Showing papers in "Progress of Theoretical Physics in 2012"

Subbarrier Fusion Reactions and Many-Particle Quantum Tunneling

Abstract: Low-energy heavy-ion fusion reactions are governed by quantum tunneling through the Coulomb barrier formed by the strong cancellation of the repulsive Coulomb force with the attractive nuclear interaction between the colliding nuclei. Extensive experimental as well as theoretical studies have revealed that fusion reactions are strongly influenced by couplings of the relative motion of the colliding nuclei to several nuclear intrinsic motions. Heavy-ion subbarrier fusion reactions thus provide a good opportunity to address the general problem of quantum tunneling in the presence of couplings, which has been a popular subject in recent decades in many branches of physics and chemistry. Here, we review theoretical aspects of heavy-ion subbarrier fusion reactions from the viewpoint of quantum tunneling in systems with many degrees of freedom. Particular emphases are put on the coupled-channels approach to fusion reactions and the barrier distribution representation for multichannel penetrability. We also discuss an application of the barrier distribution method to elucidate the mechanism of the dissociative adsorption of H2 molecules in surface science. Subject Index: 062, 211, 223, 226, 330

Bosenova Collapse of Axion Cloud around a Rotating Black Hole

Abstract: Motivated by possible existence of stringy axions with ultralight mass, we study the behavior of an axion field around a rapidly rotating black hole (BH) obeying the sine-Gordon equation by numerical simulations. Due to superradiant instability, the axion field extracts the rotational energy of the BH and the nonlinear self-interaction becomes important as the field grows larger. We present clear numerical evidences that the nonlinear effect leads to a collapse of the axion cloud and a subsequent explosive phenomena, which is analogous to the “bosenova” observed in experiments of Bose-Einstein condensate. The criterion for the onset of the bosenova collapse is given. We also discuss the reason why the bosenova happens by constructing an effective theory of a wavepacket model under the nonrelativistic approximation. Subject Index: 420, 430, 451

A Note on the Partition Function of ABJM Theory on S-3

Abstract: and it was shown that the free energy F = − logZN,k exhibits the correct N 32 scaling as predicted by the holographic dual gravity theory. The ABJM theory in the ’t Hooft limit is holographically dual to the type IIA theory on AdS4 × CP, which appears from the S1 reduction of the M-theory on AdS4 × S/Zk when k N 15 . However, if we are interested in the dynamics of M2-branes in the truly M-theory regime, or in the strong coupling regime of type IIA theory, we need to know the behavior of ZN,k at finite k, since the IIA string coupling is inversely proportional to k. Of particular interest is the ABJM theory at k = 1, which is conjectured to describe the M2-branes on the flat eleven dimensional Minkowski space. Therefore we might want to develop a technique to analyze the partition function ZN,k in the M-theory regime where N → ∞, k = finite . (1.2)

Time-Reversal Symmetry in Non-Hermitian Systems

Abstract: For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys � 2 = −1, but no such a degeneracy exists when � 2 = +1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when � 2 = +1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split-quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail N × N Hamiltonians with N = 2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.

Exploring Three-Nucleon Forces in Lattice QCD

Abstract: 1Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan 2Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan 3Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan 4IPMU, The University of Tokyo, Kashiwa 277-8583, Japan 5Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan 6Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan 7Nihon University, College of Bioresource Sciences, Fujisawa 252-0880, Japan 8Department of Physics, Tohoku University, Sendai 980-8578, Japan

Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order

Abstract: We extend our previous results of the 14th post-Newtonian (PN) order expansion of gravitational waves for a test particle in circular orbits around a Schwarzschild black hole to the 22PN order, i.e. $v^{44}$ beyond the leading Newtonian approximation where $v$ is the orbital velocity of a test particle. Comparing our 22PN formula for the energy flux with high precision numerical results, we find that the relative error of the 22PN flux at the innermost stable circular orbit is about $10^{-5}$. We also estimate the phase difference between the 22PN waveforms and numerical waveforms after a two-year inspiral. We find that the dephase is about $10^{-9}$ for $\mu/M=10^{-4}$ and $10^{-2}$ for $\mu/M=10^{-5}$ where $\mu$ is the mass of the compact object and $M$ the mass of the central supermassive black hole. Finally, we construct a hybrid formula of the energy flux by supplementing the 4PN formula of the energy flux for circular and equatorial orbits around a Kerr black hole with all the present 22PN terms for the case of a Schwarzschild black hole. Comparing the hybrid formula with the the full numerical results, we examine the performance of the hybrid formula for the case of Kerr black hole.

