Dynamical Degrees Of Freedom Research Articles

Turning on gravity with the Higgs mechanism

We investigate how a Higgs mechanism could be responsible for the emergence of gravity in extensions of Einstein theory, with a suitable low energy limit. In this scenario, at high energies, symmetry restoration could ‘turn off’ gravity, with dramatic implications for cosmology and quantum gravity. The sense in which gravity is muted depends on the details of the implementation. In the most extreme case gravity’s dynamical degrees of freedom would only be unleashed after the Higgs field acquires a non-trivial vacuum expectation value, with gravity reduced to a topological field theory in the symmetric phase. We might also identify the Higgs and the Brans–Dicke fields in such a way that in the unbroken phase Newton’s constant vanishes, decoupling matter and gravity. We discuss the broad implications of these scenarios.

Dirac-Born-Infeld inflation model with kinetic coupling to Einstein gravity

In this paper we study a new class of inflation models which generalize the Dirac-Born-Infeld (DBI) action with the addition of a nonminimal kinetic coupling (NKC) term. We dubbed this model as the {\it new DBI inflation model}. The NKC term does not bring new dynamical degree of freedom, so the equations of motion remain of second order. However, with such a coupling, the action is no longer linear with respect to the Einstein curvature term ($R$ or $G^{\mu\nu}$), which leads to a correction term of $k^4$ in the perturbations. The new DBI inflation model can be viewed as theories beyond Horndeski. Without violating nearly scale-invariance, such a correction may lead to new effects on the inflationary spectra that could be tested by future observations.

Statics And Kinematics Of Semirigid Steel Frames Under Seismic Action

Abstract Intended contribution emphasizes the statics and kinematics of semi-rigid steel frames seismically acted upon. The dynamic model of analyzed structures consists of multi degree of freedom systems with lumped masses located at floor levels. The dynamic degrees of freedom are the lateral seismically induced floor displacements. A cyclic behavior of semi-rigid beam – column connections associated with the four parameters analytical bending moment M – relative rotation θr is considered. Time history seismic analyses are performed on multi-story steel planar frames equipped with several top and seat and web angle beam – column connections acted upon by recorded seismic actions. The computed numerical results refer to the contrary static and effects of semi-rigidity: the increase in lateral floor displacements accompanied by a decrease in the seismic base shear force. Relevant comments are drawn.

Failure of Arm Movement Control in Stroke Patients, Characterized by Loss of Complexity.

We study the mechanism of human arm-posture control by means of nonlinear dynamics and quantitative time series analysis methods. Utilizing linear and nonlinear measures in combination, we find that pathological tremors emerge in patient dynamics and serve as a main feature discriminating between normal and patient groups. The deterministic structure accompanied with loss of complexity inherent in the tremor dynamics is also revealed. To probe the underlying mechanism of the arm-posture dynamics, we further analyze the coupling patterns between joints and components, and discuss their roles in breaking of the organization structure. As a result, we elucidate the mechanisms in the arm-posture dynamics of normal subjects responding to the gravitational force and for the reduction of the dynamic degrees of freedom in the patient dynamics. This study provides an integrated framework for the origin of the loss of complexity in the dynamics of patients as well as the coupling structure in the arm-posture dynamics.

Leggett’s modes in magnetic systems with Jahn–Teller distortion

Leggett’s mode is a collective excitation corresponding to the oscillation of the relative phase of the order parameters in a two band superconductor, with frequency proportional to interband coupling. We report on the existence of modes, similar to Leggett’s mode, in magnetic systems with Jahn–Teller distortion. The minimal Kugel–Khomskii model, which describes simultaneously both the spin and the orbital order, is studied. The dynamical degrees of freedom are spin-s operators of localized spins and pseudospin-τ operators, which respond to the orbital degeneracy and satisfy the similar commutation relation with those of the spin operators. In the case of “G-type antiferro” spin and pseudospin order the system possesses two antiferromagnetic magnons with equal spin-wave velocities and two Leggett’s modes with equal gaps proportional to the square root of the spin–pseudospin interaction constant. In the case of “ferro” spin and pseudospin order the system possesses one ferromagnetic magnon and one Leggett’s mode with gap proportional to the spin–pseudospin interaction constant. We conclude that Leggett’s modes, in the spectrum of the magnetic systems with Jahn–Teller distortion, are generic features of these systems.

