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Fri, 08 Jun 2001 00:00:00 +0200Fri, 08 Jun 2001 00:00:00 +0200Wannier-Stark Resonances in optical and semiconductor superlattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1289
In this work, we discuss the resonance states of a quantum particle in a periodic potential plus static force. Originally this problem was formulated for a crystalline electron subject to the static electric field and is known nowadays as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and, in this sense, solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems like optical or semiconductor superlattices.Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korschpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1289Fri, 08 Jun 2001 00:00:00 +0200Semiclassical Approximations in Phase Space with Coherent States
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1285
We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.Michel Baranger; Marcus A. M. de Aguiar; Frank Keck; Hans-Jürgen Korsch; Bernd Schellhaaßpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1285Thu, 31 May 2001 00:00:00 +0200Bloch particle in presence of dc and ac fields: Statistics of the Wigner delay time
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1165
The paper studies quantum states of a Bloch particle in presence of external ac and dc fields. Provided the period of the ac field and the Bloch period are commensurate, an effective scattering matrix is introduced, the complex poles of which are the system quasienergy spectrum. The statistics of the resonance width and the Wigner delay time shows a close relation of the problem to random matrix theory of chaotic scattering.Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1165Sat, 16 Sep 2000 00:00:00 +0200Bloch particle in presence of dc and ac fields
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/879
The paper studies metastable states of a Bloch electron in the presence of external ac and dc fields. Provided resonance condition between period of the driving frequency and the Bloch period, the complex quasienergies are numerically calculated for two qualitatively different regimes (quasiregular and chaotic) of the system dynamics. For the chaotic regime an effect of quantum stabilization, which suppresses the classical decay mechanism, is found. This effect is demonstrated to be a kind of quantum interference phenomenon sensitive to the resonance condition.Markus Glück; A. R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/879Sat, 02 Sep 2000 00:00:00 +0200A truncated shift - operator technique for the calculation of resonances in Stark systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/870
A novel method is presented which allows a fast computation of complex energy resonance states in Stark systems, i.e. systems in a homogeneous field. The technique is based on the truncation of a shift-operator in momentum space. Numerical results for space periodic and non-periodic systems illustrate the extreme simplicity of the method.Markus Glück; A. R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/870Sat, 02 Sep 2000 00:00:00 +0200Semiclassical analysis of tunneling splittings in periodically driven quantum systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/872
For periodically driven systems, quantum tunneling between classical resonant stability islands in phase space separated by invariant KAM curves or chaotic regions manifests itself by oscillatory motion of wave packets centered on such an island, by multiplet splittings of the quasienergy spectrum, and by phase space localisation of the quasienergy states on symmetry related ,ux tubes. Qualitatively di,erent types of classical resonant island formation | due to discrete symmetries of the system | and their quantum implications are analysed by a (uniform) semiclassical theory. The results are illustrated by a numerical study of a driven non-harmonic oscillator.Hans Jürgen Korsch; Bruno Mirbach; Bernd Schellhaaßarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/872Sat, 02 Sep 2000 00:00:00 +0200Chaotic Wannier-Bloch resonance states
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/906
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.+bMarkus Glück; A. R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/906Sat, 02 Sep 2000 00:00:00 +0200Stark Resonances in dc fields from short time propagation of the field-free Hamiltonian
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/907
A new method for calculating Stark resonances is presented and applied for illustration to the simple case of a one-particle, one-dimensional model Hamiltonian. The method is applicable for weak and strong dc fields. The only need, also for the case of many particles in multi-dimensional space, are either the short time evolution matrix elements or the eigenvalues and Fourier components of the eigenfunctions of the field-free Hamiltonian.Nimrod Moiseyev; Markus Glück; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/907Sat, 02 Sep 2000 00:00:00 +0200Lifetime statistics for a Bloch particle in ac and dc fields
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/908
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.Markus Glück; A. R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/908Sat, 02 Sep 2000 00:00:00 +0200A generalized entropy measuring quantum localization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/865
We present an entropy concept measuring quantum localization in dynamical systems based on time averaged probability densities. The suggested entropy concept is a generalization of a recently introduced [PRL 75, 326 (1995)] phase-space entropy to any representation chosen according to the system and the physical question under consideration. In this paper we inspect the main characteristics of the entropy and the relation to other measures of localization. In particular the classical correspondence is discussed and the statistical properties are evaluated within the framework of random vector theory. In this way we show that the suggested entropy is a suitable method to detect quantum localization phenomena in dynamical systems.Bruno Mirbach; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/865Wed, 30 Aug 2000 00:00:00 +0200Selective Quasienergies from Short Time Cross-Correlation Probability Amplitudes by the Filter-Diagonalization Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/866
The Filter-Diagonalization Method is applied to time periodic Hamiltonians and used to find selectively the regular and chaotic quasienergies of a driven 2D rotor. The use of N cross-correlation probability amplitudes enables a selective calculation of the quasienergies from short time propagation to the time T (N). Compared to the propagation time T (1) which is required for resolving the quasienergy spectrum with the same accuracy from auto-correlation calculations, the cross-correlation time T (N) is shorter by the factor N , that is T (1) = N T (N).Markus Glück; Hans Jürgen Korsch; Nimrod Moiseyevarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/866Wed, 30 Aug 2000 00:00:00 +0200A quantum/classical entropy concept for measuring phase-space localization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/867