Feasibility Study of Observing η' Mesic Nuclei with (p,d) Reaction

Abstract: A novel method is proposed to measure eta'(958) meson bound states in 11C nuclei by missing mass spectroscopy of the 12C(p,d) reaction near the eta' production threshold. It is shown that peak structures will be observed experimentally in an inclusive measurement in case that the in-medium eta' mass reduction is sufficiently large and that the decay width of eta' mesic states is narrow enough. Such a measurement will be feasible with the intense proton beam supplied by the SIS synchrotron at GSI combined with the good energy resolution of the fragment separator FRS.

Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse

Abstract: 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 mh = 140 ± 20 GeV and θ =0 . Subject Index: 129

Analytical Calculation on Critical Magnetic Field in Holographic Superconductors with Backreaction

Abstract: We investigate the effect of spacetime backreaction on the upper critical magnetic field for s-wave holographic superconductors by using the matching method. The backreaction of the constant external magnetic field and the electric field to the background geometry leads to a dyonic black hole solution. The magnetic fields as well as the electric fields acting as gravitational sources tend to depress the critical temperature of the superconductor. We derive the analytical expression for the upper critical magnetic field up to O(kappa(2)) order and find that backreaction makes the upper critical magnetic field stronger. The result is consistent with the previous numerical and analytical results.

A Boundary Integral SPH Formulation --- Consistency and Applications to ISPH and WCSPH ---

Abstract: One of the historical problems appearing in SPH formulations is the inconsistencies coming from the inappropriate implementation of boundary conditions. In this work, this problem has been investigated; instead of using typical methodologies such as extended domains with ghost or dummy particles where severe inconsistencies are found, we included the boundary terms that naturally appear in the formulation. First, we proved that in the 1D smoothed continuum formulation, the inclusion of boundary integrals allows for a consistent O (h) formulation close to the boundaries. Second, we showed that the corresponding discrete version converges to a certain solution when the discretization SPH parameters tend to zero. Typical tests with the first and second derivative operators confirm that this boundary condition implementation works consistently. The 2D Poisson problem, typically used in ISPH, was also studied, obtaining consistent results. For the sake of completeness, two practical applications, namely, the duct flow and a sloshing tank, were studied with the results showing a rather good agreement with former experiments and previous results. Subject Index: 024

An Analytical Approximation of the Luminosity Distance in Flat Cosmologies with a Cosmological Constant

Abstract: We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is written simply in terms of a rational function. We also show the approximate formulae for the Dyer-Roeder distance (empty beam case) and the generalized angular diameter distance from redshift $z_1$ to $z_2$, which are particularly useful in analyzing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter $0.3 \leq \Omega_{\rm m} \leq 1$ and redshift $0.03 \leq z \leq 1000$, the relative error for the luminosity distance by our formula is always smaller than that of the recent work by Wickramasinghe and Ukwatta (2010). Hence, we hope that our formulae will be an efficient and useful tool for exploring various problems in observational cosmology.

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

Abstract: We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux for a particle in circular orbit around a Schwarzschild black hole, i.e. v 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 accuracies comparable to the ones resulting from high precision numerical waveforms.

Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

Abstract: We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general nonlinear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C×CP N−1 . We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that YangMills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.

