Strong Coupling Problem Research Articles

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

In this work, we discuss the polarization contents of Einstein-\ae ther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-\ae ther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-\ae ther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-\ae ther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Inflationary magneto-(non)genesis, increasing kinetic couplings, and the strong coupling problem

We study the generation of magnetic fields during inflation making use of a coupling of the inflaton and moduli fields to electromagnetism via the photon kinetic term, and assuming that the coupling is an increasing function of time. We demonstrate that the strong coupling problem of inflationary magnetogenesis can be avoided by incorporating the destabilization of moduli fields after inflation. The magnetic field always dominates over the electric one, and thus the severe constraints on the latter from backreaction, which are the demanding obstacles in the case of a decreasing coupling function, do not apply to the current scenario. However, we show that this loophole to the strong coupling problem comes at a price: the normalization of the amplitude of magnetic fields is determined by this coupling term and is therefore suppressed by a large factor after the moduli destabilization completes. From this we conclude that there is no self-consistent and generic realization of primordial magnetogenesis producing scale-invariant fields in the case of an increasing kinetic coupling.

Modal space three-state feedback control for electro-hydraulic servo plane redundant driving mechanism with eccentric load decoupling

The shaking table based on electro-hydraulic servo parallel mechanism has the advantage of strong carrying capacity. However, the strong coupling caused by the eccentric load not only affects the degree of freedom space control precision, but also brings trouble to the system control. A novel decoupling control strategy is proposed, which is based on modal space to solve the coupling problem for parallel mechanism with eccentric load. The phenomenon of strong dynamic coupling among degree of freedom space is described by experiments, and its influence on control design is discussed. Considering the particularity of plane motion, the dynamic model is built by Lagrangian method to avoid complex calculations. The dynamic equations of the coupling physical space are transformed into the dynamic equations of the decoupling modal space by using the weighted orthogonality of the modal main mode with respect to mass matrix and stiffness matrix. In the modal space, the adjustments of the modal channels are independent of each other. Moreover, the paper discusses identical closed-loop dynamic characteristics of modal channels, which will realize decoupling for degree of freedom space, thus a modal space three-state feedback control is proposed to expand the frequency bandwidth of each modal channel for ensuring their near-identical responses in a larger frequency range. Experimental results show that the concept of modal space three-state feedback control proposed in this paper can effectively reduce the strong coupling problem of degree of freedom space channels, which verify the effectiveness of the proposed model space state feedback control strategy for improving the control performance of the electro-hydraulic servo plane redundant driving mechanism.

Generation of helical magnetic field in a viable scenario of inflationary magnetogenesis

We study the generation of helical magnetic fields in a model of inflationary magnetogenesis which is free from the strong coupling and back-reaction problems. To generate helical magnetic fields, we add an $f^2 \tilde{F}^{\mu\nu} F_{\mu\nu}$ term to the lagrangian of Ratra model. The strong coupling and back-reaction problems are avoided if we take a particular behaviour of coupling function $f$, in which $f$ increases during inflation and decreases post inflation to reheating. The generated magnetic field is fully helical and has a blue spectrum, $d\rho_B/d\ln k \propto k^4$. This spectrum is obtained when coupling function $f\propto a^2$ during inflation. The scale of reheating in our model has to be lower than $4000$ GeV to avoid back-reaction post inflation. The generated magnetic field spectrum satisfies the $\gamma$-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are $\sim 4 \times 10^{-11} $ G and $70$ kpc respectively, if reheating takes place at 100 GeV. For reheating at the QCD scales of $150$ MeV, the field strength increases to $\sim$ nano gauss, with coherence scale of $0.6$ Mpc.

