121391144
Universal metric properties of an approximate Poincaré map for Duffing's equation with negative stiffness
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.
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.
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.
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
119413415
Influence Action and Decoherence of Hydrodynamic Modes
We derive an influence action for the heat diffusion equation and from its spectral dependence show that long wavelength hydrodynamic modes are more readily decohered. The result is independent of the details of the microscopic dynamics, and follows from general principles alone.
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.
116999371
New View on Quantum Gravity and the Origin of the Universe
This essay is based on a physics lecture given at the Hong Kong University of Science and Technology on May 24, 2006, Hong Kong. It has 5 sections and one page of references and suggested reading. The section titles are: 1. Origin of the Universe and Quantum Gravity 2. Two major paradigms in Physics and Two directions of Research in Cosmology 3. The Mescoscopic Structures of Spacetime and Stochastic Gravity 4. One Vein of the Hydro View: Spacetime as Condensate? 5. Implications for the Origin of the Universe and other issues.
34920552
Nonequilibrium dynamics of a thermal plasma in a gravitational field
We introduce functional methods to study the non-equilibrium dynamics of a quantum massless scalar field at finite temperature in a gravitational field. We calculate the close time path (CTP) effective action and, using its formal equivalence with the influence functional, derive the noise and dissipation kernels of the quantum open system in terms of quantities in thermodynamical equilibrium. Using this fact, we formally prove the existence of a fluctuation-dissipation relation (FDR) at all temperatures between the quantum fluctuations of the plasma in thermal equilibrium and the energy dissipated by the external gravitational field. What is new is the identification of a stochastic source (noise) term arising from the quantum and thermal fluctuations in the plasma field, and the derivation of a Langevin-type equation which describes the non-equilibrium dynamics of the gravitational field influenced by the plasma. The back reaction of the plasma on the gravitational field is embodied in the FDR. From the CTP effective action the contribution of the quantum scalar field to the thermal graviton polarization tensor can also be derived and it is shown to agree with other techniques, most notably, linear response theory (LRT). We show the connection between the LRT, which is applicable for near-equilibriummore » conditions and the functional methods used in this work which are useful for fully nonequilibrium conditions. {copyright} {ital 1998} {ital The American Physical Society}« less
118584779
Reconstruction of the primordial power spectra with Planck and BICEP2 data
By using the cubic spline interpolation method, we reconstruct the shape of the primordial scalar and tensor power spectra from the recently released Planck temperature and BICEP2 polarization cosmic microwave background data. We find that the vanishing scalar index running (dn(s)= d ln k) model is strongly disfavored at more than 3 sigma confidence level on the k = 0.0002 Mpc(-1) scale. Furthermore, the power-law parametrization gives a blue-tilt tensor spectrum, no matter using only the first five bandpowers n(t) = 1.20(-0.64)(+0.56) (95% C.L.) or the full nine bandpowers nt 1.24(-0.58)(+0.51) (95% C.L.) of BICEP2 data sets. Unlike the large tensor-to-scalar ratio value (r similar to 0.20) under the scale-invariant tensor spectrum assumption, our interpolation approach gives r(0.002) < 0.060 (95% C.L.) by using the first five bandpowers of BICEP2 data. After comparing the results with/without BICEP2 data, we find that Planck temperature with small tensor amplitude signals and BICEP2 polarization data with large tensor amplitude signals dominate the tensor spectrum reconstruction on the large and small scales, respectively. Hence, the resulting blue tensor tilt actually reflects the tension between Planck and BICEP2 data.