Uniform version of Weyl-von Neumann theorem

We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable simplifications in uniform K-homology theory, namely it shows that one can represent all the uniform K-homology classes on a fixed Hilbert space with a fixed *-representation of C_0(X), for a large class of spaces X

Acoustic Wave Based MEMS Devices, Development and Applications

Acoustic waves based MEMS devices offer a promising technology platform for a wide range of applications due to their high sensitivity and the capability to operate wirelessly. These devices utilize acoustic waves propagating through or on the surface of a piezoelectric material. An acoustic wave device typically consists of two layers, metal transducers on top of piezoelectric substrate or thin films. The piezoelectric material has inherent capabilities of generating acoustic waves related to the input electrical sinusoidal signals placed on the transducers. Using this characteristic, different transducer designs can be placed on top of the piezoelectric material to create acoustic wave based filters, resonators or sensors. Historically, acoustic wave devices have been and are still widely used in telecommunications industry, primarily in mobile cell phones and base stations. Surface Acoustic Wave (SAW) devices are capable of performing powerful signal processing and have been successfully functioning as filters, resonators and duplexers for the past 60 years. Although SAW devices are technological mature and have served the telecommunication industry for several decades, these devices are typically fabricated on piezoelectric substrates and are packaged as discrete components. Considering the wide flexibility and capabilities of the SAW device to form filters, resonators there has been motivation to integrate such devices on silicon substrates as demonstrated in (Nordin et al., 2007; M. J. Vellekoop et al., 1987; Visser et al., 1989). One such example is illustrated in (Nordin et al., 2007) where a CMOS SAW resonator was fabricated using 0.6 m AMIs CMOS technology process with additional MEMS post-processing. The traditional SAW structure of having the piezoelectric at the bottom was inverted. Instead, the IDTs were cleverly manufactured using standard complementary-metal-oxide-semiconductor (CMOS) process and the piezoelectric layer was placed on the top. Active circuitry can be placed adjacent to the CMOS resonator and can be connected using the integrated metal layers. A SAW device can also be designed to have a long propagation path between the input and output transducer. The propagating acoustic waves will then be very sensitive to ambient changes, allowing the device to act as a sensor. Any variations to the characteristics of the propagation path affect the velocity or amplitude of the wave. Important application for acoustic wave devices as sensors include torque and tire pressure sensors (Cullen et al., 1980; Cullen et al., 1975; Pohl et al., 1997), gas sensors (Levit et al., 2002; Nakamoto et al., 1996; Staples, 1999; Wohltjen et al., 1979), biosensors for medical applications (Andle et al., 1995; Ballantine et al., 1996; Cavic et al., 1999; Janshoff et al., 2000), and industrial and commercial applications (vapor, humidity, temperature, and mass sensors) (Bowers et al., 1991; Cheeke et al., 1996; Smith, 2001; N. J. Vellekoop et al., 1999; Vetelino et al., 1996; Weld et al., 1999). In recent years, the interest in the development of highly sensitive acoustic wave devices as biosensor platforms has grown. For biological applications the acoustic wave device is integrated in a microfluidic system and the sensing area is coated with a biospecific layer. When a bioanalyte interacts with this sensing layer, physical, chemical, and/or biochemical changes are produced. Typically, mass and viscosity changes of the biospecific layer can be detected by analyzing changes in the acoustic wave properties such as velocity, attenuation and resonant frequency of the sensor. An important advantage of the acoustic wave biosensors is simple electronic readout that characterizes these sensors. The measurement of the resonant frequency or time delay can be performed with high degree of precision using conventional electronics. This chapter is focused on two important applications of the acoustic-wave based MEMS devices; (1) biosensors and (2) telecommunications. For biological applications these devices are integrated in a microfluidic system and the sensing area is coated with a biospecific layer. When a bioanalyte interacts with this sensing layer, physical, chemical, and/or biochemical changes are produced. Typically, mass and viscosity changes of the biospecific layer can be detected by analyzing changes in the acoustic wave properties such as velocity, attenuation and resonant frequency of the sensor. An important advantage of the acoustic wave biosensors is simple electronic readout that characterizes these sensors. The measurement of the resonant frequency and time delay can be performed with high degree of precision using conventional electronics. Only few types of acoustic wave devices could be integrated in microfluidic systems without significant degradation of the quality factor. The acoustic wave based MEMS devices reported in the literature as biosensors are film bulk acoustic wave resonators (FBAR) and surface acoustic waves (SAW) resonators and SAW delay lines. Different approaches to the realization of FBARs and SAW resonators and SAW delay lines used for various biochemical applications are presented. Next, acoustic wave MEMS devices used in telecommunications applications are presented. Telecommunication devices have different requirements compared to sensors, where acoustic wave devices operating as a filter or resonator are expected to operate at high frequencies (GHz), have high quality factors and low insertion losses. Traditionally, SAW devices have been widely used in the telecommunications industry, however with advancement in lithographic techniques, FBARs are rapidly gaining popularity. FBARs have the advantage of meeting the stringent requirement of telecommunication industry of having Qs in the 10,000 range and silicon compatibility

