Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Full Counting Statistics of Superconductor--Normal-Metal Heterostructures

The article develops a powerful theoretical tool to obtain the full counting statistics. By a slight extension of the standard Keldysh method we can access immediately all correlation functions of the current operator. Embedded in a quantum generalization of the circuit theory of electronic transport, we are able to study the full counting statistics of a large class of two-terminal contacts and multi-terminal structures, containing superconductors and normal metals as elements. The practical use of the method is demonstrated in many examples.Comment: 35 pages, contribution to "Quantum Noise", ed. by Yu.V. Nazarov and Ya.M. Blanter, minor changes in text, references adde

Keldysh technique and non-linear sigma-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear sigma-model for disordered metals and superconductors. We discuss such topics as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equation, etc. The sections devoted to disordered superconductors include Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a substantial extension of arXiv:cond-mat/0412296.)Comment: Review: 103 pages, 19 figure

Locking electron spins into magnetic resonance by electron-nuclear feedback

The main obstacle to coherent control of two-level quantum systems is their coupling to an uncontrolled environment. For electron spins in III-V quantum dots, the random environment is mostly given by the nuclear spins in the quantum dot host material; they collectively act on the electron spin through the hyperfine interaction, much like a random magnetic field. Here we show that the same hyperfine interaction can be harnessed such that partial control of the normally uncontrolled environment becomes possible. In particular, we observe that the electron spin resonance frequency remains locked to the frequency of an applied microwave magnetic field, even when the external magnetic field or the excitation frequency are changed. The nuclear field thereby adjusts itself such that the electron spin resonance condition remains satisfied. General theoretical arguments indicate that this spin resonance locking is accompanied by a significant reduction of the randomness in the nuclear field.Comment: 6 pages, 5 figures, 4 pages supplementary materia

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388

Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV

Inclusive transverse momentum spectra of primary charged particles in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV have been measured by the ALICE Collaboration at the LHC. The data are presented for central and peripheral collisions, corresponding to 0-5% and 70-80% of the hadronic Pb-Pb cross section. The measured charged particle spectra in $|\eta|<0.8$ and $0.3 < p_T < 20$ GeV/$c$ are compared to the expectation in pp collisions at the same $\sqrt{s_{\rm NN}}$, scaled by the number of underlying nucleon-nucleon collisions. The comparison is expressed in terms of the nuclear modification factor $R_{\rm AA}$. The result indicates only weak medium effects ($R_{\rm AA} \approx$ 0.7) in peripheral collisions. In central collisions, $R_{\rm AA}$ reaches a minimum of about 0.14 at $p_{\rm T}=6$-7GeV/$c$ and increases significantly at larger $p_{\rm T}$. The measured suppression of high-$p_{\rm T}$ particles is stronger than that observed at lower collision energies, indicating that a very dense medium is formed in central Pb-Pb collisions at the LHC.Comment: 15 pages, 5 captioned figures, 3 tables, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/98