arXiv subjects

Michael Schreiber

Publications and source records attributed to Michael Schreiber.

At least 109 records · Page 6Linked to original sources

arXiv2004

Bernoulli potential in type-I and weak type-II superconductors: III. Electrostatic potential above the vortex lattice

The electrostatic potential above the Abrikosov vortex lattice, discussed earlier by Blatter {\em et al.} {[}PRL {\bf 77}, 566 (1996){]}, is evaluated within the Ginzburg-Landau theory. Unlike previous studies we include the surface dipole. Close to the critical temperature, the surface dipole reduces the electrostatic potential to values below a sensitivity of recent sensors. At low temperatures the surface dipole is less effective and the electrostatic potential remains observable as predicted earlier.

cond-mat.supr-con↗

arXiv2004

Supersymmetric Embedding of the Quantum Hall Matrix Model

We develop a supersymmetric extension of the Susskind-Polychronakos matrix theory for the quantum Hall fluids. This is done by considering a system combining two sets of different particles and using both a component field method as well as world line superfields. Our construction yields a class of models for fractional quantum Hall systems with two phases U and D involving, respectively $N_1$ bosons and $N_2$ fermions. We build the corresponding supersymmetric matrix action, derive and solve the supersymmetric generalization of the Susskind-Polychronakos constraint equations. We show that the general U(N) gauge invariant solution for the ground state involves two configurations parameterized by the bosonic contribution $k_{1}$ (integer) and in addition a new degree of freedom $k_{2}$, which is restricted to 0 and 1. We study in detail the two particular values of $k_{2}$ and show that the classical (Susskind) filling factor $ν$ receives no quantum correction. We conclude that the Polychronakos effect is exactly compensated by the opposite fermionic contributions.

hep-th↗

arXiv2004

A Matrix Model for Bilayered Quantum Hall Systems

We develop a matrix model to describe bilayered quantum Hall fluids for a series of filling factors. Considering two coupling layers, and starting from a corresponding action, we construct its vacuum configuration at ν=q_iK_{ij}^{-1}q_j, where K_{ij} is a 2\times 2 matrix and q_i is a vector. Our model allows us to reproduce several well-known wave functions. We show that the wave function Ψ_{(m,m,n)} constructed years ago by Yoshioka, MacDonald and Girvin for the fractional quantum Hall effect at filling factor {2\over m+n} and in particular Ψ_{(3,3,1)} at filling {1\over 2} can be obtained from our vacuum configuration. The unpolarized Halperin wave function and especially that for the fractional quantum Hall state at filling factor {2\over 5} can also be recovered from our approach. Generalization to more than 2 layers is straightforward.

hep-th↗

arXiv2004

Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-α}$. We study the dependence of the localization-length exponent $ν$ on the correlation-strength exponent $α$. % For fixed disorder $W$, there is a critical $α_{\rm c}$, such that for $α< α_{\rm c}$, $ν=2/α$ and for $α> α_{\rm c}$, $ν$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $ν$ is independent of $α$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.

cond-mat.dis-nn↗

arXiv2003

Two Coupled Harmonic Oscillators on Non-commutative Plane

We investigate a system of two coupled harmonic oscillators on the non-commutative plane \RR^2_θ by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle α. The obtained eigenstates as well as the eigenvalues depend on the non-commutativity parameter θ. Focusing on the ground state wave function before the transformation, we calculate the density matrix ρ_0(θ) and find that its traces {\rm Tr}(ρ_{0}(θ)) and {\rm Tr}(ρ_0^2(θ)) are not affected by the non-commutativity. Evaluating the Wigner function on \RR^2_θ confirms this. The uncertainty relation is explicitly determined and found to depend on θ. For small values of θ, the relation is shifted by a θ^2 term, which can be interpreted as a quantum correction. The calculated entropy does not change with respect to the normal case. We consider the limits α=1 and α={π\over 2}. In first case, by identifying θto the squared magnetic length, one can recover basic features of the Hall system.

