Electron self-energy near a nematic quantum critical point

We consider an isotropic Fermi liquid in two dimensions near the n=2 Pomeranchuk instability in the charge channel. The order parameter is a quadrupolar stress tensor with two polarizations, longitudinal and transverse to the quadrupolar momentum tensor. Longitudinal and transverse bosonic modes are characterized by dynamical exponents z_parallel=3 and z_perp=2, respectively. Previous studies have found that such a system exhibits multiscale quantum criticality with two different energy scales omega ~ xi^{-z_{parallel,perp}}, where xi is the correlation length. We study the impact of the multiple energy scales on the electron Green function. The interaction with the critical z_parallel =3 mode is known to give rise to a local self-energy that develops a non-Fermi liquid form, Sigma(omega) ~ omega^{2/3} for frequencies larger than the energy scale omega ~ xi^{-3}. We find that the exchange of transverse z_perp=2 fluctuations leads to a logarithmically singular renormalizations of the quasiparticle residue Z and the vertex Gamma. We derive and solve renormalization group equations for the flow of Z and Gamma and show that the system develops an anomalous dimension at the nematic quantum-critical point (QCP). As a result, the spectral function at a fixed omega and varying k has a non-Lorentzian form. Away from the QCP, we find that the flow of Z is cut at the energy scale omega_{FL} ~ xi^{-1}, associated with the z=1 dynamics of electrons. The z_perp=2 energy scale, omega ~ xi^{-2}, affects the flow of Z only if one includes into the theory self-interaction of transverse fluctuations.Comment: 14 pages, 10 figures; (v2) minor changes, published versio

An optimal stopping problem in a diffusion-type model with delay

We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit condition. The problem can be interpreted as pricing special perpetual average American put options in a diffusion-type model with delay.Optimal stopping, stochastic delay differential equation, diffusion process, sufficient statistic, free-boundary problem, smooth fit, Girsanov’s theorem, Ito’s formula

Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas

We present Quantum Monte Carlo calculations with up to N=576000 interacting bosons in a quasi two-dimensional trap geometry closely related to recent experiments with atomic gases. The density profile of the gas and the non-classical moment of inertia yield intrinsic signatures for the Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body density matrix, we compute the condensate fraction, which is quite large for small systems. It decreases slowly with increasing system sizes, vanishing in the thermodynamic limit. We interpret our data in the framework of the local-density approximation, and point out the relevance of our results for the analysis of experiments.Comment: 4 pages, 4 figure

Continuous quantum measurement with independent detector cross-correlations

We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot quantum measurement, the measurement is maximally efficient if the detectors are twins. For weak continuous measurement, cross-correlations allow a violation of the Korotkov-Averin bound for the detector's signal-to-noise ratio. A vanishing noise background provides a nontrivial test of ideal independent quantum detectors. We further investigate the correlations of non-commuting operators, and consider possible deviations from the independent detector model for mesoscopic conductors coupled by the screened Coulomb interaction.Comment: 4 pages, 2 figure