H. J. Korsch

• Prof. Dr.
• Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

The quantum dynamics of a damped and forced harmonic oscillator described by a Lindblad master equation is analyzed. The master equation is converted into a matrix-vector representation and the resulting non-Hermitian Schr\"odinger equation is solved by Lie-algebraic techniques allowing the construction of the general solution for the density opera...

The quantum dynamics of a damped and forced harmonic oscillator is investigated in terms of a Lindblad master equation. Elementary algebraic techniques are employed allowing for example to analyze the long time behavior, i.e.~the quantum limit cycle. The time evolution of various expectation values is obtained in closed form as well as the entropy...

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is base...

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is base...

Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of m molecules of type A into n molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed su(2) algebra. In the mean-field limit of large particle numbers, these systems beco...

Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic...

Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic...

Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ $m$-atomic molecules into $m$ $n$-atomic ones. These Hamiltonians are analyzed in terms of generators of a polynomially deformed $su(2)$ algebra. In the mean-field limit of large particle numbers, the system is classical and it...

The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part....

The two-mode Bose-Hubbard model in the mean-field approximation is revisited emphasizing a geometric interpretation where the system orbits appear as intersection curves of a (Bloch) sphere and a cylinder oriented parallel to the mode axis, which provide a generalization of Viviani's curve studied already in 1692. In addition, the dynamics is shown...

Optical techniques are widely used for the read-out of micro- and nanoresonators. Absorption of the employed light heats the device, thereby altering its mechanical properties, in particular, its eigenfrequency. To describe this effect, we present a model of a non-linear point mass resonator presuming an exponentially changing eigenfrequency, which...

We study the influence of particle interaction on a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding non-interacting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here we use this topological quantity to distinguish coherent...

The nonlinear Schrödinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schrödinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary sta...

The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier-Stark system exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analyzed....

We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band split up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the stud...

We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wid...

We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of a...

We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field approximation for this non-Hermitian many-particle system yielding an alternative complex nonlinear Schr\"odinger equatio...

The dynamics of cold Bose atoms in driven tilted optical lattices is analyzed focusing on destruction of Wannier-Stark localization and the phenomenon of band collapse. It is argued that an understanding of the experimental results requires thorough account for interaction effects. These are suppression of the ballistic spreading of atoms for reson...

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with...

For the stationary one-dimensional nonlinear Schrödinger equation (or Gross–Pitaevskii equation), nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-)analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a s...

For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a...

The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrat...

The resonance states and the decay dynamics of the nonlinear Schrödinger (or Gross–Pitaevskii) equation are studied for a simple, but flexible, model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the reso...

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartiti...

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which...

We investigate an N-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular, the fixed point structures showing characte...

The resonance states and the decay dynamics of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation are studied for a simple, however flexible model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the...

In this paper we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schrödinger equation share with the linear one: for unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an ex...

We investigate an $N$-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular the fixed point structures showing charact...

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case...

The kicked rotor is a prototype of a classical nonlinear system with regular and chaotic behavior. Its dynamics can be reduced to a simple and accessible two-dimensional area preserving map in phase space. Despite its simplicity, the kicked rotor is not merely a toy system but serves as a basis for recent research in quantum dynamics. We discuss th...

We study a non-Hermitian $PT-$symmetric generalization of an $N$-particle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on c...

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation fo...

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized SU(M) coherent states yields a Liouvillian flow in the macroscopic limit, which...

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approxim...

This new edition strives yet again to provide readers with a working knowledge of chaos theory and dynamical systems through parallel introductory explanations in the book and interaction with carefully-selected programs supplied on the accompanying diskette. The programs enable readers, especially advanced-undergraduate students in physics, engine...

Dynamical systems are often expressed in terms of ordinary differential equations. An example are the canonical equations of motion in Hamiltonian systems $$ \dot p_i = - \frac{{\partial H}} {{\partial q_i }},{\text{ }}\dot q_i = \frac{{\partial H}} {{\partial p_i }}, $$ (12.1) where the time derivatives of the canonical coordinates and momenta are...