hep-th↗

arXiv2003

Anisotropic Quantum Hall Matrix Model

We consider the anisotropic effect in the quantum Hall systems by applying a confining potential that is not of parabolic type. This can be done by extending Susskind--Polychronakos's approach to involve the matrices of two coupled harmonic oscillators. Starting from its action, we employ a unitary transformation to diagonalize the model. The operators for building up the anisotropic ground state and creating the collective excitations can be constructed explicitly. Evaluating the area of the quantum Hall droplet, we obtain the corresponding filling factor which is found to depend on the anisotropy parameter and to vary with the magnetic field strength. This can be used to obtain the observed anisotropic filling factors, i.e. {9\over 2}, {11\over 2} and others.

hep-th↗

arXiv2003

Stochastic unraveling of Redfield master equations and its application to electron transfer problems

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g. to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.

physics.chem-ph↗

arXiv2003

Magneto-transport in periodic and quasiperiodic arrays of mesoscopic rings

We study theoretically the transmission properties of serially connected mesoscopic rings threaded by a magnetic flux. Within a tight-binding formalism we derive exact analytical results for the transmission through periodic and quasiperiodic Fibonacci arrays of rings of two different sizes. The role played by the number of scatterers in each arm of the ring is analyzed in some detail. The behavior of the transmission coefficient at a particular value of the energy of the incident electron is studied as a function of the magnetic flux (and vice versa) for both the periodic and quasiperiodic arrays of rings having different number of atoms in the arms. We find interesting resonance properties at specific values of the flux, as well as a power-law decay in the transmission coefficient as the number of rings increases, when the magnetic field is switched off. For the quasiperiodic Fibonacci sequence we discuss various features of the transmission characteristics as functions of energy and flux, including one special case where, at a special value of the energy and in the absence of any magnetic field, the transmittivity changes periodically as a function of the system size.

cond-mat.mes-hall↗

arXiv2002

Numerical investigations of scaling at the Anderson transition

At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with finite resistance R to insulating behavior with R=infinity as T -> 0. This well-studied phenomenon is called the disorder-driven metal-insulator transition and it is characteristic to non-crystalline solids. In this review of recent advances, we have presented results of transport studies in disordered systems, ranging from modifications of the standard Anderson model of localization to effects of a two-body interaction. Of paramount importance in these studies was always the highest possible accuracy of the raw data combined with the careful subsequent application of the finite-size scaling technique. In fact, it is this scaling method that has allowed numerical studies to move beyond simple extrapolations and reliably construct estimates of quantities as if one were studying an infinite system.

cond-mat.dis-nn↗

arXiv2002

Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians

Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of aperiodic tight-binding models and the corresponding level statistics, which are well reproduced by random matrix theory. The eigenstates are characterised by multifractal analysis, and a construction of peculiar multifractal states on the Penrose tiling is discussed. We also consider quantum diffusion, and present some results on interacting electron systems in one dimension.

cond-mat.dis-nn↗

arXiv2002

Stochastic unraveling of time-local quantum master equations beyond the Lindblad class

A new method for stochastic unraveling of general time-local quantum master equations (QME) which involve the reduced density operator at time t only is proposed. The present kind of jump algorithm enables a numerically efficient treatment of QMEs which are not of Lindblad form. So it opens new large fields of application for stochastic methods. The unraveling can be achieved by allowing for trajectories with negative weight. We present results for the quantum Brownian motion and the Redfield QMEs as test examples. The algorithm can also unravel non-Markovian QMEs when they are in a time-local form like in the time-convolutionless formalism.

quant-ph↗

arXiv2002

Interacting particles at a metal-insulator transition

We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations -- in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach.

cond-mat.dis-nn↗

arXiv2001

The Hartree-Fock based diagonalization - an efficient algorithm for the treatment of interacting electrons in disordered solids

