply laced affine Toda theories considering them as perturbed non-affine Toda theories, which possess the extended conformal symmetry. We calculate the reflection amplitudes, in non-affine Toda theories and use them to derive the quantization condition for the vacuum wave function, describing zero-mode dynamics. The solution of this quantization conditions for the ground state energy determines the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with Thermodynamic Bethe Ansatz (TBA) results. To make the comparison with TBA possible, we give the exact relations between parameters of the action and masses of particles as well as the bulk free energies for non-simply laced affine Toda theories.

COUPLED CLUSTER EXPANSIONS FOR (2 + 1) DIMENSIONAL U(1) LATTICE GAUGE THEORY WITH IMPROVED HAMILTONIAN

Using coupled cluster method, we calculate the vacuum wave function and the mass gaps of (2 + 1)-dimensional U(1) lattice gauge theory with improved Hamiltonian up to the seventh order. The results are compared with those from the unimproved Hamiltonian.

FINITE VEV'S FROM A LARGE DISTANCE VACUUM WAVE FUNCTIONAL

We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can reconstruct the contribution from rapidly varying fields.

Reflection amplitudes of ADE Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.

Flutter Limits and Behaviors of a Flexible Thin Sheet in High-Speed Flow— I: Analytical Method for Prediction of the Sheet Behavior

An analytical method is proposed for the prediction of fluttering of a flexible thin sheet or web swept by fluid flow. It assumes self-excited aeroelastic oscillation of the sheet with infinitesimally small amplitude. The flow and the sheet motion are expressed by distributed vortices over the sheet and the wake, and by bending motions of a number of short segments constituting the sheet. The obtained system of equations determines the flutter limits, the oscillation modes and frequencies. The method treats particularly well the situation of very low mass ratios where the modes are far from those in vacuum and progressive waves are predominant. [S0098-2202(00)01101-9]

Phononlike excitations of the instanton liquid

The phonon-like excitations of (anti)-instanton ($\bar II$) liquid due to adiabatic variations of vacuum wave functions are studied in this paper. The kinetic energy term is found and the proper effective Lagrangian for such excitations is evaluated. The properties of their spectrum, while corresponding masses are defined by $\Lambda_{QCD}$, are investigated.

Trying to understand confinement in the schrödinger picture

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.

Attached and radiated electromagnetic fields of an electric point dipole

The standard dyadic Green function description of the electromagnetic field generated by an electric point dipole is modified (and corrected) so that a rigorous classical theory for the attached and radiated parts of the near field appears. The present propagator formalism follows from analysis of the transverse and longitudinal dipole electrodynamics. Elimination of both the transverse and the longitudinal self-fields leads to a description of the radiated dipole field that enables one to obtain the associated energy flux in the near- and mid-field zones also and that is correctly retarded (with the vacuum speed of light) everywhere in space. The related retarded transverse propagator exists in the time (space) domain, whereas the standard propagator exists only in the frequency (space) domain. As a forerunner to an analysis of the Weyl expansions for the standard, longitudinal self-field and retarded transverse propagators, the plane-wave mode expansions of these propagators are investigated, and contour integrations are specified in such a manner that the rigorous Green function description is regained. It is found that, in order for the retarded transverse propagator description to be consistent in the near-field zone, the Weyl expansion for this propagator has to contain evanescent components not only for wave numbers larger than the vacuum wave number but in the entire angular spectrum. The present theory may influence our view of optical near-field phenomena and (classical) photon tunneling because in both of these fields a proper identification of attached and radiated fields seems needed.

Instantons and the QCD vacuum wave functional

We analyze the instanton transitions in the framework of the gauge invariant variational calculation in the pure Yang-Mills theory. Instantons are identified with the saddle points in the integration over the gauge group which projects the Gaussian wave functional onto the gauge invariant physical Hilbert space. We show that the dynamical mass present in the best variational state provides an infrared cutoff for the instanton sizes. The instantons of the size $\rho<1/M$ are suppressed and the large size instanton problem arising in the standard WKB calculation is completely avoided in the present variational framework.