Group manifold approach to higher spin theory

We consider the group manifold approach to higher spin theory. The deformed local higher spin transformation is realized as the diffeomorphism transformation in the group manifold $\textbf{M}$. With the suitable rheonomy condition and the torsion constraint imposed, the unfolded equation can be obtained from the Bianchi identity, by solving which, fields in $\textbf{M}$ are determined by the multiplet at one point, or equivalently, by $(W^{[a(s-1),b(0)]}_{\mu},H)$ in $AdS_{4}\subset \textbf{M}$. Although the space is extended to $\textbf{M}$ to get the geometrical formulation, the dynamical degrees of freedom are still in $AdS_{4}$. The $4d$ equations of motion for $(W^{[a(s-1),b(0)]}_{\mu},H)$ are obtained by plugging the rheonomy condition into the Bianchi identity. The proper rheonomy condition allowing for the maximum on-shell degrees of freedom is given by Vasiliev equation. We also discuss the theory with the global higher spin symmetry, which is in parallel with the WZ model in supersymmetry.

Organization of Postural Coordination Patterns as a Function of Scaling the Surface of Support Dynamics

ABSTRACTThe number and nature of the dynamical degrees of freedom (DFs) in postural coordination patterns was investigated as a function of practice over the continuously scaled frequency of the support surface dynamics. The modal number of dynamical DFs of the coordination pattern was reduced with practice particularly in the higher frequency conditions. The ankle-knee and knee-hip couplings were highly variable across the platform frequencies and practice. The findings show that practice and higher platform frequency both contribute to reducing the number of dynamical DFs of movement organization in compensatory postural control and that this is related to an increase in the strength of particularly the ankle and hip synergy.

Conformal geometrodynamics regained: Gravity from duality

There exist several ways of constructing general relativity from ‘first principles’: Einstein’s original derivation, Lovelock’s results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and Hojman–Kuchař-Teitelboim’s derivation of the Hamiltonian form of the theory from the symmetries of space–time, to name a few. Here I propose a different set of first principles to obtain general relativity in the canonical Hamiltonian framework without presupposing space–time in any way. I first require consistent propagation of scalar spatially covariant constraints (in the Dirac picture of constrained systems). I find that up to a certain order in derivatives (four spatial and two temporal), there are large families of such consistently propagated constraints. Then I look for pairs of such constraints that can gauge-fix each other and form a theory with two dynamical degrees of freedom per space point. This demand singles out the ADM Hamiltonian either in (i) CMC gauge, with arbitrary (finite, non-zero) speed of light, and an extra term linear in York time, or (ii) a gauge where the Hubble parameter is conformally harmonic.

Relations Between Different Notions of Degrees of Freedom of a Quantum System and Its Classical Model

There are at least three different notions of degrees of freedom (DF) that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the other to the structure of the system and the third to the properties of dynamical orbits. In this paper, definitions and comparison in classical and quantum systems of the tree types of DF are formulated and discussed. In particular, we concentrate on comparison of the number of the so called dynamical DF in a quantum system and its classical model. The comparison involves analyzes of relations between integrability of the classical model, dynamical symmetry and separability of the quantum and the corresponding classical systems and dynamical generation of appropriately defined quantumness. The analyzes is conducted using illustrative typical systems. A conjecture summarizing the observed relation between generation of quantumness by the quantum dynamics and dynamical properties of the classical model is formulated.

Vector form factor of the pion in chiral effective field theory

The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.

The topological long range order in QCD. Applications to heavy ion collisions and cosmology

We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. A similar phenomenon is known to occur in some topologically ordered condensed matter systems with a gap. We also discuss possible cosmological applications of this long range order in strongly coupled gauge theories. In particular, we argue that the de Sitter behaviour might be dynamically generated as a result of the long range order. In this framework the inflaton is an auxiliary field which effectively describes the dynamics of topological sectors in a gauge theory in the expanding universe, rather than a new dynamical degree of freedom.

Probable Errors of Dynamic Method at Conservative System Stability Analysis

Application of dynamic method for conservative system stability analysis is considered. It is shown that the use of this method may cause essential errors. A detailed analysis of error causes is given. A number of models is considered, at which stability analysis, errors occur. Threat evaluation of such errors is given. It is shown that the physical nature of probable errors is in that in degenerated dynamic system these forms of stability loss correspond to the original system from which all dynamic degrees of freedom are excluded. Recommendations which allow excluding probable errors are given. Method which may be called degenerated system dynamic method is proposed. This method is especially effective at time dynamic analysis of linear degenerated system subjected to short-term loads.

