120868242
Frenkel-Kontorova model with toda interactions
We have studied the Frenkel-Kontorova (FK) model with Toda interactions. The phase diagram is found to be asymmetric due to the exponential form of the Toda interaction. The reflection symmetry observed in the standard FK model is broken here. The singularity spectrum and the generalized dimension are calculated and their dependence on the nonlinearity parameter is discussed. The critical exponents of the gap in the phonon spectrum, the correlation length, and the Peierls-Nabarro barrier are found to be the same as those in the standard FK model and are independent of the nonlinearity parameter.
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.
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.
119177404
Searching for primordial localized features with CMB and LSS spectra
Inspired by the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, we search for a primordial localized feature imprinted in cosmic microwave background and large-scale structure formation observables. We find some common oscillatory patterns both in the Planck CMB temperature-temperature power spectrum and the WiggleZ galaxy spectrum. By performing independent searches with these two data sets, we find a coincidence in the most significant mode previously found by Achucarro et al. in 2013 by using only Planck data. Furthermore, the joint data analysis shows that the oscillation frequency of the feature gets better constrained, and the amplitude marginally deviates from zero, unlike what was observed using only Planck data. Besides the parameter estimation, we also discuss the Bayesian evidence. The addition of WiggleZ data mildly enhances the significance of the best mode found in the Planck data. © 2015 American Physical Society.
119180316
Disentanglement of two harmonic oscillators in relativistic motion
We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time ('sudden death'). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.
119270462
Stress-energy tensor correlators of a quantum field in Euclidean R N and AdS N spaces via the generalized zeta-function method
In this paper we calculate the vacuum expectation values of the stress-energy bitensor of a massive quantum scalar field with general coupling to $N$-dimensional Euclidean spaces and hyperbolic spaces which are Euclidean sections of the anti-de Sitter spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [B. L. Hu and E. Verdaguer, Living Rev. Relativity 11, 3 (2008).][B. L. Hu and E. Verdaguer, Classical Quantum Gravity 20, R1 (2003).] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because these spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta function [J. S. Dowker and R. Critchley, Phys. Rev. D 13, 224 (1976); J. S. DowkerR. Critchley, Phys. Rev. D 13, 3224 (1976).][S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).]. Upon taking the second functional variation of the generalized zeta function introduced in [N. G. Phillips and B. L. Hu, Phys. Rev. D 55, 6123 (1997).] we obtain the correlators of the stress tensor for these two classes of spacetimes. Both the short and the large geodesic distance limits of the correlators are presented for dimensions up to 11. We mention current research problems in early universe cosmology, black hole physics and gravity-fluid duality where these results can be usefully applied to.
118029650
Future CMB integrated-Sachs-Wolfe-lensing bispectrum constraints on modified gravity in the parametrized post-Friedmann formalism
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross-correlation between ISW-Lensing bispectrum and power spectrum can be safely neglected when performing the joint analysis. For simplicity, we only investigate the likelihood of one parameter ({$B_0$}) and fix all other cosmological parameters to their best-fit values in WMAP7yr results.
15446534
Critical Dynamics in the Early Universe ∗
Methods and concepts for the study of phase transitions mediated by a time-dependent order-parameter field in curved spacetimes are discussed. A practical example is the derivation of an effective (quasi)potential for the description of ‘slow-roll’ inflation in the early universe. We first summarize our early results on viewing the symmetry behavior of constant background fields in curved but static spacetimes as finite size effect, and the use of derivative expansions for constructing effective actions for slowly-varying background fields. We then introduce the notion of dynamical finite size effect to explain how an exponential expansion of the scale factor imparts a finite size to the system and how the symmetry behavior in de Sitter space can be understood qualitatively in this light. We reason why the exponential inflation can be described equivalently by a scale transformation, thus rendering this special class of dynamics as effectively static. Finally we show how, in this view, one can treat the class of ‘slow-roll’ inflation as a dynamic perturbation off the effectively static class of exponential inflation and understand it as a dynamical critical phenomenon