A Micromechanics-Based Elastoplastic Damage Model for Rocks with a Brittle–Ductile Transition in Mechanical Response

As confining pressure increases, crystalline rocks of moderate porosity usually undergo a transition in failure mode from localized brittle fracture to diffused damage and ductile failure. This transition has been widely reported experimentally for several decades; however, satisfactory modeling is still lacking. The present paper aims at modeling the brittle–ductile transition process of rocks under conventional triaxial compression. Based on quantitative analyses of experimental results, it is found that there is a quite satisfactory linearity between the axial inelastic strain at failure and the confining pressure prescribed. A micromechanics-based frictional damage model is then formulated using an associated plastic flow rule and a strain energy release rate-based damage criterion. The analytical solution to the strong plasticity-damage coupling problem is provided and applied to simulate the nonlinear mechanical behaviors of Tennessee marble, Indiana limestone and Jinping marble, each presenting a brittle–ductile transition in stress–strain curves.

BOMP‐based angle estimation with polarimetric MIMO radar with spatially spread crossed‐dipole

For polarimetric multi-input multi-output (MIMO) radar with spatially spread crossed-dipole, this article studies the problem of joint direction of arrival (DOA) and polarisation parameter estimation based on block-orthogonal matching pursuit (BOMP) algorithm. First, the signal model of polarimetric MIMO radar with spatially spread crossed-dipole is established, and then the covariance matrix of the received data is calculated. Using the relationship between polarisation parameter and DOA in the crossed-dipole, sparse dictionary matrix is constructed within only DOA parameter and it will be translated into a block sparse problem. Then, fast BOMP algorithm is used to estimate their support positions and their amplitudes. Last, DOA estimation is calculated by support positions and polarisation parameter is estimated by the amplitudes of the support positions. The proposed algorithm has three advantages. One is that overcomplete dictionary is constructed within only the DOA, which has a small computational complexity. Another one is that the problem of strong mutual coupling among collocated crossed-dipole is solved by using the spatially spread crossed-dipole. The last one is that the DOA and polarisation estimations can pair automatically without any additional processing. Computer simulation results demonstrate the effectiveness of the proposed algorithm.

Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators

Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems.Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint space control and work space control.

Challenges in inflationary magnetogenesis: Constraints from strong coupling, backreaction, and the Schwinger effect

Models of inflationary magnetogenesis with a coupling to the electromagnetic action of the form $f^2 F_{\mu\nu}F^{\mu\nu}$, are known to suffer from several problems. These include the strong coupling problem, the back reaction problem and also strong constraints due to Schwinger effect. We propose a model which resolves all these issues. In our model, the coupling function, $f$, grows during inflation and transits to a decaying phase post inflation. This evolutionary behaviour is chosen so as to avoid the problem of strong coupling. By assuming a suitable power law form of the coupling function, we can also neglect back reaction effects during inflation. To avoid back reaction post-inflation, we find that the reheating temperature is restricted to be below $ \approx 1.7 \times 10^4$ GeV. The magnetic energy spectrum is predicted to be non-helical and generically blue. The estimated present day magnetic field strength and the corresponding coherence length taking reheating at the QCD epoch(150 MeV) are $ 1.4 \times 10^{-12}$ G and $6.1 \times 10^{-4}$ Mpc, respectively. This is obtained after taking account of nonlinear processing over and above the flux freezing evolution after reheating. If we consider also the possibility of a non-helical inverse cascade, as indicated in direct numerical simulations, the coherence length and the magnetic field strength are even larger. In all cases mentioned above, the magnetic fields generated in our models satisfy the $\gamma$-ray bound below a certain reheating temperature.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

Study of long-range orders of hard-core bosons coupled to cooperative normal modes in two-dimensional lattices

Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half filling and from a superfluid to a diagonal striped solid [with crystalline ordering wavevector $\vec{Q}=(2\pi/3,2\pi/3)$ or $(2\pi/3,4\pi/3)$] at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\rm La}_{2-x}{\rm Sr}_x{\rm NiO_4}$ at $x=1/2$ and $x=1/3$.

Inflationary Magnetogenesis with On-shell Local U(1) Symmetry

We propose a new mechanism for inflationary magnetogenesis in which the local U(1) symmetry is broken during inflation. Nevertheless it is shown that the U(1) symmetry is recovered on-shell. We find that it is free from both the strong coupling and back reaction problems, and can explain the origin of cosmic magnetic fields on intergalactic scales, whose existence has been strongly suggested by recent observations.

