Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation

V. O. Vakhnenko and E. J. Parkes — 2012-04-17T09:00:00+09:00

Authors: V. O. Vakhnenko and E. J. Parkes
In this paper the inverse scattering method is applied to theVakhnenko-Parkes equation. We describe a procedure for using theinverse scattering transform to find the solutions that areassociated with both the bound state spectrum and continuousspectrum of the spectral problem. The suggested special form of thesingularity function gives rise to the multi-mode periodicsolutions. Sufficient conditions are obtained in order that thesolutions become real functions. The interaction of the solitons andmulti-mode periodic waves is studied. The procedure is illustratedby considering a number of examples.

Decay Forms of the Time Correlation Functions for Turbulence and Chaos

Hazime Mori and Makoto Okamura — 2012-04-17T09:00:00+09:00

Authors: Hazime Mori and Makoto Okamura
Taking the Rubin model for the one-dimensional Brownian motion and the chaotic Kuramoto-Sivashinsky equation for the one-dimensional turbulence, we derive a generalized Langevin equation in terms ofthe projection operator formalism, and then investigatethe decay forms of the time correlation functionU_{k}(t) and its memory function Γ_{k}(t) for a normal modeu_{k}(t) of the system with a wavenumber k.Let τ_{k}^{(u)} and τ_{k}^{(γ)} be the decay times of U_{k}(t) and Γ_{k}(t), respectively, with τ_{k}^{(u)} ≥τ_{k}^{(γ)}.Here, τ_{k}^{(u)} is a macroscopic time scale if k ≪1, but a microscopic time scale if k \gtrsim1, whereas τ_{k}^{(γ)} is always a microscopic time scale.Changing the length scale k^{-1} and the time scales τ_{k}^{(u)}, τ_{k}^{(γ)}, we can obtain various aspects of the systems as follows.If τ_{k}^{(u)} ≫τ_{k}^{(γ)}, then the time correlation function U_{k}(t) exhibits the decay of macroscopic fluctuations, leading toan exponential decay U_{k}(t) ∝exp(-t/τ_{k}^{(u)}).At the singular point where τ_{k}^{(u)} = τ_{k}^{(γ)}, however, bothU_{k}(t) and Γ_{k}(t) exhibit anomalous microscopic fluctuations,leading to the power-law decay U_{k}(t) ∝t^{-3/2}cos[(2t/τ_{k}^{(u)})-(3π/4)]for t →∞.The above decay forms give us important information on the macroscopicand microscopic fluctuations in the systems and their dissipations.

Quantum Decoherence and Entanglement Induced by Nonlinear Dissipative Environment

Hosny A. Hessian — 2012-04-17T09:00:00+09:00

Authors: Hosny A. Hessian
The analytical description of the dynamics of a nonlinearatom-field system described by a diagonal f-deformedJaynes-Cummings model for a chosen initial state is obtained. Thepurity loss of the global system, and the atomic and fieldsubsystems are discussed. Information on entanglementbetween the field and matter is studied by comparing the resultsfor mutual entropy, which is a measure of the total correlation, andthe negativity as a measure of the amount of entanglement. It isfound that the nonlinearity of the dissipation tends toaccelerate the decoherence of the global, field, and atomic states. Inaddition, we find that the so-called entanglement sudden death canoccur when both of the nonlinearity couplings between thecavity field and the dissipation are combined.

Analysis of Popper's Experiment and Its Realization

Tabish Qureshi — 2012-04-17T09:00:00+09:00

Authors: Tabish Qureshi
An experiment proposed by Karl Popper to test the standard interpretationof quantum mechanics was realized by Kim and Shih. We use a quantummechanical calculation to analyze Popper's proposal, and find a surprisingresult for the location of the virtual slit. We also analyze Kimand Shih's experiment, and demonstrate that although it ingeniouslyovercomes the problem of temporal spreading of the wave-packet, it isinconclusive about Popper's test. We point out that another experimentwhich (unknowingly) implements Popper's test in a conclusive way, hasactually been carried out. Its results are in contradiction withPopper's prediction, and agree with our analysis.