Destabilization of diocotron modes inside structured anode cavities

Previous stability analysis of low space charge ωe2/Ω2≪1, E×B drifting flows inside smooth anode cavities has shown that they are practically stable against slow wave ω/ck≪1 diocotron instabilities when the flow touches the cathode (cathode layer). It is shown here that the presence of periodically structured anode destabilizes cathode layer modes when their phase velocity matches that of an empty cavity eigenmode, as structured cavities support slow waves in vacuum. An analytic dispersion relation that self-consistently includes the structured anode effects is obtained in the guiding center approximation. The growth rate, related to the onset of magnetron oscillations, scales as γ/ω∼ωD/ω≃1/kd; it is independent of, and remains finite as, ωe2/Ω2→0. The most unstable frequency corresponds to a resonant layer below the flow surface (slightly below the Buneman–Hartree frequency) and the growth rate is found symmetric relative to the detuning from resonance.

Fluttering Behavior of a Flexible Thin Sheet in High-Speed Flow. 1st Report. Theoretical Method for Prediction of the Sheet Behavior for Small Perturbed Motion.

A theoretical method has been proposed for prediction of the fluttering of a flexible thin sheet or web of such as paper blown in high speed flow of fluid. It assumes self-excited aeroelastic oscillation of the sheet with infinitesimally small amplitude. The flow and the sheet motion are expressed terms of discretized vortices over the sheet and the wake, and motions of a number of short segments of flexible beams connected each other. The connecting conditions yield a homogeneous linear simultaneous equations concerning the unknowns including the strength of vortices and the sheet motions at each connecting points. The coefficient matrix of the equations determines the oscillation modes, the frequencies, the amplifying/damping rates, and thus the modes and the stability/instability of the system. The method is particularly suited to solve the situation where the oscillation modes are far from those in vacuum and progressive waves are predominant.

The Schrödinger wave functional and vacuum states in curved spacetime II: Boundaries and foliations

In a companion paper, general solutions for the vacuum wave functionals in the Schrödinger picture were given for a variety of classes of curved spacetimes. Here, we describe a number of simple examples which illustrate how the presence of spacetime boundaries influences the vacuum wave functional and how physical quantities are independent of the choice of spacetime foliation used in the Schrödinger approach despite the foliation dependence of the wave functionals themselves.

The Schrödinger wave functional and vacuum states in curved spacetime

New developments in the Schrödinger picture description of vacuum states in curved spacetime are presented. General solutions for the vacuum wave functional are given for both static and dynamic (Bianchi type I) spacetimes and for conformally static spacetimes of Robertson-Walker type. The formalism is illustrated for a simple ‘cosmological’ model with a time-dependent metric and the phenomenon of particle creation is related to a special form of the kernel in the vacuum wave functional.

Continuous coordinates for all impulsive pp-waves

We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.

Method for extracting the glueball wave function

We describe a nonperturbative method for calculating the QCD vacuum and glueball wave functions, based on an eigenvalue equation approach to Hamiltonian lattice gauge theory. Therefore, one can obtain more physical information than the conventional simulation methods. For simplicity, we take the 2+1 dimensional U(1) model as an example. The generalization of this method to 3+1 dimensional QCD is straightforward.

Magneto-electric Aharonov–Bohm effect in metal rings

The quantum-mechanical phase of the wavefunction of an electron can be changed by electromagnetic potentials, as was predicted by Aharonov and Bohm1 in 1959. Experiments on propagating electron waves in vacuum have revealed both the magnetic2,3,4 and electrostatic5 Aharonov–Bohm effect. Surprisingly, the magnetic effect was also observed in micrometre-sized metal rings6,7,8, demonstrating that electrons keep their phase coherence in such samples despite their diffusive motion. The search for the electrostatic contribution to the electron phase in these metal rings9,10 was hindered by the high conductivity of metal, which makes it difficult to apply a well defined voltage difference across the ring. Here we report measurements of quantum interference of electrons in metal rings that are interrupted by two small tunnel junctions. In these systems, a well defined voltage difference between the two parts of the ring can beapplied. Using these rings we simultaneously explore the influence of magnetic and electrostatic potentials on the Aharonov–Bohm quantum-interference effect, and we demonstrate that these two potentials play interchangeable roles.

Frequency domain wave-splitting techniques for plane stratified bianisotropic media

A plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered. A covariant wave-splitting approach, based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept, is presented. It encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions, including the physical and vacuum wave splittings treated earlier in the literature, and provides a convenient means for both analytical investigation and numerical calculation of evolution operators (Green’s functions) and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media. The potentialities of the approach are illustrated by its application to the problems of reflection, transmission, and guided propagation, and by generalizing the method of multiple reflections to the case of stratified bianisotropic media.