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- Fachbereich Physik (35) (remove)

We consider N coupled linear oscillators with time-dependent coecients. An exact complex amplitude - real phase decomposition of the oscillatory motion is constructed. This decomposition is further used to derive N exact constants of motion which generalise the so-called Ermakov-Lewis invariant of a single oscillator. In the Floquet problem of periodic oscillator coecients we discuss the existence of periodic complex amplitude functions in terms of existing Floquet solutions.

We report on the exchange bias effect as a function of the in-plane direction of the applied field in twofold symmetric, epitaxial Ni 80 Fe 20 /Fe 50 Mn 50 bilayers grown on Cu~110! single-crystal substrates. An enhancement of the exchange bias field, H eb , up to a factor of 2 is observed if the external field is nearly, but not fully aligned perpendicular to the symmetry direction of the exchange bias field. From the measurement of the exchange bias field as a function of the in-plane angle of the applied field, the unidirectional, uniaxial and fourfold anisotropy contributions are determined with high precision. The symmetry direction of the unidirectional anisotropy switches with increasing NiFe thickness from [110] to [001].

Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations
(1998)

Abstract: Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.

The greybody factors in BTZ black holes are evaluated from 2D CFT in the spirit of AdS3/CFT correspondence. The initial state of black holes in the usual calculation of greybody factors by effective CFT is described as Poincar'e vacuum state in 2D CFT. The normalization factor which cannot be fixed in the effective CFT without appealing to string theory is shown to be determined by the normalized bulk-to-boundary Green function. The relation among the greybody factors in different dimensional black holes is exhibited. Two kinds of (h; _h) = (1; 1) operators which couple with the boundary value of massless scalar field are discussed.

The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.

A formalism is developed for calculating the quasienergy states and spectrum for time-periodic quantum systems when a time-periodic dynamical invariant operator with a nondegenerate spectrum is known. The method, which circumvents the integration of the Schr-odinger equation, is applied to an integrable class of systems, where the global invariant operator is constructed. Furthermore, a local integrable approximation for more general non-integrable systems is developed. Numerical results are presented for the doubleresonance model.

The light-cone Hamiltonian approach is applied to the super D2- brane, and the equivalent area-preserving and U(1) gauge-invariant effective Lagrangian, which is quadratic in the U(1) gauge field, is derived. The latter is recognised to be that of the three- dimensional U(1) gauge theory, interacting with matter supermultiplets, in a special external induced supergravity metric and the gravitino field, depending on matter fields. The duality between this theory and 11d supermembrane theory is demonstrated in the light-cone gauge.

Abstract: The effect of intracavity Electromagnetically Induced Transparency on the properties of optical resonators and active laser devices is discussed theoretically. A pronounced frequency pulling and cavity linewidth narrowing are predicted. The effect can be used to substantially reduce classical and quantum phase noise of the beat-note of optical oscillators. Fundamental limits of this stabilization mechanism are discussed as well as its potential application to high-resolution spectroscopy.

Abstract: We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.

Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.

The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schr"odinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first- or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.

Superselection rules induced by the interaction with the environment are investigated with the help of exactly soluble Hamiltonian models. Starting from the examples of Araki and of Zurek more general models with scattering are presented for which the projection operators onto the induced superselection sectors do no longer commute with the Hamiltonian. The example of an environment given by a free quantum field indicates that infrared divergence plays an essential role for the emergence of induced superselection sectors. For all models the induced superselection sectors are uniquely determined by the Hamiltonian, whereas the time scale of the decoherence depends crucially on the initial state of the total system.

The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings.