Average Number of the Lightest Supersymmetric Particles in Decay of Superheavy Particle with Long Lifetime

Yasuhiro Kurata and Nobuhiro Maekawa — 2012-04-17T09:00:00+09:00

Authors: Yasuhiro Kurata and Nobuhiro Maekawa
We calculate the average number ν of the lightestsupersymmetric particles (LSPs) in a shower from the decay of the superheavy particle X by generalized DGLAP equations. If the primary decayed particles have color charges and the virtualityis approximately 10^{13} - 10^{14} GeV, the averagenumber of the LSPs can become O(100).The result shows that the upper limit of the mass of the superheavy particle, whose decay can produce the observed abundance of dark matter, can increase from 10^{12} GeV to 10^{14} GeV. Since the typical scale of the inflaton mass of the chaotic inflation is approximately 10^{13} GeV, the decay of the inflaton can produce the observed dark matter abundance if the reheating temperature is on the orderof 1 GeV. Even for standard model particles with a virtuality Q∼10 - 100 TeV, the average number of LSPs becomes O(0.1) for gluon, and O(0.01) for Higgs, which strongly constrains the scenario of nonthermal LSP production from the decayof moduli with a 10 - 100 TeV mass range.

Boundary State Analysis on the Equivalence of T-Duality and Nahm Transformation in Superstring Theory

Tsuguhiko Asakawa, Ursula Carow-Watamura, Yoshiro Teshima and Satoshi Watamura — 2012-04-17T09:00:00+09:00

Authors: Tsuguhiko Asakawa, Ursula Carow-Watamura, Yoshiro Teshima and Satoshi Watamura
We investigated the equivalence of the T-duality for a bound state of D2 and D0-branes with the Nahm transformation of the corresponding gauge theory on a 2-dimensional torus, using the boundary state analysis in superstring theory. In contrast to the case of a 4-dimensional torus, it changes a sign in a topological charge, which seems puzzling when regarded as a D-brane charge.Nevertheless, it is shown that it agrees with the T-duality of the boundary state, including a minus sign.We reformulated boundary states in the RR-sector using a new representation of zeromodes, and show that the RR-coupling is invariant under the T-duality.Finally, the T-duality invariance at the level of the Chern-Simon coupling is shown by deriving the Buscher rule for the RR potentials, known as the `Hori formula', including the correct sign.

Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse

Hikaru Kawai and Takashi Okada — 2012-04-17T09:00:00+09:00

Authors: Hikaru Kawai and Takashi Okada
We propose a solution of the naturalness problem in the context of the multiverse wavefunction without the anthropic argument. If we include microscopic wormhole configurations in the path integral, the wave function becomes a superposition of universes with various values of the coupling constants such as the cosmological constant, the parameters in the Higgs potential, and so on. We analyze the quantum state of the multiverse, and evaluate the density matrix of one universe. We show that the coupling constants induced by the wormholes are fixed in such a way that the density matrix is maximized. In particular, the cosmological constant, which is in general time-dependent, is chosen such that it takes an extremely small value in the far future. We also discuss the gauge hierarchy problem and the strong CP problem in this context. Our study predicts that the Higgs mass is m_{h} = 140 ±20 GeV and θ= 0.

Exploring Three-Nucleon Forces in Lattice QCD

2012-04-17T09:00:00+09:00

Authors: Takumi Doi, Sinya Aoki, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Noriyoshi Ishii, Keiko Murano, Hidekatsu Nemura and Kenji Sasaki (HAL QCD Collaboration)
Three-nucleon forces (3NF) are investigated from two-flavor lattice QCD simulations. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF in the same framework. As a first exploratory study,we extract 3NF in which three nucleons are aligned linearly with an equal spacing. This is the simplest geometrical configuration which reduces the huge computational cost of calculating the NBS wave function.Quantum numbers of the three-nucleon system are chosen to be(I, J^{P}) = (1/2,1/2^{+}) (the triton channel).Lattice QCD simulations are performed using N_{f} = 2 dynamical clover fermion configurationsat the lattice spacing of a = 0.156 fm on a 16^{3} ×32 latticewith a large quark mass corresponding to m_{π}= 1.13 GeV.We find repulsive 3NF at short distance in the triton channel.Several sources of systematic errors are also discussed.

Skyrme-Hartree-Fock plus Tensor Correction for Nuclear Matter

Yannan Wang, Jinniu Hu, Hiroshi Toki and Hong Shen — 2012-04-17T09:00:00+09:00

Authors: Yannan Wang, Jinniu Hu, Hiroshi Toki and Hong Shen
We study the equation of states of symmetric and pure neutron matter in the Skyrme-Hartree-Fock (SHF) model with tensor corrections.We are aware now that the pion exchange interaction has a significant contribution to nuclear structure in light nuclei. The pion generates a strong tensor interaction between two nucleons, which cannot be treatedwithin the Hartree-Fock framework for the spin-saturated system such as homogeneous nuclear matter. Therefore, we study the role of the tensor interaction based on the SHFmodel, in which we extend it by explicitly introducing two-particle-two-hole (2p-2h) excitations for the treatment ofthe tensor interaction in symmetric nuclear matter and pure neutron matter. We are able to describe infinite mattervery well using the SHF model with tensor corrections. We also discuss the connection between the symmetry energy and the tensor interaction in this framework.

