121742412
Universality and asymptotic limits of the scaling exponents in circle maps
Abstract In he quasiperiodic route to chaos as modeled by the circle map, the universal behavior is dictated by the degree of inflection z . Using a polynomial form of the circle map, we have studied the dependence of the scaling exponents α and δ on z . The asymptotic limits of α( z ) and δ( z ) as z →∞ have also been found.
117912244
Galilean structure of the Poincaré group on the light-cone
SummaryIt is observed that the isomorphism between the Poincaré subgroup in the L.C. (light-cone) co-ordinates and the two-dimensional Galilean group can be trivially extended to higher dimensions. The case of five dimension is explicitly shown, and the generalization to any finite dimensionn (> 2) is immediate.RiassuntoSi osserva che l’isomorfismo fra il sottogruppo di Poincaré nelle coordinate del cono di luce (L.C.) ed il gruppo galileano bidimensionale può essere esteso in modo banale a dimensioni superiori. Si presenta esplicitamente il caso delle cinque dimensioni, e la generalizzazione a qualunque dimensione finitan (>2) è immediata.РеэюмеОтмечается, что иэоморфиэм между подгруппой Пуанкаре в координата светового конуса и двумерной группой Галилея может быть тривиально распространен на случай больщего числа иэмерений. Явным обраэом исследуется пятимерный случай. Обобшение на случай любого числа иэмеренийп (>2) получается непосредственно.
120428117
Crossover phenomena in the multifractal behavior of invariant circles
Abstract The singularity spectrum f(α) and the generalized dimension Dq of the critical invariant circle in an area-preserving twist map with a variable degree of inflection z is studied. The scaling behavior is found to depend on z, and there is a crossover from the simple fixed point to the standard fixed point when z varies from 2 to 3. Thus z plays a role quite similar to that of dimensionality in phase transition, with z = 2 and 3 corresponding to the lower and upper critical dimensions respectively.
122878082
Induced Topological Terms, Hidden Local Symmetry, and Anyon Superconductivity
We show how the topological Chern-Simons term in three dimensions and the θ-term, in four dimensions can be dynamically generated due to quantum fluctuations in Nambu-Jona-Lasinio models. These results give a vivid demonstration of hidden local symmetry at work. The fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity. Possible phenomenological implications of this approach in particle physics are also discussed.
209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
14771278
Nonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic timeperiodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Their geometric phases are found to be independent of \, and equal to 2(n11/2) times the classical nonadiabatic Hannay angle. @S1050-2947~98!03311-3# The Berry phase is one of the most important findings on the fundamental problem of quantum mechanics in recent years @1#. It reveals the gauge structure associated with a phase shift in adiabatic processes in quantum mechanics. This quantal phase is connected with a classical angle, namely, the Hannay angle, by a simple and elegant expression in the semiclassical limit @2#. The next important advance was the relaxation of the adiabatic approximation @3,4#. Aharanov and Anandan studied the phase associated with a cyclic evolution in quantum mechanics, which occurs when a state returns to its initial condition. They showed that the phase is a geometrical property of the curve in the projective Hilbert space which is naturally associated with the motion @3#. For the special case of an adiabatic evolution, this phase factor is a gauge-invariant generalization of the Berry phase. The significance of Aharanov and Anandan’s generalization lies in the following: ~i! the cyclic evolution of a physical system is of the most interest in physics both experimentally and theoretically; ~ii! the universal existence of the cyclic evolution is guaranteed for any quantum system. The second point can be easily recognized by considering the eigenvectors of the unitary evolution operator for a quantum system. An explicit example is a time-periodic Hamiltonian system where the Floquet theorem applies. The eigenfunctions of the Floquet operator, which are the socalled Bloch wave functions in condensed-matter physics, are obviously cyclic solutions and are of great interest in physics. However, unlike the adiabatic case, in the nonadiabatic case calculating the eigenvectors and extracting the nonadiabatic geometric phase from the quasienergy term for a time-dependent Hamiltonian is far from a trivial task, except in the special case of the spin particle in a magnetic field. Recent works of Ge and Child@5# made a further step in this direction. They found a special cyclic state of the Gaussian wave packet’s form for a generalized harmonic oscillator. The nonadiabatic geometric phase is explicitly calculated and found to be one-half of the classical nonadiabatic Hannay angle. In this paper, we would like to suggest an alternative approach—the squeezed-state approach to study the general cyclic evolutions of the generalized harmonic oscillator. In particular, we shall construct a class of quantum states based on the superposition of an infinite number of squeezed states. We find that the condition for them to be cyclic evolutions is nothing but the quantization rule without Maslov-Morse correction. The nonadiabatic geometric phases are obtained analytically, and found to be related to the classical Hannay angle by an explicit expression.