The Hartree-Fock based diagonalization is a computational method for the investigation of the low-energy properties of correlated electrons in disordered solids. The method is related to the quantum-chemical configuration interaction approach. It consists in diagonalizing the Hamiltonian in a reduced Hilbert space built of the low-energy states of the corresponding disordered Hartree-Fock Hamiltonian. The properties of the method are discussed for the example of the quantum Coulomb glass, a lattice model of electrons in a random potential interacting via long-range Coulomb interaction. Particular attention is paid to the accuracy of the results as a function of the dimension of the reduced Hilbert space. It is argued that disorder actually helps the approximation.

cond-mat.dis-nn↗

arXiv2001

Localization and conductance in the quantum Coulomb glass

We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin. After introducing these models we explain our computational method, the Hartree-Fock based diagonalization. We then discuss the conductance and compare spinless fermions and electrons. It turns out that spin degrees of freedom do not play an essential role in the systems considered. Finally, we analyze localization and decay of single-particle excitations. We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.

cond-mat.dis-nn↗

arXiv2001

Exciton scattering in light-harvesting systems of purple bacteria

Using the reduced density matrix formalism the exciton scattering in light-harvesting systems of purple bacteria is calculated. The static disorder (fluctuations of the site energies) as well as the dynamic disorder (dissipation) is taken into account in this work. Circular aggregates with 18 pigments are studied to model the B850 ring of bacteriochlorophylls with LH2 complexes. It can be shown that the influence of dissipation may not be neglected in the simulation of the time-dependent anisotropy of fluorescence. Also an elliptical deformation of the ring could be essential.

physics.chem-ph↗

arXiv2001

A density matrix approach to photoinduced electron injection

Electron injection from an adsorbed molecule to the substrate (heterogeneous electron transfer) is studied. One reaction coordinate is used to model this process. The surface phonons and/or the electron-hole pairs together with the internal degrees of freedom of the adsorbed molecule as well as possibly a liquid surrounding the molecule provide a dissipative environment, which may lead to dephasing, relaxation, and sometimes excitation of the relevant system. In the process studied the adsorbed molecule is excited by a light pulse. This is followed by an electron transfer from the excited donor state to the quasi-continuum of the substrate. It is assumed that the substrate is a semiconductor. The effects of dissipation on electron injection are investigated.

physics.chem-ph↗

arXiv2001

Localization properties of two interacting particles in a quasi-periodic potential with a metal-insulator transition

We study the influence of many-particle interactions on a metal-insulator transition. We consider the two-interacting-particle problem for onsite interacting particles on a one-dimensional quasiperiodic chain, the so-called Aubry-André model. We show numerically by the decimation method and finite-size scaling that the interaction does not modify the critical parameters such as the transition point and the localization-length exponent. We compare our results to the case of finite density systems studied by means of the density-matrix renormalization scheme.

cond-mat.dis-nn↗

arXiv2001

Influence of Static and Dynamic Disorder on the Anisotropy of Emission in the Ring Antenna Subunits of Purple Bacteria Photosynthetic Systems

Using the reduced density matrix formalism the time dependence of the exciton scattering in light-harvesting ring systems of purple bacteria is calculated. In contrast to the work of Kumble and Hochstrasser (J. Chem. Phys. 109 (1998) 855) static disorder (fluctuations of the site energies) as well as dynamic disorder (dissipation) is taken into account. For the description of dissipation we use Redfield theory in exciton eigenstates without secular approximation. This is shown to be equivalent to the Markovian limit of Capek's theory in local states. Circular aggregates with 18 pigments are studied to model the B850 ring of bacteriochlorophyls within LH2 complexes. It can be demonstrated that the dissipation is important for the time-dependent anisotropy of the fluorescence. Smaller values of static disorder are sufficient to produce the same decay rates in the anisotropy in comparison with the results by Kumble and Hochstrasser.

physics.chem-ph↗