Rate of equilibration of a one-dimensional Wigner crystal

We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.Comment: Prepared for the proceedings of the International School and Workshop on Electronic Crystals, ECRYS-201

Accelerated Algorithm of Least-Sguares Approximation of Signals by Exponentials for Wideband Frequency-Domain Reflectometry

In the paper the possibility of acceleration of procedure of best least-squares approximation of signals by exponentials was considered. For this purpose the analytical expressions for components of gradient vector and Hessian matrix of the objective function were obtained. The algorithms of quasisolution searching were constructed. Method of conjugate gradient and modified Newton method were used. The obtained algorithms were compared with modification of Nelder-Mead method which used information about only values of objective function. The comparison of the novel method and Prony’s method and matrix pencil method was held.В статье рассмотрена возможность ускорения аппроксимации сигналов экспонентами методом наименьших квадратов. Для этого были получены аналитические выражения для компонент вектора градиента и матрицы Гессе оптимизируемой функции. Был сконструирован алгоритм поиска квазирешения. Использовались метод сопряженных градиентов и модифицированный метод Ньютона. Полученные алгоритмы были сравнены с модификацией метода Нелдера-Мида, который использует информацию только о значениях оптимизируемой функции. Было проведено сравнение нового метода с методом Прони и методом пучка матриц.У статті розглянуто можливість прискорення апроксимації сигналів експонентами методом найменших квадратів. Для цього було отримано аналітичні вирази для компонент вектора градієнта та матриці Гессе функції, що оптимізується. Було сконструйовано алгоритм пошуку квазірозв’язку. Використано метод спряжених градієнтів та модифікований метод Ньютона. Отримані алгоритми були порівняні з модифікацією методу Нелдера-Міда, який використовує інформацію тільки про значення функції, що оптимізується. Було проведене порівняння нового методу з методом Проні та методом пучка матриць

Thermopower of a single electron transistor in the regime of strong inelastic cotunneling

We study Coulomb blockade oscillations of thermoelectric coefficients of a single electron transistor based on a quantum dot strongly coupled to one of the leads by a quantum point contact. At temperatures below the charging energy E_C the transport of electrons is dominated by strong inelastic cotunneling. In this regime we find analytic expressions for the thermopower as a function of temperature T and the reflection amplitude $r$ in the contact. In the case when the electron spins are polarized by a strong external magnetic field, the thermopower shows sinusoidal oscillations as a function of the gate voltage with the amplitude of the order of $e^{-1}|r|\frac{T}{E_C}$. We obtain qualitatively different results in the absence of the magnetic field. At temperatures between $E_C$ and $E_C|r|^2$ the thermopower oscillations are sinusoidal with the amplitude of order $e^{-1}|r|^2 \ln \frac{E_C}{T}$. On the other hand, at $T\ll E_C|r|^2$ we find non-sinusoidal oscillations of the thermopower with the amplitude $\sim e^{-1} |r| \sqrt{T/E_C} \ln(E_C/T)$.Comment: 14 pages, 3 figure

Coulomb blockade in metallic grains at large conductance

We study Coulomb blockade effects in the thermodynamic quantities of a weakly disordered metallic grain coupled to a metallic lead by a tunneling contact with a large conductance $g_T$. We consider the case of broken time-reversal symmetry and obtain expressions for both the {\em ensemble averaged} amplitude of the Coulomb blockade oscillations of the thermodynamic potential and the correlator of its {\em mesoscopic fluctuations} for a finite mean level spacing $\delta$ in the grain. We develop a novel method which allows for an exact evaluation of the functional integral arising from disorder averaging. The results and the method are applicable in the temperature range $\delta \ll T \ll E_C$.Comment: 18 pages, 3 figures (revised version

Quantum Disorder and Quantum Chaos in Andreev Billiards

We investigate the crossover from the semiclassical to the quantum description of electron energy states in a chaotic metal grain connected to a superconductor. We consider the influence of scattering off point impurities (quantum disorder) and of quantum diffraction (quantum chaos) on the electron density of states. We show that both the quantum disorder and the quantum chaos open a gap near the Fermi energy. The size of the gap is determined by the mean free time in disordered systems and by the Ehrenfest time in clean chaotic systems. Particularly, if both times become infinitely large, the density of states is gapless, and if either of these times becomes shorter than the electron escape time, the density of states is described by random matrix theory. Using the Usadel equation, we also study the density of states in a grain connected to a superconductor by a diffusive contact.Comment: 20 pages, 10 figure

DC and AC Josephson Effect in a Superconductor-Luttinger Liquid-Superconductor System

We calculate both the DC and the AC Josephson current through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. We treat the (repulsive) Coulomb interaction in the framework of the one-channel, spin-$1/2$ Luttinger model. The Josephson current is obtained for two geometries of experimental relevance: a quantum wire and a ring. At zero temperature, the critical current is found to decay algebraically with increasing distance $d$ between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperatures $T$, lower than the superconducting transition temperature $T_c$, there is a crossover from algebraic to exponential decay of the critical current as a function of $d$, at a distance of the order of $\hbar v_F/k_B T$. Moreover, the dependence of critical current on temperature shows non-monotonic behavior. If the Luttinger liquid is confined to a ring of circumference $L$, coupled capacitively to a gate voltage and threaded by a magnetic flux, the Josephson current shows remarkable parity effects under the variation of these parameters. For some values of the gate voltage and applied flux, the ring acts as a $\pi$-junction. These features are robust against thermal fluctuations up to temperatures on the order of $\hbar v_F/k_B L$. For the wire-geometry, we have also studied the AC-Josephson effect. The amplitude and the phase of the time-dependent Josephson current are affected by electron-electron interactions. Specifically, the amplitude shows pronounced oscillations as a function of the bias voltage due to the difference between the velocities of spin and charge excitations in the Luttinger liquid. Therefore, the AC Josephson effect can be used as a tool for the observation o

Magnetic Field Effects on Neutron Diffraction in the Antiferromagnetic Phase of UPt3UPt_3

We discuss possible magnetic structures in UPt$_3$ based on our analysis of elastic neutron-scattering experiments in high magnetic fields at temperatures $T<T_N$. The existing experimental data can be explained by a single-{\bf q} antiferromagnetic structure with three independent domains. For modest in-plane spin-orbit interactions, the Zeeman coupling between the antiferromagnetic order parameter and the magnetic field induces a rotation of the magnetic moments, but not an adjustment of the propagation vector of the magnetic order. A triple-{\bf q} magnetic structure is also consistent with neutron experiments, but in general leads to a non-uniform magnetization in the crystal. New experiments could decide between these structures.Comment: 5 figures included in the tex

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters