117090129
Universality in Commensurate-Incommensurate Phase Transitions
To investigate the problem of universality in commensurate-incommensurate phase transitions, we have studied certain generalized Frenkel-Kontorova models with different interparticle and external potentials. Many new and interesting features have been found.
209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
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.
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.
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.
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.
73552208
Quantum entanglement and entropy in particle creation
We investigate the basic theoretical issues in the quantum entanglement of particle pairs created from the vacuum in a time-dependent background field or spacetime. Similar to entropy generation from these processes which depends on the choice of physical variables and how certain information is coarse grained, entanglement dynamics hinges on the choice of measurable quantities and how the two parties are selected as well as the background dynamics of the field or spacetime. We discuss the conditions of separability of quantum states in particle creation processes and point out the differences in how the von Neumann entropy is used as a measure of entropy generation versus for entanglement dynamics. We show by an explicit construction that adoption of a different set of physical variables yields a different entanglement entropy. As an application of these theoretical considerations we show how the particle number and the quantum phase enter the entanglement dynamics in cosmological particle production.
204002791
Phase transitions in the early universe: geometric effects.
37498893
Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion
We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time $t=0$. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green's function over the particle's entire past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode-sum regularization and for any other analytical approximations to self-force calculations.
10803451
Fluctuations of Energy Density and Validity of Semiclassical Gravity
From calculations of the variance, or the fluctuations, and the mean energy densityof a massless scalar field in the Minkowski vacuum as a function of an intrinsicscale defined by the world function between two nearby points (as used in pointseparation regularization), we show that, contrary to prior claims, the ratio ofvariance to its mean squared being of the order unity does not imply a failureof semiclassical gravity. It is more a consequence of the quantum nature of thestate of the matter field than any inadequacy of the theory of spacetime withquantum matter as source.