123110822
Corrections to scaling for period doubling
We have studied a multiple scaling which describes corrections to scaling. For the period doubling in one-dimensional dissipative maps, two-dimensional areapreserving maps, and four-dimensional symplectic maps, the multiple scaling is seen to be well-obeyed, and new scaling factors have been found. The multiple scaling is also seen to be a very powerful tool for searching for scaling behavior.
209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
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.
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.
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.
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.
1421646
Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
A method is given to compute the noise kernel, defined as the symmetrized connected 2-point function of the stress tensor, for the conformally invariant scalar field in the Hartle-Hawking state in Schwarzschild spacetime. We consider the two points to be separated in a timelike or a spacelike direction and use a Gaussian approximation of the same type as that used by Page to compute an approximate form of the stress tensor for this field in Schwarzschild spacetime. Several components of the noise kernel have been explicitly computed and the expression for one of them is displayed.
35739592
Self-force on extreme mass ratio inspirals via curved spacetime effective field theory
In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the self-force on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object ${r}_{m}$ and the radius of curvature of the background spacetime $\mathcal{R}$ such that $\ensuremath{\epsilon}\ensuremath{\equiv}{r}_{m}/\mathcal{R}\ensuremath{\ll}1$, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. The equation of motion of an effective relativistic point particle coupled to the gravitational waves generated by its motion in a curved background spacetime can be derived without making a slow motion or weak field approximation, as was assumed in earlier EFT treatment of post-Newtonian binaries. Ultraviolet divergences are regularized using Hadamard's partie finie to isolate the nonlocal finite part from the quasilocal divergent part. The latter is constructed from a momentum space representation for the graviton retarded propagator and is evaluated using dimensional regularization in which only logarithmic divergences are relevant for renormalizing the parameters of the theory. As a first important application of this framework we explicitly derive the first-order self-force given by Mino, Sasaki, Tanaka, Quinn, and Wald. Going beyond the point particle approximation, to account for the finite size of the object, we demonstrate that for extreme mass ratio inspirals the motion of a compact object is affected by tidally induced moments at $O({\ensuremath{\epsilon}}^{4})$, in the form of an effacement principle. The relatively large radius-to-mass ratio of a white dwarf star allows for these effects to be enhanced until the white dwarf becomes tidally disrupted, a potentially $O({\ensuremath{\epsilon}}^{2})$ process, or plunges into the supermassive black hole. This work provides a new foundation for further exploration of higher order self-force corrections, gravitational radiation, and spinning compact objects.
123204005
Dissipation in Quantum Fields and Semiclassical Gravity
We discuss the theoretical and physical meaning of dissipation of background fields due to particle creation and statistical effects in interacting quantum field theories and in semiclassical gravitational theories. We indicate the possible existence of a fluctuation-dissipation relation for non-equilibrium quantum fields as occuring in cosmological particle creation and backreaction processes. We also conjecture that all effective theories, including quantum gravity, could manifest dissipative behavior.
118519926
Nonequilibrium dynamics of charged particles in a quantized electromagnetic field: causal, stable and self-consistent dynamics from 1/c expansion
We derive a set of stochastic equations of motion for a system of ordinary quantum-mechanical, spinless charged particles in a second-quantized electromagnetic field based on a consistent application of a dimensionful 1/c expansion, which is analogous to the post-Newtonian expansion in gravity. All relativistic corrections up to order 1/c3 are found, including electrostatic interactions (Coulomb), magnetostatic backreaction (Biot–Savart), dissipative backreaction (Abraham–Lorentz) and quantum-field fluctuations at zero and finite temperatures. With self-consistent backreaction of the EM field included, we show that this approach yields causal and runaway-free equations of motion, provides new insights into charged-particle backreaction and naturally leads to equations consistent with the (classical) Darwin Hamiltonian, and has quantum operator ordering consistent with the Breit Hamiltonian. To order 1/c3 the approach leads to a nonstandard mass renormalization which is associated with magnetostatic self-interactions, and no cutoff is required to prevent runaways. Our results also show that the pathologies of the standard Abraham–Lorentz equations can be seen as a consequence of applying an inconsistent (i.e. incomplete, mixed-order) expansion in 1/c, if, from the start, the analysis is viewed as generating an effective theory with all relativistic corrections considered perturbatively. Finally, we show that the 1/c expansion within a Hamiltonian framework yields well-behaved noise and dissipation, in addition to the multiple-particle interactions.