Spectral Statistics in Chaotic Systems with Two Identical Connected Cells

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells introduces an additional classical time scale that is manifest also in the spectral form factor. If the two cells are related by a spatial symmetry, the spectrum shows doublets, reflected in the form factor as a positive peak around the Heisenberg time. We combine a semiclassical analysis with an independent random-matrix approach to the doublet splittings to obtain the form factor on all time (energy) scales. Its only free parameter is the characteristic time of exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho

Optical probes of the quantum vacuum: The photon polarization tensor in external fields

The photon polarization tensor is the central building block of an effective theory description of photon propagation in the quantum vacuum. It accounts for the vacuum fluctuations of the underlying theory, and in the presence of external electromagnetic fields, gives rise to such striking phenomena as vacuum birefringence and dichroism. Standard approximations of the polarization tensor are often restricted to on-the-light-cone dynamics in homogeneous electromagnetic fields, and are limited to certain momentum regimes only. We devise two different strategies to go beyond these limitations: First, we aim at obtaining novel analytical insights into the photon polarization tensor for homogeneous fields, while retaining its full momentum dependence. Second, we employ wordline numerical methods to surpass the constant-field limit.Comment: 13 pages, 4 figures; typo in Eq. (5) corrected (matches journal version

Electromagnetic fields in a 3D cavity and in a waveguide with oscillating walls

We consider classical and quantum electromagnetic fields in a three-dimensional (3D) cavity and in a waveguide with oscillating boundaries of the frequency $\Omega$. The photons created by the parametric resonance are distributed in the wave number space around $\Omega/2$ along the axis of the oscillation. When classical waves propagate along the waveguide in the one direction, we observe the amplification of the original waves and another wave generation in the opposite direction by the oscillation of side walls. This can be understood as the classical counterpart of the photon production. In the case of two opposite walls oscillating with the same frequency but with a phase difference, the interferences are shown to occur due to the phase difference in the photon numbers and in the intensity of the generated waves.Comment: 8 pages revTeX including 1 eps fi

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update

Geometry of spin-field coupling on the worldline

We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the loop-space approach to gauge theory. In particular, we employ the loop (or area) derivative operator on the space of all holonomies which can immediately be applied to the worldline representation of the effective action. This results in a spin factor that associates the information about spin with "zigzag" motion of the fluctuating field. Concentrating on the case of quantum electrodynamics in external fields, we obtain a purely geometric representation of the Pauli term. To one-loop order, we confirm our formalism by rederiving the Heisenberg-Euler effective action. Furthermore, we give closed-form worldline representations for the all-loop order effective action to lowest nontrivial order in a small-N_f expansion.Comment: 18 pages, v2: references added, minor changes, matches PRD versio

An Optical Approach to the Dynamical Casimir Effect

We recently proposed a new approach to analyze the parametric resonance in a vibrating cavity based on the analysis of classical optical paths. This approach is used to examine various models of cavities with moving walls. We prove that our method is useful to extract easily basic physical outcome.Comment: 9 page

Finite quantum dissipation: the challenge of obtaining specific heat

We consider a free particle coupled with finite strength to a bath and investigate the evaluation of its specific heat. A harmonic oscillator bath of Drude type with cutoff frequency omega_D is employed to model an ohmic friction force with dissipation strength gamma. Two scenarios for obtaining specific heat are presented. The first one uses the measurement of the kinetic energy of the free particle while the second one is based on the reduced partition function. Both descriptions yield results which are consistent with the Third Law of thermodynamics. Nevertheless, the two methods produce different results that disagree even in their leading quantum corrections at high temperatures. We also consider the regime where the cutoff frequency is smaller than the friction strength, i.e. omega_D<gamma. There, we encounter puzzling results at low temperatures where the specific heat based on the thermodynamic prescription becomes negative. This anomaly is rooted in an ill-defined density of states of the damped free particle which assumes unphysical negative values when gamma/omega_D>1.Comment: 16 pages, 4 figure

Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization

The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to the quasi 1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.