In der vorliegenden Arbeit wird die Methode der Molekulardynamik benutzt, um das Transmissionsverhalten von niederenergetischen Sauerstoffionen durch dünne Edelgasfilme mit Hilfe von klassischen Wechselwirkungs-Potentialen zu untersuchen. In einer quantenmechanischen Form, der sogenannten Tight-Binding Näherung, wird die Molekulardynamik verwendet, um die Dynamik des Phasenübergangs von der Flüssigkeit, oder vom Gas, zur amorphen Phase von Silizium, oder von hydrogenisiertem Silizium, zu untersuchen. Ich simuliere ein Experiment von N. J. Sack et. al., in dem Sauerstoffionen durch Elektronenbeschuß von einer WOx-Oberfläche desorbiert wurden und deren Transmissionsverhalten durch dünne Edelgasfilme gemessen wurde. Wenn in der Simulation nur elastische Streuung durch Paarpotentiale zugelassen wird, finde ich gute Übereinstimmung für die Transmissionsausbeuten zwischen Experiment und Simulation für Xe- und Kr-Filme. Die große Anzahl der gefundenen Transmissionen kann auf den kleinen Wechselwirkungsradius der Sauerstoffionen zurückgeführt werden. Die Diskrepanz zwischen Experiment und Simulation, die für Ar-Filme zu verzeichnen ist, wird auf elektronisch inelastische Wechselwirkungen oder strukturelle Effekte im Experiment zurückgeführt. In einem einfachen geometrischen Modell kann ich die Transmissions-Daten der Simulation für Xe- und Kr- Filme interpretieren, nicht jedoch die Daten für Ar-Filme. Dieses geometrische Modell wird dann zur Interpretation eines weiteren, ähnlichen Experiments von N. J. Sack et. al. herangezogen. Neue dynamische Gleichungen für klassische und quantenmechanische Molekulardynamik im kanonischen - , Enthalpie - und freien Enthalpie Ensemble werden vorgeschlagen. Ich zeige, daß Atome, die in den neuen dynamischen Gleichungen in der Zeit propagiert werden, die Phasenraum-Verteilungsfunktionen der entsprechenden Ensembles korrekt abtasten. Basierend auf einem verallgemeinerten Liouville Theorem werden numerische Integrations-Algorithmen entwickelt, die die fundamentalen Symmetrieen der dynamischen Gleichungen respektieren. Silizium gehört zu den am besten studierten Materialien überhaupt. In theoretischen Untersuchungen wird flüssiges und amorphes Silizium üblicherweise ohne Kontrolle des Drucks untersucht. In dieser Arbeit wird gezeigt, daß Druckkontrolle in der Beschreibung sowohl einer thermodynamischen Phase als auch in Phasenübergängen in der Simulation wichtig ist. Der Übergang von der flüssigen zur amorphen Phase von Silizium in einer Tight-Binding Beschreibung mit und ohne Druckkontrolle führt zu Strukturen, die halbleitend mit Druckkontrolle und nicht halbleitend ohne Druckkontrolle sind. Weiterhin werden Evidenzen gefunden, die die Erweiterung der üblichen minimalen Valenzbasis des Siliziums durch d-Orbitale nahelegen, um korrekte Resultate speziell für flüssiges Silizium zu erhalten. Amorphes hydrogenisiertes Silizium ist technisch wichtig, da die Bandlücke durch Wasserstoffgehalt und Herstellung beeinflußt werden kann. In dieser Arbeit wird ein mikroskopisches Modell für amorphes Silizium, erhalten durch Abkühlung eines Silizium-Wasserstoff Gases, mit Hilfe der Molekulardynamik in einer Tight-Binding Beschreibung simuliert. Die Rolle des Wasserstoffs im amorphen Netzwerk wird mit Hilfe einer Vielzahl von Korrelationsfunktionen aufgezeigt. Diese Korrelationsfunktionen demonstrieren die hohe Flexibilität des Wasserstoffs. In Übereinstimmung mit neueren NMR-Daten von Y. Wu et. al finde ich im amorphen Netzwerk eine Klusterung der Wasserstoffatome, die die Tendenz zweier Wasserstoffatome reflektiert unabgesättigte Silizium Bindung, die sich ohne Wasserstoff zu ungünstigen Bindungsgeometrien vereinigen würden, zu passivieren.

Annual Report 1997
(1998)

We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schrödinger operator. We prove the feasibility of our method by constructing a new "\(AG_3\) model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the \(B_3\) model. In order to better understand features of our construction we exhibit the \(F_4\) rational model with our method.

Abstract: We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schrödinger operator. We prove the feasibility of our method by constructing an " AG_3 model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the B_3 model. In order to better understand features of our construction we exhibit the F_4 rational model with our method.

Abstract: Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. We focus on the bulk of the spectrum. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three-point correlation functions.

The dispersions of dipolar (Damon-Eshbach modes) and exchange dominated spin waves are calculated for in-plane magnetized thin and ultrathin cubic films with (111) crystal orientation and the results are compared with those obtained for the other principal planes. The properties of these magnetic excitations are examined from the point of view of Brillouin light scattering experiments. Attention is paid to study the spin-wave frequency variation as a function of the magnetization direction in the film plane for different film thicknesses. Interface anisotropies and the bulk magnetocrystalline anisotropy are considered in the calculation. A quantitative comparison between an analytical expression obtained in the limit of small film thickness and wave vector and the full numerical calculation is given.

The paper discusses the metastable states of a quantum particle in a periodic potential under a constant force (the model of a crystal electron in a homogeneous electric ,eld), which are known as the Wannier-Stark ladder of resonances. An ecient procedure to ,nd the positions and widths of resonances is suggested and illustrated by numerical calculation for a cosine potential.

The Wannier-Bloch resonance states are metastable states of a quantum particle in a space-periodic potential plus a homogeneous field. Here we analyze the states of quantum particle in space- and time-periodic potential. In this case the dynamics of the classical counterpart of the quantum system is either quasiregular or chaotic depending on the driving frequency. It is shown that both the quasiregular and the chaotic motion can also support quantum resonances. The relevance of the obtained result to the problem a of crystal electron under simultaneous influence of d.c. and a.c. electric fields is briefly discussed. PACS: 73.20Dx, 73.40Gk, 05.45.+b

We study the statistics of the Wigner delay time and resonance width for a Bloch particle in ac and dc fields in the regime of quantum chaos. It is shown that after appropriate rescaling the distributions of these quantities have universal character predicted by the random matrix theory of chaotic scattering.

Abstract: Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account non-cooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a non-linear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.

Abstract: We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum uctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.

Abstract: Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.

Abstract: We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive toolto design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses) there exists a higher-order trapping state, which is an exact constant of motion and analytic solutions for the atomic dynamics can be derived.

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.

The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space- and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. The experimental results are in good qualitative agreement with numerical simulations.

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.