Analysis of the second order exchange self energy of a dense electron gas

We investigate the evaluation of the six-fold integral representation for the second order exchange contribution to the self energy of a three dimensional electron gas at the Fermi surface.Comment: 6 page

CMB anisotropies in the presence of a stochastic magnetic field

Primordial magnetic fields present since before the epoch of matter-radiation equality have an effect on the anisotropies of the cosmic microwave background. The CMB anisotropies due to scalar perturbations are calculated in the gauge invariant formalism for magnetized adiabatic initial conditions. Furthermore the linear matter power spectrum is calculated. Numerical solutions are complemented by a qualitative analysis.Comment: 26 pages, 21 figures; sections 2 and 4 expanded; matches version published in PR

Time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator

We present a theoretical study of time-dependent quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator within the non-equilibrium Green's function technique. An arbitrary voltage is applied to the tunnel junction and electrons in the leads are considered to be at zero temperature. The transient and the steady state behavior of the system is considered here in order to explore the quantum dynamics of the oscillator as a function of time. The properties of the phonon distribution of the nanomechnical oscillator strongly coupled to the electrons on the dot are investigated using a non-perturbative approach. We consider both the energy transferred from the electrons to the oscillator and the Fano factor as a function of time. We discuss the quantum dynamics of the nanomechanical oscillator in terms of pure and mixed states. We have found a significant difference between a quantum and a classical oscillator. In particular, the energy of a classical oscillator will always be dissipated by the electrons whereas the quantum oscillator remains in an excited state. This will provide useful insight for the design of experiments aimed at studying the quantum behavior of an oscillator.Comment: 24 pages, 10 figure

Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature

We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was previously shown that upon increasing d from 0 to infinity, five different structures of the bilayer Wigner crystal become energetically favored, starting from a hexagonal lattice (phase I, d=0) and ending at a staggered hexagonal lattice (phase V, d -> infinity). In this paper, we derive new series representations of the ground-state energy for all five bilayer structures. The derivation is based on a sequence of transformations for lattice sums of Coulomb two-particle potentials plus the neutralizing background, having their origin in the general theory of Jacobi theta functions. The new series provide convenient starting points for both analytical and numerical progress. Its convergence properties are indeed excellent: Truncation at the fourth term determines in general the energy correctly up to 17 decimal digits. The accurate series representations are used to improve the specification of transition points between the phases and to solve a controversy in previous studies. In particular, it is shown both analytically and numerically that the hexagonal phase I is stable only at d=0, and not in a finite interval of small distances between the plates as was anticipated before. The expansions of the structure energies around second-order transition points can be done analytically, which enables us to show that the critical behavior is of the Ginzburg-Landau type, with a mean-field critical index beta=1/2 for the growth of the order parameters

Analytic invariant charge and the lattice static quark-antiquark potential

A recently developed model for the QCD analytic invariant charge is compared with quenched lattice simulation data on the static quark-antiquark potential. By employing this strong running coupling one is able to obtain the confining quark-antiquark potential in the framework of the one-gluon exchange model. To achieve this objective a technique for evaluating the integrals of a required form is developed. Special attention is paid here to removing the divergences encountered the calculations. All this enables one to examine the asymptotic behavior of the potential at both small and large distances with high accuracy. An explicit expression for the quark-antiquark potential, which interpolates between these asymptotics, and satisfies the concavity condition, is proposed. The derived potential coincides with the perturbative results at small distances, and it is in a good agreement with the lattice data in the nonperturbative physically-relevant region. An estimation of the parameter $\Lambda_{QCD}$ is obtained for the case of pure gluodynamics. It is found to be consistent with all the previous estimations of $\Lambda_{QCD}$ in the framework of approach in hand.Comment: LaTeX2e, 10 pages with 3 EPS figure