Structure of 10ΛBe and 10ΛB Hypernuclei Studied with the Four-Body Cluster Model

Abstract: The structure of the isodoublet hypernuclei, 10 Ba nd 10 Be within the framework of an α + α + Λ + N four-body cluster model is studied. Interactions between the constituent subunits are determined to reproduce reasonably well the observed low-energy properties of the αα, αN , αΛ, ααΛ ,a ndααN subsystems. Furthermore, the two-body ΛN interaction is adjusted to reproduce the 0 + -1 + splitting of 4H. The Λ binding energies of 10 Ba nd 10 Be are 8.76 MeV and 8.94 MeV, respectively. The energy splitting of the 1 − -2 − levels in 10 Bi s 0.08 MeV, which does not contradict the experimental report in BNL-E930. An even-state ΛN charge symmetry breaking (CSB) interaction determined from the A = 4 systems works repulsively by +0.1 MeV (attractively by �0. 1M eV) in 10 Be ( 10 B). We discuss a possibility that an odd-state CSB interaction improves the fitting to the experimental data of A =1 0 double Λ hypernuclei. Subject Index: 214

Quantum Probabilities and Violation of CHSH-Inequality from Classical Random Signals and Threshold Type Detection Scheme

Abstract: We present a purely wave model (based on classical random field) which reproduces quantum probabilities (given by the fundamental law of quantum mechanics, Born’s rule) including probabilities for joint detection of a pair of quantum observables (e.g., spin or polarization projections). The crucial point of our approach is that the presence of detector’s threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. The presence of the background field (vacuum fluctuations) is also the key-element of our prequantum model. It is of the classical signal type and the methods of classical signal theory (including statistical radiophysics) are used for its development. We stress that our prequantum model is not objective, i.e., the values of observables (clicks of detectors) cannot be assigned in advance, i.e., before measurement. Hence, the dilemma, nonobjectivity or nonlocality, is resolved in favor of nonobjectivity (our model is local of the classical field type). In particular, we reproduce the probabilities for the EPR-experiment for photon polarization and, hence, violate CHSH inequality for classical random signals (measured by the threshold type and properly calibrated detectors acting in the presence of the background field). Subject Index: 060

Radiation magnetohydrodynamics for black hole-torus system in full general relativity: A step toward physical simulation

Abstract: A radiation-magnetohydrodynamic simulation for the black hole-torus system is per- formed in the framework of full general relativity for the first time. A truncated moment formalism is employed for a general relativistic neutrino radiation transport. Several systems in which the black hole mass is MBH =3o r 6M� , the black hole spin is zero, and the torus mass is ≈ 0.14-0.38Mare evolved as models of the remnant formed after the merger of binary neutron stars or black hole-neutron star binaries. The equation of state and micro- physics for the high-density and high-temperature matter are phenomenologically taken into account in a semi-quantitative manner. It is found that the temperature in the inner region of the torus reaches > 10 MeV which enhances a high luminosity of neutrinos ∼ 10 51 ergs/s for MBH =6 Mand ∼ 10 52 ergs/s for MBH =3 M� . It is shown that neutrinos are likely to be emitted primarily toward the outward direction in the vicinity of the rotational axis and their energy density may be high enough to launch a low-energy short gamma-ray burst via the neutrino-antineutrino pair-annihilation process with the total energy deposition ∼ 10 47 - 10 49 ergs. It is also shown in our model that for MBH =3 M� , the neutrino luminosity is larger than the electromagnetic luminosity while for MBH =6 M� , the neutrino luminosity is comparable to or slightly smaller than the electromagnetic luminosity. Subject Index: 420, 425

The Chiral Heat Effect

Abstract: (Received January 3, 2012; Revised May 1, 2012)We consider the thermal response of a (3+1)-dimensional theory with a chiral anomalyonacurved space motivatedbythechiralmagneticeffect. Wefind anew phenomenon, calledthe chiral heat effect, such that the thermal current is induced transverse to a gradient ofthe temperature even on a flat space. We study a similar topological effect on the spacetimewith a torsion.