The topological long range order in QCD. Applications to heavy ion collisions and cosmology

We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. A similar phenomenon is known to occur in some topologically ordered condensed matter systems with a gap. We also discuss possible cosmological applications of this long range order in strongly coupled gauge theories. In particular, we argue that the de Sitter behaviour might be dynamically generated as a result of the long range order. In this framework the inflaton is an auxiliary field which effectively describes the dynamics of topological sectors in a gauge theory in the expanding universe, rather than a new dynamical degree of freedom.

The Weyl tensor correlator in cosmological spacetimes

We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ϵ and δ, and the result is shown to have the correct de Sitter limit as ϵ, δ → 0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.

Effective Lagrangian for Nonrelativistic Systems

The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing $1$ dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in $1+1$ dimensions.

Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems.

A robust energy transfer mechanism is found in nonlinear wave systems, which favors transfers toward modes interacting via triads with nonzero frequency mismatch, applicable in meteorology, nonlinear optics and plasma wave turbulence. We emphasize the concepts of truly dynamical degrees of freedom and triad precession. Transfer efficiency is maximal when the triads' precession frequencies resonate with the system's nonlinear frequencies, leading to a collective state of synchronized triads with strong turbulent cascades at intermediate nonlinearity. Numerical simulations confirm analytical predictions.

Leptogenesis with a dynamical seesaw scale

In the simplest type-I seesaw leptogenesis scenario right-handed neutrino annihilation processes are absent. However, in the presence of new interactions these processes are possible and can affect the resulting B-L asymmetry in an important way. A prominent example is provided by models with spontaneous lepton number violation, where the existence of new dynamical degrees of freedom can play a crucial role. In this context, we provide a model-independent discussion of the effects of right-handed neutrino annihilations. We show that in the weak washout regime, as long as the scattering processes remain slow compared with the Hubble expansion rate throughout the relevant temperature range, the efficiency can be largely enhanced, reaching in some cases maximal values. Moreover, the B-L asymmetry yield turns out to be independent upon initial conditions, in contrast to the ''standard'' case. On the other hand, when the annihilation processes are fast, the right-handed neutrino distribution tends to a thermal one down to low temperatures, implying a drastic suppression of the efficiency which in some cases can render the B-L generation mechanism inoperative.

Parametrizing and constraining scalar corrections to general relativity

We parametrize a large class of corrections to general relativity which include a long-ranged gravitational scalar field as a dynamical degree of freedom in two ways: parametrizing the structure of the correction to the action, and parametrizing the scalar hair (multipole structure) that compact objects and black holes attain. The presence of this scalar hair violates the no-hair theorems present in general relativity, which leads to several important effects. The effects we consider are (i) the interaction between an isolated body and an external scalar field, (ii) the scalar multipole-multipole interaction between two bodies in a compact binary, (iii) the additional pericenter precession of a binary, (iv) the scalar radiation from a binary, and (v) the modification to the gravitational wave phase from a binary. We apply this framework to example theories including Einstein-dilaton-Gauss-Bonnet gravity and dynamical Chern-Simons gravity, and estimate the size of the effects. Finally, we estimate the bounds that can be placed on parameters of the theories from the precession of pulsar binaries and from gravitational waves.

Yang--Mills Thermodynamics: an Effective Theory Approach

We derive the Polyakov-loop thermodynamic potential in the perturbative approach to pure SU(3) Yang-Mills theory. The potential expressed in terms of the Polyakov loop in the fundamental representation corresponds to that of the strong-coupling expansion, of which the relevant coefficients of the gluon energy distribution are specified by characters of the SU(3) group. At high temperatures the derived gluon potential exhibits the correct asymptotic behavior, whereas at low temperatures, it disfavors gluons as appropriate dynamical degrees of freedom. In order to quantify the Yang-Mills thermodynamics in a confined phase, we propose a hybrid approach which matches the effective gluon potential to the one of glueballs constrained by the QCD trace anomaly in terms of a dilaton. We also discuss the interplay between the chromomagnetic and chromoelectric gluon dynamics.

THE ROLE OF THE Δ(1232)-RESONANCE IN COVARIANT BARYON CHIRAL PERTURBATION THEORY

We stress, on theoretical and phenomenological grounds, the importance of the Δ(1232)-resonance in a chiral effective field theory approach to the study of πN scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from πN scattering data.