Re-Formation of Many-Quark Model with the su(4)-Algebraic Structure in the Schwinger Boson Realization

2012-04-17T09:00:00+09:00

Authors: Yasuhiko Tsue, Constança Providência, João da Providência and Masatoshi Yamamura
The energy eigenstates for the su(4)-algebraic model for many-quark system obtained by the present authors in the Schwinger boson space are reconsidered in the original fermion space. Through this task, the structures of the single-quark and the quark-triplet are clarified. Variations of the su(4)-generators which have been adopted by the present authors are discussed.

Color-Singlet Three-Quark States in the su(4)-Algebraic Many-Quark Model

2012-04-17T09:00:00+09:00

Authors: Yasuhiko Tsue, Constança Providência, João da Providência and Masatoshi Yamamura
As announced in the previous paper by the present authors, the color-singlet three-quark states are investigated for the case of the spherical j-j coupling and L-S coupling shell models. The latter case automatically leads to the su(4) ⊗su(4)-model. For a certain type of Hamiltonian, the states of individual“nucleons" are characterized.

Fast Quantum Gate with Superconducting Flux Qubits Coupled to a Cavity

Chui-Ping Yang — 2012-04-17T09:00:00+09:00

Authors: Chui-Ping Yang
We present a way for fast implementation of a two-qubit controlledphase gate with superconducting flux qubits coupled to a cavity. Adistinct feature of this proposal is that since only qubit-cavityresonant interaction and qubit-pulse resonant interaction areused, the gate can be performed much faster when compared with theprevious proposals. This proposal does not require adjustment ofthe qubit level spacings during the gate operation. In addition,neither uniformity in the qubit parameters nor exact placement ofqubits in the cavity is needed by this proposal.

Non-Equilibrium Critical Relaxation of the 3D Heisenberg Magnets with Long-Range Correlated Disorder

Pavel V. Prudnikov and Maria A. Medvedeva — 2012-03-19T09:00:00+09:00

Authors: Pavel V. Prudnikov and Maria A. Medvedeva
Monte Carlo simulations of the short-time dynamic behavior arereported for three-dimensional Heisenberg model with long-rangecorrelated disorder at criticality, in the case corresponding tolinear defects. The static and dynamic critical exponents aredetermined for systems starting from an ordered initial state.The obtained values of the exponents arein good agreement with results of the field-theoretic descriptionof the critical behavior of this model in the two-loopapproximation.

Ghost Interference and Quantum Erasure

Pravabati Chingangbam and Tabish Qureshi — 2012-03-19T09:00:00+09:00

Authors: Pravabati Chingangbam and Tabish Qureshi
The two-photon ghost interference experiment,generalized to the case of massive particles, is theoretically analyzed.It is argued that the experiment is intimately connected to a double-slitinterference experiment where, which-path information exists. The reasonfor not observing first order interference behind the double-slit, is clarified.It is shown that the underlying mechanism for the appearance of ghostinterference is, the more familiar, quantum erasure.

The Worldline Quantum Mechanics Model at Finite Temperature, Which Is Dual to the Static Patch Observer in de Sitter Space

Ryuichi Nakayama — 2012-03-19T09:00:00+09:00

Authors: Ryuichi Nakayama
A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in de Sitter spacetime seen by a static patch observer. It is found that the action integral of this model is automatically expressed by a complex integral over the time variable t along a closed contour in a way that is typical to the Schwinger-Keldysh formalism of a thermofield theory. Hence, this model is at finite temperature. The case of conformally coupled scalar fields in 3D Schwarzschild de Sitter space is also considered, and then a large N matrix model is obtained.

Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory

Kengo Kikuchi — 2012-03-19T09:00:00+09:00

Authors: Kengo Kikuchi
The purpose of this paper is to present our study on therestoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of the exact renormalization group equations, to the Lifshitz-type theory.Analyzing the equation for a z = 2, d = 3 + 1 Lifshitz-type scalar model, and using some variable transformations, we found that broken symmetry terms vanish in the infrared region.This shows that the Lifshitz-type scalar model dynamically restores the Lorentzsymmetry at low energy. Our result provides a definition of ultravioletcomplete renormalizable scalar field theories. These theories can havenontrivial interaction terms of φ^{n} (n = 4, 6, 8, 10) even when theLorentz symmetry is restored at low energy.

