A new numerical approach to Anderson (de)localization

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with small disorder allows states that are dynamically delocalized with positive probability. This approach is based on a recent result by Abakumov-Liaw-Poltoratski which is rooted in the study of spectral behavior under rank-one perturbations, and states that every non-zero vector is almost surely cyclic for the singular part of the operator. The numerical work presented is rather simplistic compared to other numerical approaches in the field. Further, this method eliminates effects due to boundary conditions. While we carried out the numerical experiment almost exclusively in the case of the two dimensional discrete random Schroedinger operator, we include the setup for the general class of Anderson models called Anderson-type Hamiltonians. We track the location of the energy when a wave packet initially located at the origin is evolved according to the discrete random Schroedinger operator. This method does not provide new insight on the energy regimes for which diffusion occurs.Comment: 15 pages, 8 figure

The Spectral Structure of the Electronic Black Box Hamiltonian

We give results on the absence of singular continuous spectrum of the one-particle Hamiltonian underlying the electronic black box model.Comment: 11 page

Einfluss gewisser Faktoren auf die Bestimmung des biochemischen Sauerstoffbedarfs (BSB) der Zellstoffabwasser

U prethodnim radovima praćena je promjena BPK u inkubacionom periodu od O do 5 dana u otpadnim vodama proizvodnje celuloze. Uočene poteškoće kod određivanja se sistematizuju i prati se njihov uticaj na rezultat testa. Ispitivanjima su utvrđeni optimalni uslovi za dobijanje reproduktivnih rezultata.In den vorläufigen Arbeiten hat man die Änderung von BSB während der Inkubationsperiode von 0-5 Tagen bei den Zellstoffabwässern gefolgt. Die bei der Bestimmung bemerkten Schwierigkeiten wurden systematisiert und deren Einfluss auf die Testergebnisse wurde gefolgt. Durch Untersuchungen wurden die optimalen Bedingungen bestimmt die zur Erreichung von reproduzierbaren Ergebnissen führen

Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases

We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We establish that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature $T$, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics--they need not be in a state of thermal equilibrium. The temperature $T$ to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy $k_{\mathrm B}T$ is equal to an appropriately defined average of the scatterers' kinetic energy. In the equilibrated state, particle motion is diffusive

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared

The application of hydrogen-palladium electrode for potentiometric acid-base determinations in tetrahydrofuran

The application of the hydrogen-palladium electrode (H2/Pd) as the indicator electrode for the determination of relative acidity scale (Es, mV) of tetrahydrofuran (THF) and the potentiometric titrations of acids in this solvent was investigated. The relative acidity scale tetrahydrofuran was determined from the difference half-neutralization potentials of perchloric acid and tetrabutylammonium hydroxide (TBAH), which were measured by using both H2/Pd-SCE and glass-SCE electrode pairs. The experimentally obtained value of Es scale THF with a H2/Pd-SCE electrode pair was 1155 mV, and those obtained with glass-SCE electrode pair 880 mV. By using a H2/Pd indicator electrode, the individual acids (benzoic acid, palmitic acid, maleic acid, acetyl acetone, α-naphthol) and two component acid mixtures (benzoic acid + α-naphthol, palmitic acid + α-naphthol, maleic acid + α-naphthol and maleic acid + ftalic acid) were titrated with a standard solution of TBAH. In addition, sodium methylate and potassium hydroxide proved to be very suitable titrating agents for titrating of the individual acids and the acids in mixtures, respectively. The relative error of the determination of acids in mixture was less than 3%. The results are in agreement with those obtained by a conventional glass electrode. The advantages of H2/Pd electrode over a glass electrode in potentiometric acid-base determinations in tetrahydrofuran lie in the following: this electrode gives wider relative acidity scale THF, higher the potential jumps at the titration end-point and relatively fast response time; furthermore, it is very durable, simple to prepare and can be used in the titrations of small volumes. [Projekat Ministarstva nauke Republike Srbije, br.172051

Nonequilibrium Steady States and Fano-Kondo Resonances in an AB Ring with a Quantum Dot

Electron transport through a strongly correlated quantum dot (QD) embedded in an Aharonov-Bohm (AB) ring is investigated with the aid of the finite-U slave-boson mean-field (SBMF) approach extended to nonequilibrium regime. A nonequilibrium steady state (NESS) of the mean-field Hamiltonian is constructed with the aid of the C*-algebraic approach for studying infinitely extended systems. In the linear response regime, the Fano-Kondo resonances and AB oscillations of the conductance obtained from the SBMF approach are in good agreement with those from the numerical renormalization group technique (NRG) by Hofstetter et al. by using twice larger Coulomb interaction. At zero temperature and finite bias voltage, the resonance peaks of the differential conductance tend to split into two. At low bias voltage, the split of the asymmetric resonance can be observed as an increase of the conductance plateau. We also found that the differential conductance has zero-bias maximum or minimum depending on the background transmission via direct tunneling between the electrodes.Comment: 24 pages,17 figure

The Diffusion of the Magnetization Profile in the XX-model

By the $C^*$-algebraic method, we investigate the magnetization profile in the intermediate time of diffusion. We observe a transition from monotone profile to non-monotone profile. This transition is purely thermal.Comment: Accepted for publication in Phys. Rev.

Simplicity of eigenvalues in Anderson-type models

We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schr\"odinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not restricted to the localization regime. We establish general criteria for the simplicity of eigenvalues which can be interpreted as separately excluding the absence of local and global symmetries, respectively. The criteria are applied to Anderson models with matrix-valued potential as well as with single-site potentials supported on a finite box.Comment: 20 page

Out of equilibrium correlations in the XY chain

We study the transversal XY spin-spin correlations in the non-equilibrium steady state constructed in \cite{AP03} and prove their spatial exponential decay close to equilibrium