We present an entropy concept measuring phase-space localization in dynamical systems based on time-averaged phase-space densities. This entropy has a direct classical counterpart; its local scaling with ln _h.Bruno Mirbach; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/867Wed, 30 Aug 2000 00:00:00 +0200Phase space entropies and global quantum phase space organisation: A two-dimensional anharmonic system
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/868
The global dynamical properties of a quantum system can be conveniently visualized in phase space by means of a quantum phase space entropy in analogy to a Poincare section in classical dynamics for two-dimensional time independent systems. Numerical results for the Pullen Edmonds systems demonstrate the properties of the method for systems with mixed chaotic and regular dynamics.Hans Jürgen Korsch; Georg Groh; W. Schweizerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/868Wed, 30 Aug 2000 00:00:00 +0200Resonances from short time complex-scaled cross-correlation probability amplitudes by the Filter-Diagonalization Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/873
The Filter-Diagonalization Method is used to ,nd the broad and even overlapping resonances of a 1D Hamiltonian used before as a test model for new resonance theories and computational methods. It is found that the use of several complex-scaled cross-correlation probability amplitudes from short time propagation enables the calculation of broad overlapping resonances, which can not be resolved from the amplitude of a single complex-scaled autocorrelation calculation.Hans Jürgen Korsch; Nimrod Moiseyev; Edvardas Narevicius; Daniel Neuheuserarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/873Mon, 03 Apr 2000 00:00:00 +0200Global and local dynamical invariants and quasienergy states of time-periodic Hamiltonians
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/874
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.Bruno Mirbach; Hans Jürgen Korsch; D.B. Monteolivaarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/874Mon, 03 Apr 2000 00:00:00 +0200The 'Ermakov-Lewis' invariants for Coupled Linear Oscillators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/875
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.Karl-Erik Thylwe; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/875Mon, 03 Apr 2000 00:00:00 +0200Quantum mechanical and quasi-classical dynamics of coupled quasiparticle-boson systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/876
Hans Jürgen Korsch; R. Steib; J.L. Schoendorff; P. Reineckerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/876Mon, 03 Apr 2000 00:00:00 +0200Quantum Chaos
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/877
The study of dynamical quantum systems, which are classically chaotic, and the search for quantum manifestations of classical chaos, require large scale numerical computations. Special numerical techniques developed and applied in such studies are discussed: The numerical solution of the time-dependent Schr-odinger equation, the construction of quantum phase space densities, quantum dynamics in phase space, the use of phase space entropies for characterizing localization phenomena, etc. As an illustration, the dynamics of a driven one-dimensional anharmonic oscillator is studied, both classically and quantum mechanically. In addition, spectral properties and chaotic tunneling are addressed.Hans Jürgen Korsch; Henning Wiescherarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/877Mon, 03 Apr 2000 00:00:00 +0200Calculation of Wannier-Bloch and Wannier-Stark states
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/869
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.Markus Glück; A. R. Kolovsky; Hans Jürgen Korsch; Nimrod Moseyevpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/869Mon, 03 Apr 2000 00:00:00 +0200Wannier-Stark Ladders in Driven Optical Lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1058
The paper studies the effect of a weak periodic driving on metastable Wannier-Stark states. The decay rate of the ground Wannier-Stark states as a continuous function of the driving frequency is calculated numerically. The theoretical results are compared with experimental data of Wilkinson et at. [Phys.Rev.Lett.76, 4512 (1996)] obtained for cold sodium atoms in an accelerated optical lattice.Markus Glück; Hankel Michael; Andrey R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1058Fri, 10 Mar 2000 00:00:00 +0100About universality of lifetime statistics in quantum chaotic scattering
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1059
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced earlier in Ref. [5,6]. The coarse-grained distribution of the resonance widths is shown to be in good agreement with the prediction of Random Matrix Theory (RMT). The behavior of the survival probability shows, however, some deviation from RMT.Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1059Fri, 10 Mar 2000 00:00:00 +0100Resonant Tunneling of Wannier-Stark-States
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1060
Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korschpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1060Fri, 10 Mar 2000 00:00:00 +0100Induced transitions between Wannier ladders
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1061
We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several order of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using nonhermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.Markus Glück; Hankel Michael; Andrey R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1061Fri, 10 Mar 2000 00:00:00 +0100Fractal stabilization of Wannier-Stark resonances
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1062
The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to have a fractal structure as function of the so-called electric matching ratio, which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal nature of the spectrum in the system "atom in a standing laser wave", which is a quantum optical realization of a Bloch electron. It is shown that for an appropriate choice of the system parameters the atomic survival probability (a quantity measured in laboratory experiments) also develops a fractal structure as a function of the electric matching ratio. Numerical simulations under classically chaotic scattering conditions show good agreement with theoretical predictions based on random matrix theory.Markus Glück; Andrey R. Kolovsky; Hans Jürgen Korscharticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1062Fri, 10 Mar 2000 00:00:00 +0100Quantum and Classical Momentum Distributions. I. Theory and elementary examples
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1063
Hans Jürgen Korsch; B. Schnellhaßarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1063Fri, 10 Mar 2000 00:00:00 +0100