Response of Uniformly Accelerated Particle Detectors in the Presence of Co-Accelerated Mirrors

Nistor Nicolaevici — 2012-03-19T09:00:00+09:00

Authors: Nistor Nicolaevici
We obtain the transition rates for an Unruh-DeWitt particle detector which uniformly accelerates in the presence of a perfectly reflecting spherical mirror that contracts and expands with constant acceleration. We also consider the case when the detectoraccelerates between two such mirrors, as well as the corresponding reduced configurations in a two dimensional Minkowski space. The mirror and detector accelerations are chosen such that the transition rates are independent of time. In all cases we find that theresponse respects the detailed balance condition for the Unruh-Davies temperature associated to the detector's acceleration. An interesting fact is that for the detector between the mirrors the transition spectrum in two dimensions is discrete, while infour dimensions it is continuous.

Re-Examining Bogoliubov's Theory of an Interacting Bose Gas

A. Ettouhami — 2012-03-19T09:00:00+09:00

Authors: A. Ettouhami
As is well-known, in the conventional formulation of Bogoliubov's theory of an interacting Bose gas,the Hamiltonian \hatH is written as a decoupled sum of contributions fromdifferent momenta of the form\hatH = ∑_{k≠0}\hatH_{k}. Then, each of the single-mode Hamiltonians \hatH_{k}is diagonalized separately, and the resulting ground state wavefunction of thetotal Hamiltonian \hatHis written as a simple product of the ground state wavefunctions of each of thesingle-mode Hamiltonians\hatH_{k}. While this way of diagonalizing the totalHamiltonian \hatH may seem to be valid from the perspective of the standard, number non-conserving Bogoliubov's method, where the k = 0 state is removed from the Hilbert space and hence the individual Hilbert spaces where the Hamiltonians{\hatH_{k}} are diagonalized are disjoint from one another,we argue that from a number-conserving perspectivethis diagonalization method may not be adequate since the true Hilbert spaceswhere the Hamiltonians {\hatH_{k}} should be diagonalizedall have the k = 0 state in common, and hence theground state wavefunction of the total Hamiltonian \hatHmay not be written as a simple product of the ground state wavefunctionsof the \hatH_{k}'s.In this paper, we give a thorough review of Bogoliubov's method, and discuss avariational and number-conserving formulation of this theory in which the k = 0 state is restored to the Hilbert space of the interacting gas, and where, instead of diagonalizing the Hamiltonians\hatH_{k} separately, we diagonalize the total Hamiltonian\hatH as a whole.When this is done, we find that the ground state energy is lowered below theBogoliubov result, and the depletion of bosons is significantly reduced with respect to the one obtained in the number non-conserving treatment.We also find that the spectrum of the usual α_{k}excitations of Bogoliubov's method changes from a gapless one, as predicted by the standard, number non-conserving formulation of thistheory, to one which exhibits a finite gap in the k →0 limit.We discuss the presence of a gap in the spectrum of the α_{k}'s in light of Goldstone's theorem,and show that there is no contradiction with the latter.

Radiation Magnetohydrodynamics for Black Hole-Torus System in Full General Relativity: A Step toward Physical Simulation

Masaru Shibata and Yuichiro Sekiguchi — 2012-03-19T09:00:00+09:00

Authors: Masaru Shibata and Yuichiro Sekiguchi
A radiation-magnetohydrodynamic simulation for the blackhole-torus system is performed in the framework of full generalrelativity for the first time. A truncated moment formalism isemployed for a general relativistic neutrino radiation transport.Several systems in which the black hole mass is M_{ BH} = 3 or6M_{⊙}, the black hole spin is zero, and the torus mass is≈0.14–0.38M_{⊙} are evolved as models of the remnantformed after the merger of binary neutron stars or black hole-neutronstar binaries. The equation of state and microphysics for thehigh-density and high-temperature matter are phenomenologically takeninto account in a semi-quantitative manner. It is found that the temperature inthe inner region of the torus reaches \gtrsim 10 MeV which enhances ahigh luminosity of neutrinos ∼10^{51} ergs/s for M_{BH} = 6M_{⊙} and ∼10^{52} ergs/s for M_{ BH} = 3M_{⊙}.It is shown that neutrinos are likely to be emitted primarily towardthe outward direction in the vicinity of the rotational axis and their energydensity may be high enough to launch a low-energy short gamma-rayburst via the neutrino-antineutrino pair-annihilation process with thetotal energy deposition ∼10^{47}–10^{49} ergs. It is alsoshown in our model that for M_{ BH} = 3M_{⊙}, the neutrino luminosity is larger than the electromagnetic luminosity while for M_{ BH} = 6M_{⊙}, the neutrino luminosity is comparable to or slightlysmaller than the electromagnetic luminosity.