(Invited) On the Theory of Nanotube-Graphene Crossiton: A New Class of Topological Solutions

aIoffe Institute, 26 Polytekhnicheskaya, St. Petersburg, 194021, Russia bDepartment of Physics, Department of Material Science; the Center for Advanced Materials & Nanotechnology and the Center for Photonics & Nanoelectronics, Lehigh University, Bethlehem, Pennsylvania 18015, United States A problem of strong (aka non-perturbative) coupling between quantum systems has been in the focus of physics research for many decades, having both fundamental interest and value for applications from quantum information to spintronics. Most recently it received attention due to technological capability to couple electronic systems of different dimensionality, for example, one-dimensional (1d) to 2d-systems. Cross-dimensional excitation were shown here to form a new class of solutions of strongly coupled Hamiltonians. We use the formalism of coupled Dyson equations, and propose an efficient method of obtaining a distinct family of non-perturbative solutions. It reproduces known ``polariton''-family in the limit of the same symmetry of the coupled systems. On contrary, when the symmetry of one system makes a sub-group of the other, and the coupling interaction preserves a sub-set of quantum numbers, like a wavevector along 1d-axis, a special class of solutions - crossiton - is found. Green's functions (GF) of crossiton sub-modes can be expressed via GFs of uncoupled systems and interaction vertexes. The general crossiton Hamiltonian can be mapped on a wide range of quantum-mechanical problems (like Fano-Anderson problem) that, otherwise, are not obviously related. Such a solution, to the best of our knowledge, was not demonstrated before. We emphasize on that the problem is solved non-perturbatively, presenting full solution, beyond weak coupling model. This research is supported by the NSF ECCS-1509786 (SVR) and RFBR 14-02-01223А (AGP). Fig. 1. Bare (dashed) and renormalized (solid) GF of the crossiton in the 1d-system. Figure 1

Magnetogenesis in matter—Ekpyrotic bouncing cosmology

In the recent past there have been many attempts to associate the generation of primordial magnetic seed fields with the inflationary era, but with limited success. We thus take a different approach by using a model for nonsingular bouncing cosmology. A coupling of the electromagnetic Lagrangian FμνFμν with a non background scalar field has been considered for the breaking of conformal invariance. We have shown that non singular bouncing cosmology supports magnetogenesis evading the long standing back reaction and strong coupling problems which have plagued inflationary magnetogenesis. In this model, we have achieved a scale invariant power spectrum for the parameter range compatible with observed CMB anisotropies. The desired strength of the magnetic field has also been obtained that goes in accordance with present observations. It is also important to note that no BKL instability arises within this parameter range. The energy scales for different stages of evolution of the bouncing model are so chosen that they solve certain problems of standard Big Bang cosmology as well.

Inflating Kahler moduli and primordial magnetic fields

We study the production of primordial magnetic fields in inflationary models in type IIB string theory where the role of the inflaton is played by a Kahler modulus. We consider various possibilities to realise the Standard Model degrees of freedom in this setting and explicitly determine the time dependence of the inflaton coupling to the Maxwell term in the models. Using this we determine the strength and scale dependence of the magnetic fields generated during inflation. The usual “strong coupling problem” for primordial magnetogenesis manifests itself by cycle sizes approaching the string scale; this appears in a certain class of fibre inflation models where the standard model is realised by wrapping D7-branes on cycles in the geometric regime.