118483015
Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data
We introduce EFTCAMB/EFTCosmoMC as publicly available patches to the commonly used CAMB/CosmoMC codes. We briefly describe the structure of the codes, their applicability and main features. To illustrate the use of these patches, we obtain constraints on parametrized pure EFT and designer $f(R)$ models, both on $\Lambda$CDM and $w$CDM background expansion histories, using data from Planck temperature and lensing potential spectra, WMAP low-$\ell$ polarization spectra (WP), and baryon acoustic oscillation (BAO). Upon inspecting theoretical stability of the models on the given background, we find non-trivial parameter spaces that we translate into viability priors. We use different combinations of data sets to show their individual effects on cosmological and model parameters. Our data analysis results show that, depending on the adopted data sets, in the $w$CDM background case this viability priors could dominate the marginalized posterior distributions. Interestingly, with Planck+WP+BAO+lensing data, in $f(R)$ gravity models, we get very strong constraints on the constant dark energy equation of state, $w_0\in(-1,-0.9997)\,\,(95% {\rm C.L.})$.
121689351
Intrinsic measures of field entropy in cosmological particle creation
Abstract Using the properties of quantum parametric oscillators, two quantities are identified which increase monotonically in time in the process of parametric amplification. The use of these quantities as possible measures of entropy generation in vacuum cosmological particle creation is suggested. These quantities which are of complementary nature are both related to the number of particles spontaneously created.
122768225
Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects
We present a detailed and systematic analysis of the nonperturbative, nonequilibrium dynamics of a quantum field in the reheating phase of inflationary cosmology, including full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field. We use the O(N) field theory with unbroken symmetry in a spatially flat Friedmann-Robertson-Walker (FRW) universe to study the dynamics of the inflaton in the post-inflation, preheating stage. Oscillations of the inflaton{close_quote}s zero mode induce parametric amplification of quantum fluctuations, resulting in a rapid transfer of energy to the inhomogeneous modes of the inflaton field. The large-amplitude oscillations of the mean field, as well as stimulated emission effects require a nonperturbative formulation of the quantum dynamics, while the nonequilibrium evolution requires a statistical field theory treatment. We adopt the coupled nonperturbative equations for the mean field and variance derived in a preceding paper [S. A. Ramsey and B. L. Hu, this issue, Phys. Rev. D {bold 56}, 661 (1997)] by means of a two-particle-irreducible (2PI), closed-time-path (CTP) effective action for curved spacetimes while specialized to a dynamical FRW background, up to leading order in the 1/N expansion. Adiabatic regularization is employed to yield a covariantly conserved,more » renormalized energy-momentum tensor. The renormalized dynamical equations are evolved numerically from initial data which are generic to the end state of slow roll in many inflationary cosmological scenarios. The initial conditions consist of a large-amplitude, quasiclassical, oscillating mean field {l_angle}{Phi}{r_angle} with variance {l_angle}{Phi}{sup 2}{r_angle}{minus}{l_angle}{Phi}{r_angle}{sup 2} around the de Sitter-invariant vacuum. (Abstract Truncated)« less
15718551
Early Universe Quantum Processes in BEC Collapse Experiments
We show that in the collapse of a Bose–Einstein condensate (BEC)4certain processes involved and mechanisms at work share a common origin with corresponding quantum field processes in the early universe such as particle creation, structure formation, and spinodal instability. Phenomena associated with the controlled BEC collapse observed in the experiment of Donley et al. (Donley, E., et al. (2001), Nature412, 295; Claussen, N. (2003), PhD Thesis, University of Colorado; Claussen, N., et al. (2003), Physical Review A67, 060701(R))(they call it “Bose–Nova,” see also Chin, J., Vogels, J., and Ketterle, W. (2003), Physical Review Letters90, 160405) such as the appearance of bursts and jets can be explained as a consequence of the squeezing and amplification of quantum fluctuations above the condensate by the dynamics of the condensate. Using the physical insight gained in depicting these cosmological processes, our analysis of the changing amplitude and particle contents of quantum excitations in these BEC dynamics provides excellent quantitative fits with the experimental data on the scaling behavior of the collapse time and the amount of particles emitted in the jets. Because of the coherence properties of BEC and the high degree of control and measurement precision in atomic and optical systems, we see great potential in the design of tabletop experiments for testing out general ideas and specific (quantum field) processes in the early universe, thus opening up the possibility for implementing “laboratory cosmology.”
650862
Theory of optomechanics: Oscillator-field model of moving mirrors
Chad R. Galley, 2 Ryan O. Behunin, and B. L. Hu 5 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91125, USA Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91106, USA Center for Nonlinear Studies and Los Alamos National Laboratory, Theoretical Division, Los Alamos, New Mexico 87545, USA Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA Institute for Advanced Study and Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China (Dated: May 10, 2014)