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

Quantum Free Yang-Mills on the Plane

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the $N=\infty$ limit of U(N) quantum Yang-Mills theory on the plane.Comment: 24 pages, tikz figure

Depression and breast cancer; postoperative short-term implications

Introduction. Pre and postoperative psychological status is an important aspect in patients diagnosed with breast cancer, having a great impact on their quality of life. Considering the high incidence, mortality rate, and the added effect on self-image, breast cancer is considered a major stressor for women worldwide, almost 50% of these experiencing psychological distress. Methods. Our study retrospectively analysed the relationship between preoperative diagnosed depression and the number of medical care days, on patients diagnosed with breast cancer and admitted for surgical treatment in Colțea Clinical Hospital between 2017 and 2018. Results. We had 62 patients scheduled for breast cancer surgery, who had been preoperatively evaluated using psychological tests. Of those patients, 18 had scores indicating significant symptoms of depression (moderate or severe symptoms, HDSR \u3e17). Patients with high HDSR scores needed an 18.4% longer hospitalization than patients without symptoms of depression. They also had 35.4% more ambulatory visits in the month following discharge, and a higher incidence of postoperative complications. Conclusions. There seem to be both physiological and somatic determinants responsible for the need of prolonged medical care, but the mechanisms responsible for these effects remain unclear. Identifying high-risk patients could not only lower the postoperative morbidity, but also increase the therapeutic outcomes

Multiplication law and S transform for non-hermitian random matrices

We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define the corresponding non-hermitian S transform being a natural generalization of the Voiculescu S transform. In addition we extend the classical hermitian S transform approach to deal with the situation when the random matrix ensemble factors have vanishing mean including the case when both of them are centered. We use planar diagrammatic techniques to derive these results.Comment: 25 pages + 11 figure

Complete diagrammatics of the single ring theorem

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio

Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect

For models of non-interacting fermions moving within sites arranged on a surface in three dimensional space, there can be obstructions to finding localized Wannier functions. We show that such obstructions are $K$-theoretic obstructions to approximating almost commuting, complex-valued matrices by commuting matrices, and we demonstrate numerically the presence of this obstruction for a lattice model of the quantum Hall effect in a spherical geometry. The numerical calculation of the obstruction is straightforward, and does not require translational invariance or introducing a flux torus. We further show that there is a $Z_2$ index obstruction to approximating almost commuting self-dual matrices by exactly commuting self-dual matrices, and present additional conjectures regarding the approximation of almost commuting real and self-dual matrices by exactly commuting real and self-dual matrices. The motivation for considering this problem is the case of physical systems with additional antiunitary symmetries such as time reversal or particle-hole conjugation. Finally, in the case of the sphere--mathematically speaking three almost commuting Hermitians whose sum of square is near the identity--we give the first quantitative result showing this index is the only obstruction to finding commuting approximations. We review the known non-quantitative results for the torus.Comment: 35 pages, 2 figure

Multiplying unitary random matrices - universality and spectral properties

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $\theta=\pi$ for a specific critical evolution time $t_c$.Comment: 12 pages, 2 figure

Random matrix techniques in quantum information theory

The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review, combined with more detailed examples -- coming from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels