Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

Effect of electron-phonon coupling on transmission through Luttinger liquid hybridized with resonant level

We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level.

Impurity scattering in a Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Impurity scattering in Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

High performance liquid level monitoring system based on polymer fiber Bragg gratings embedded in silicone rubber diaphragm

Liquid-level sensing technologies have attracted great prominence, because such measurements are essential to industrial applications, such as fuel storage, flood warning and in the biochemical industry. Traditional liquid level sensors are based on electromechanical techniques; however they suffer from intrinsic safety concerns in explosive environments. In recent years, given that optical fiber sensors have lots of well-established advantages such as high accuracy, costeffectiveness, compact size, and ease of multiplexing, several optical fiber liquid level sensors have been investigated which are based on different operating principles such as side-polishing the cladding and a portion of core, using a spiral side-emitting optical fiber or using silica fiber gratings. The present work proposes a novel and highly sensitive liquid level sensor making use of polymer optical fiber Bragg gratings (POFBGs). The key elements of the system are a set of POFBGs embedded in silicone rubber diaphragms. This is a new development building on the idea of determining liquid level by measuring the pressure at the bottom of a liquid container, however it has a number of critical advantages. The system features several FBG-based pressure sensors as described above placed at different depths. Any sensor above the surface of the liquid will read the same ambient pressure. Sensors below the surface of the liquid will read pressures that increase linearly with depth. The position of the liquid surface can therefore be approximately identified as lying between the first sensor to read an above-ambient pressure and the next higher sensor. This level of precision would not in general be sufficient for most liquid level monitoring applications; however a much more precise determination of liquid level can be made by linear regression to the pressure readings from the sub-surface sensors. There are numerous advantages to this multi-sensor approach. First, the use of linear regression using multiple sensors is inherently more accurate than using a single pressure reading to estimate depth. Second, common mode temperature induced wavelength shifts in the individual sensors are automatically compensated. Thirdly, temperature induced changes in the sensor pressure sensitivity are also compensated. Fourthly, the approach provides the possibility to detect and compensate for malfunctioning sensors. Finally, the system is immune to changes in the density of the monitored fluid and even to changes in the effective force of gravity, as might be obtained in an aerospace application. The performance of an individual sensor was characterized and displays a sensitivity (54 pm/cm), enhanced by more than a factor of 2 when compared to a sensor head configuration based on a silica FBG published in the literature, resulting from the much lower elastic modulus of POF. Furthermore, the temperature/humidity behavior and measurement resolution were also studied in detail. The proposed configuration also displays a highly linear response, high resolution and good repeatability. The results suggest the new configuration can be a useful tool in many different applications, such as aircraft fuel monitoring, and biochemical and environmental sensing, where accuracy and stability are fundamental. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.