Quantum backreaction in evolving FLRW spacetimes

Quantum fluctuations of a nonminimally coupled scalar field in D-dimensional homogeneous and isotropic background are calculated within the operator formalism in curved models with time evolutions of the scale factor that allow smooth transitions between contracting and expanding and between decelerating and accelerating regimes. The coincident propagator is derived and used to compute the one-loop backreaction from the scalar field. The inflationary infrared divergences are absent in Bunch-Davies vacuum when taking into account a preceding cosmological era or spatial curvature which can be either positive or negative. It is found that asymptotically, the backreaction energy density in the minimally coupled case grows logarithmically with the scale factor in quasi-de Sitter space, and in a class of models decays in slow-roll inflation and grows as a power-law during super-inflation. The backreaction increases generically in a contracting phase or in the presence of a negative nonminimal coupling. The effects of the coupling and renormalization scale upon the quantum fluctuations together with the novel features due to nontrivial time evolution and spatial curvature are clarified with exact solutions and numerical examples.Comment: 23 pages, 6 figure

Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer

We have studied the zero-temperature statistics of the charge transfer between the two edges of Quantum Hall liquids of, in general, different filling factors, $\nu_{0,1}=1/(2 m_{0,1}+1)$, with $m_0 \geq m_1\geq 0$, forming Mach-Zehnder interferometer. General expression for the cumulant generating function in the large-time limit is obtained for symmetric interferometer with equal propagation times along the two edges between the contacts and constant bias voltage. The low-voltage limit of the generating function can be interpreted in terms of the regular Poisson process of electron tunneling, while its leading large-voltage asymptotics is proven to coincide with the solution of kinetic equation describing quasiparticle transitions between the $m$ states of the interferometer with different effective flux through it, where $m\equiv 1+m_{0}+m_{1}$. For $m>1$, this dynamics reflects both the fractional charge $e/m$ and the fractional statistical angle $\pi /m$ of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.Comment: 11 two-column pages, 4 figure

Observable Dependent Quasi-Equilibrium in Slow Dynamics

We present examples demonstrating that quasi-equilibrium fluctuation-dissipation behavior at short time differences is not a generic feature of systems with slow non-equilibrium dynamics. We analyze in detail the non-equilibrium fluctuation-dissipation ratio X(t,tw) associated with a defect-pair observable in the Glauber-Ising spin chain. It turns out that $X \neq 1$ throughout the short-time regime and in particular X(tw,tw) = 3/4 for $tw \to \infty$. The analysis is extended to observables detecting defects at a finite distance from each other, where similar violations of quasi-equilibrium behaviour are found. We discuss our results in the context of metastable states, which suggests that a violation of short-time quasi-equilibrium behavior could occur in general glassy systems for appropriately chosen observables.Comment: 17 pages, 5 figures; substantially improved version of cond-mat/040571

Nonlinear screening and ballistic transport in a graphene p-n junction

We study the charge density distribution, the electric field profile, and the resistance of an electrostatically created lateral p-n junction in graphene. We show that the electric field at the interface of the electron and hole regions is strongly enhanced due to limited screening capacity of Dirac quasiparticles. Accordingly, the junction resistance is lower than estimated in previous literature.Comment: 4 pages, 2 figures. (v1) Original version (v2) Introduction largely rewritten, minor typos fixed throughou

Multiphoton resonance in a three-level system with nearly degenerate excited states

An analytic study is presented of the efficient multiphoton excitation and strong harmonic generation in three-level systems specified by a pair of nearly degenerate, strongly dipole-coupled excited states. Such systems are physically formed by the three lowest states in, e.g., the hydrogen atom or evenly charged homonuclear diatomic molecular ions under reasonably chosen laser intensities. As a detailed analytic result, we found that the laser pulse of photon energy $2{.}05\text{eV}$, duration $0{.}23\text{ps}$ and intensity $5\cdot 10^{13}\,\frac{\text{W}}{\text{cm}^2}$ is able to produce complete inversion of the initial population in the hydrogen atom through the 5-photon excitation. At the same photon energy, the pulse of duration $0{.}41\text{ps}$ and intensity $3{.}44\cdot 10^{14}\,\frac{\text{W}}{\text{cm}^2}$ was found to produce the same effect in the molecular ion but through the 9-photon excitation. We show that the accompanying scattering of light has very rich spectrum differing substantially from that of the two-level system.Comment: 9 pages, 5 figures,submitted to Phys. Rev. A, comments welcom