Explosive Nucleosynthesis in Magnetohydrodynamical Jets from Collapsars. II — Heavy-Element Nucleosynthesis of s, p, r-Processes —

Abstract: We investigate the nucleosynthesis in a massive star of 70 Mwith solar metallicity in the main sequence stage. The helium core mass after hydrogen burning corresponds to 32 M� . Nucleosynthesis calculations have been performed during the stellar evolution and the jetlike supernova explosion of a collapsar model. We focus on the production of elements heavier than iron group nuclei. Nucleosynthesis calculations have been accomplished consistently from hydrostatic to dynamic stages by using large nuclear reaction networks, where the weak s-, p-, and r-processes are taken into account. We confirm that s-elements of 60 90 are produced via photodisintegrations of seed s-elements. However, the produced p-elements are disintegrated in later stages except for 180 Ta. In the explosive nucleosynthesis, elements of 90 50) are overproduced via the p-process because of the low peak temperatures in the oxygen- and neon-rich layers. Compared with the previous study of r-process nucleosynthesis calculations in the collapsar model of 40 Mby Fujimoto et al. (S. Fujimoto, M. Hashimoto, K. Kotake and S. Yamada, Astrophys. J. 656 (2007), 382; S. Fujimoto, N. Nishimura and M. Hashimoto, Astrophys. J. 680 (2008), 1350), our jet model cannot contribute to the third peak of the solar r-elements and intermediate p-elements, which have been much produced because of the distribution of the lowest part of electron fraction in the ejecta. Averaging the overproduction factors over the progenitor masses with the use of Salpeter's IMF, we suggest that the 70 Mstar could contribute to the solar weak s-elements of 60

Massive modes in magnetized brane models

Abstract: We study higher dimensional models with magnetic fluxes, which can be derived from superstring theory. We study mass spectrum and wavefunctions of massless and massive modes for spinor, scalar and vector fields. We compute the 3-point couplings and higher order couplings among massless modes and massive modes in 4D low-energy effective field theory. These couplings have non-trivial behaviors, because wavefunctions of massless and massive modes are non-trivial.

Effective Potential Approach to Quark Ferromagnetization in High Density Quark Matter

Abstract: A possibility of spontaneous magnetization in high density symmetric quark matter is investigated using the NJL type effective model of QCD by means of an effective potential with respect to an auxiliary field It is shown that the quark ferromagnetic condensate has non-vanishing value at high baryon density due to the tensor-type four-point interaction between quarks Subject Index: 230

The Importance of the Ising Model

Abstract: Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry properties, is one of the most fundamental open questions in both statistical mechanics and quantum field theory. The importance of the two-dimensional Ising model in a magnetic field is that it is the simplest system where this relationship may be concretely studied. We here review the advances made in this study, and concentrate on the magnetic susceptibility which has revealed an unexpected natural boundary phenomenon. When this is combined with the Fermionic representations of conformal characters, it is suggested that the scaling theory, which smoothly connects the lattice with the correlation length scale, may be incomplete for H � =0 . Subject Index: 010, 040

Singularity Phenomena in Viable f(R) Gravity

Abstract: The accelerating expansion of the universe has been established by several cosmological observations, such as those from type Ia supernovae,1),2) cosmic microwave background radiation,3),4) large scale structure5) and weak lensing.6) There are two ways to explain this phenomenon. One is to add dark energy to modify matter and the other one is to modify gravity in Einstein’s equation. The simplest version for the latter is f(R) gravity,7)–9) which is by extending the Ricci scalar of R to a function of f(R) in the Einstein-Hilbert action. As a result, the late time accelerating universe can be realized in f(R) gravity. Many viable f(R) gravity models have been constructed by satisfying various conditions as well as constraints from cosmological observations.9) The finite-time singularity problems10) have been examined in many modified theories, such as f(R) models,11) modified Gauss-Bonnet models,12) f(T ) models,13) modified Horava-Lifshitz gravity14) and non-local gravity models.15) Recently, it has been pointed out in Refs. 16) and 17) that some of the viable f(R) models contain one kind of the finite-time singularities, leading to a divergence of curvature, but it can be avoided by taking a fine-tune initial condition.18),19) However, this kind of singularities must be induced and cannot be avoided when the local background density of matter becomes dense.20) Even though the singularity depends on the background density as well as the model parameters, it happens in a finite time. This behavior could exist in many physical systems, such as cluster, galaxy, nebula collide, and star collapse. However, if an additional Rn term with 1 < n ≤ 2 is introduced in the viable f(R) models,21)–23) the singularity can be avoided. We