Cosmic magnetization out from the vacuum

The large-scale magnetic fields we observe today in galaxies and galaxy clusters could be the result of a pure quantum effect taking place during inflation, to wit, the creation of particles (photons) out from the vacuum in a curved spacetime. We show that, whenever the conformal invariance of electromagnetism is broken during inflation, the actual magnetic field spectrum, in the classical limit, is given by [Formula: see text], where [Formula: see text] is the number of created photons with wave number [Formula: see text]. In particular, a scale-invariant magnetic field of order of 10[Formula: see text] G can emerge in the simplest model of cosmic magnetogenesis, the one where the inflaton is kinetically coupled to the photon. Moreover, and contrarily to the general belief, we show that such a model is free from the so-called strong-coupling and backreaction problems. This conclusion follows, indirectly, from the observation that post-inflationary electric currents, which in the literature are incorrectly supposed to freeze superhorizon magnetic fields after inflation, are indeed vanishing on superhorizon scales due to causality.

Inflationary magnetogenesis with broken local U(1) symmetry

We point out that a successful inflationary magnetogenesis could be realised if we break the local U(1) gauge symmetry during inflation. The effective electric charge is fixed as a fundamental constant, which allows us to obtain an almost scale-invariant magnetic spectrum avoiding both the strong coupling and back reaction problems. We examine the corrections to the primordial curvature perturbation due to these stochastic electromagnetic fields and find that, at both linear and non-linear orders, the contributions from the electromagnetic field are negligible compared to those created from vacuum fluctuations. Finally, the U(1) gauge symmetry is restored at the end of inflation.

Population-imbalanced lattice fermions near the BCS-BEC crossover: Thermal physics of the breached pair and Fulde-Ferrell-Larkin-Ovchinnikov phases

We study s-wave superconductivity in the two dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via Monte Carlo. The method requires iterative solution of the Bogoliubov-de-Gennes (BdG) equations for amplitude and phase fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong coupling problem, revealing $T_c$ scales an order of magnitude below the mean field estimate, highlight the spontaneous inhomogeneity in the field induced magnetization, and discover a strong non monotonicity in the temperature dependence of the low energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. This paper focuses on the magnetized but homogeneous (breached pair) superconducting state, a companion paper deals with the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) regime.

Model of inflationary magnetogenesis

We consider the possibility of inflationary magnetogenesis due to dynamical couplings of the electromagnetic fields to gravity. We find that large primordial magnetic fields can be generated during inflation without the strong coupling problem, backreaction problem, or curvature perturbation problem, which seed large-scale magnetic fields with observationally interesting strengths.

A Decoupling Control Strategy for Multilayer Register System in Printed Electronic Equipment

Register accuracy is an important index to evaluate the quality of electronic products printed by gravure printed electronic equipment. However, the complex relationships of multilayer register system make the problem of decoupling control difficult to be solved, which has limited the improvement of register accuracy for the gravure printed electronic equipment. Therefore, this paper presents an integrated decoupling control strategy based on feedforward control and active disturbance rejection control (ADRC) to solve the strong coupling, strong interference, and time-delay problems of multilayer register system. First of all, a coupling and nonlinear model is established according to the multilayer register working principle in gravure printing, and then a linear model of the register system is derived based on the perturbation method. Secondly, according to the linear model, a decoupling control strategy is designed based on feedforward control and ADRC for the multilayer register system. Finally, the results of computer simulation show that the proposed control methodology can realize a decoupling control and has good control performance for multilayer register system.

Inflationary dynamics of kinetically-coupled gauge fields

We investigate the inflationary dynamics of two kinetically-coupled massless U(1) gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can be quantized using the standard creation, annihilation operator algebra. This second constraint limits us to scenarios where the system can be diagonalized into the sum of two decoupled, massless, vector fields with a varying kinetic-term coefficient. Such a system might be interesting for magnetogenesis because of how the strong coupling problem generalizes. We explore this idea by assuming that one of the gauge fields is the Standard Model U(1) field and that the other dark gauge field has no particles charged under its gauge group. We consider whether it would be possible to transfer a magnetic field from the dark sector, generated perhaps before the coupling was turned on, to the visible sector. We also investigate whether the simple existence of the mixing provides more opportunities to generate magnetic fields. We find that neither possibility works efficiently, consistent with the well-known difficulties in inflationary magnetogenesis.