On the Regularization of Kerr-NUT Spacetime. I

Gamal G. L. Nashed — 2012-03-19T09:00:00+09:00

Authors: Gamal G. L. Nashed
Within the framework of teleparallel equivalent of generalrelativity (TEGR) theory, calculation of the total energy andmomentum of Kerr-NUT spacetimes have been employed using twomethods of the gravitational energy-momentum, which is coordinateindependent, and the Riemannian connection 1-form,\widetildeΓ_{α}^{β}. It has been shown that thetwo methods give the same unacceptable result, i.e., divergentvalue. Therefore, a local Lorentz transformation that plays a roleof a regularizing tool, which subtracts the inertial effectswithout distorting the true gravitational contribution, has beensuggested. This transformation keeps the resulting spacetime tobe a solution of the equations of motion of TEGR.

X(3872) and Its Iso-Triplet Partners

Kunihiko Terasaki — 2012-03-19T09:00:00+09:00

Authors: Kunihiko Terasaki
Decays of X(3872) and its partners as hidden-charmaxial-vector tetra-quark mesons are studied. As the result, it is seen that the iso-triplet partners of X(3872) can be broad, and therefore, higher statistics will be needed to find them.

Gravitational Radiation for Extreme Mass Ratio Inspirals to the 14th Post-Newtonian Order

Ryuichi Fujita — 2012-03-19T09:00:00+09:00

Authors: Ryuichi Fujita
We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux for a particle in circularorbit around a Schwarzschild black hole, i.e. v^{28} beyond the leading Newtonian approximation where v is the orbital velocity of a test particle. We investigate the convergence of the energy flux in the PN expansion and suggest a fitting formula which can be used to extract unknown higher order PN coefficients from accurate numerical data for more general orbits around a Kerr black hole. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral is shown to be about 10^{-7} for µ/M = 10^{-4} and 10^{-3} for µ/M = 10^{-5} where µ is the mass of a compact object and M the mass of the central supermassive black hole. In first order black hole perturbation theory, for extreme mass ratio inspirals which are one of the main targets of Laser Interferometer Space Antenna, the 14PN expressions will lead to the data analysis accuraciescomparable to the ones resulting from high precision numerical waveforms.

Parity Violation of Gravitons in the CMB Bispectrum

Maresuke Shiraishi, Daisuke Nitta and Shuichiro Yokoyama — 2012-03-19T09:00:00+09:00

Authors: Maresuke Shiraishi, Daisuke Nitta and Shuichiro Yokoyama

Recent articles in Prog. Theor. Phys.

Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation

Decay Forms of the Time Correlation Functions for Turbulence and Chaos

Quantum Decoherence and Entanglement Induced by Nonlinear Dissipative Environment

Analysis of Popper's Experiment and Its Realization

Average Number of the Lightest Supersymmetric Particles in Decay of Superheavy Particle with Long Lifetime

Boundary State Analysis on the Equivalence of T-Duality and Nahm Transformation in Superstring Theory

Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse

Exploring Three-Nucleon Forces in Lattice QCD

Skyrme-Hartree-Fock plus Tensor Correction for Nuclear Matter

Re-Formation of Many-Quark Model with the su(4)-Algebraic Structure in the Schwinger Boson Realization

Color-Singlet Three-Quark States in the su(4)-Algebraic Many-Quark Model

Fast Quantum Gate with Superconducting Flux Qubits Coupled to a Cavity

Non-Equilibrium Critical Relaxation of the 3D Heisenberg Magnets with Long-Range Correlated Disorder

Ghost Interference and Quantum Erasure

The Worldline Quantum Mechanics Model at Finite Temperature, Which Is Dual to the Static Patch Observer in de Sitter Space

Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory

Response of Uniformly Accelerated Particle Detectors in the Presence of Co-Accelerated Mirrors

Re-Examining Bogoliubov's Theory of an Interacting Bose Gas

Radiation Magnetohydrodynamics for Black Hole-Torus System in Full General Relativity: A Step toward Physical Simulation

On the Regularization of Kerr-NUT Spacetime. I

X(3872) and Its Iso-Triplet Partners

Gravitational Radiation for Extreme Mass Ratio Inspirals to the 14th Post-Newtonian Order

Parity Violation of Gravitons in the CMB Bispectrum