Higher Dimensional Charged BTZ-Like Wormhole

Abstract: It is known that some of the traversable wormhole can exist in General Relativity only if its throat contains some exotic matter. In this paper, we obtain (2 + 1)-dimensional horizonless charged magnetic brane without curvature singularity. Then, we consider a nontrivial local transformation to endow a global rotation to spacetime. After that, we generalize magnetic brane to higher dimensional solutions and use the cut-and-paste method to construct higher dimensional charged BTZ-like rotating wormholes in such a way that they reduce to charged magnetic BTZ solution in three dimensions, exactly. We also show that charged BTZ-like wormhole supported by the exotic matter at its throat r = r+. Finally, we calculate the conserved quantities of the charged BTZ-like wormhole such as mass, angular momentum and electric charge density, and show that the electric charge depends on the rotation parameters and the static wormhole does not have a net electric charge density. Subject Index: 450, 453

Charge-Exchange Excitations with Skyrme Interactions in a Separable Approximation

Abstract: Starting from a Skyrme interaction we propose an extension of the finite rank separable approximation for the case of charge-exchange nuclear modes. This approximation enables one to reduce considerably the dimensions of the matrices that must be diagonalized to perform QRPA calculations in very large configuration spaces. First, we check that the approximation reproduces reasonably well the full charge-exchange RPA results of the spindipole resonances in the nuclei 90 Zr and 132 Sn. The approach is then applied to the study of the Gamow-Teller and the spin-dipole resonances in the neutron-rich Cd isotopes, within the quasiparticle random phase approximation. Subject Index: 210, 213

A Variational Principle for Dissipative Fluid Dynamics

Abstract: In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory. Subject Index: 519

Three Views of a Secret in Relativistic Thermodynamics

Abstract: It has been shown three different views in relativistic thermodynamics can be derived from the basic formulation proposed by van Kampen and Israel. The way to decompose energy-momentum into work and heat is not uniquely determined; the different choices result in different views. Also the definition of three dimensional volume causes ambiguity of thermodynamical quantities. The present paper shows various theories are obtained depending on the choice of these two factors. Subject Index: 070

Quark-Anti-Quark Potentials from Nambu-Bethe-Salpeter Amplitudes on Lattice

Abstract: Quark--anti-quark (anti-q-q) potentials with finite quark masses are studied from the anti-q-q Nambu-Bethe-Salpeter (NBS) wave functions in quenched lattice QCD. With the use of a method which has been recently developed in the derivation of nuclear forces from lattice QCD, we derive the anti-q-q potentials from the NBS wave functions. We calculate the anti-q-q NBS wave functions in pseudo-scalar and vector channels for several quark masses. The derived potentials at each quark mass in both channels show linear plus Coulomb form. We also discuss the quark-mass and channel dependence of the anti-q-q potentials.

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

Abstract: We calculate the averaged number \ u of the lightest supersymmetric particles (LSPs) in a shower from the decay of superheavy particle X by generalized DGLAP equations. If the primary decayed particles have color charges and the virtuality is around 10^13-10^14 GeV, the averaged number of the LSPs can become O(100). As the result, the upper limit of the mass of the superheavy particle, whose decay can produce the observed abundance of the 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 around 10^13 GeV, the decay of the inflaton can produce the observed dark matter abundance if the reheating temperature is of order 1 GeV. Even for the standard model particles with virtuality Q\\sim 10-100 TeV, the averaged number of the LSPs becomes O(0.1) for gluon, and O(0.01) for Higgs, which strongly constrains the scenario of non-thermal LSP production from the decay of moduli with 10-100 TeV mass.