As already pointed out in Chap. 7, discrete iterated maps appear almost routinely in studies of nonlinear dynamical systems, e.g., as Poincaré maps. Because they are discrete, such maps are much simpler to study (both numerically and analytically) than continuous differential equations. In general, the maps can be written as $$ r_{n + 1} = F(r_n ,c...

Many systems of interest in the study of chaotic dynamics can be described by discrete mappings, as for instance, the billiard systems considered in detail in Chaps. 3, 4 and 6, the Fermi acceleration in Chap. 7, and, of course, the one- and two-dimensional maps investigated in Chaps. 9 and 11. Such iterated maps can be easily explored numerically.

The program Wedge studies the dynamics of a billiard in a gravitational field, or more precisely, a falling body in a symmetric wedge. The boundary of this billiard (compare the discussion of billiard systems in Chap. 3 ) consists of two planes symmetrically inclined with respect to a constant (e.g., gravitational) force field. The particle is refl...

In everyday life we feel safer and more comfortable with predictability and determinism: in technically controlled processes, small mechanical forces are expected to cause minor changes; the time-table of trains is hopefully reliable; the motion of the earth and moon around the sun are thought to be regular and stable.

An extremely simple example for demonstrating chaotic dynamics in conservative systems numerically is that of Birkhoff’s billiard [1], i.e., the frictionless motion of a particle on a plane billiard table bounded by a closed curve [2]–[7]. The limiting cases of strictly regular (‘integrable’) and strictly irregular (‘ergodic’ or ‘mixed’) systems ca...

The aim of this chapter is to provide an introduction to the theory of nonlinear systems. We assume that the reader has a background in classical dynamics and a basic knowledge of differential equations, but most readers of this book will only have a vague notion of chaotic dynamics. The computer experiments in the following chapters will (hopefull...

The planar double pendulum consists of two coupled pendula, i.e., two point masses m 1 and m 2 attached to massless rods of fixed lengths l 1 and l 2 moving in a constant gravitational field (compare Fig. 5.1 ). For simplicity, only a planar motion of the double pendulum is considered. Such a planar double pendulum is most easily constructed as a m...

The so-called Fermi acceleration — the acceleration of a particle through collision with an oscillating wall — is one of the most famous model systems for understanding nonlinear Hamiltonian dynamics. The problem was introduced by Fermi [1] in connection with studies of the acceleration mechanism of cosmic particles through fluctuating magnetic fie...

Nonlinear electronic networks can be used as a laboratory set-up of nonlinear systems. The dynamics directly generates an electric signal, which can be easily handled for further analysis. Such an electronic circuit is a physical system of the real world. It is, however, on account of its electronic nature, also similar to a computing device and, t...

The differential transition probabilities are studied for electron diatomic molecule scattering for initially vibrationally (n = 2, 31) and rotationally (j = 5) excited states. The manifestation of the vibrational anharmonicity in the rotational and vibrational final-state distributions is discussed for the example of e-Na2 collisions at impact ene...

The stationary nonlinear Schrödinger equation or Gross-Pitaevskii equation for one-dimensional potential scattering is studied. The nonlinear transmission function shows a distorted profile, which differs from the Lorentzian one found in the linear case. This nonlinear profile function is analyzed and related to Siegert-type complex resonances. It...

The stationary nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) for one-dimensional potential scattering is studied. The nonlinear transmission function shows a distorted profile, which differs from the Lorentzian one found in the linear case. This nonlinear profile function is analyzed and related to Siegert type complex resonances....

We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated single- and double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed transport with very little dispersion. The dynamics in the double-periodic system is dominated by Bloch-Zener oscilla...

We analyze the correspondence of many-particle and mean-field dynamics for a Bose-Einstein condensate in an optical lattice. Representing many-particle quantum states by a classical phase space ensemble instead of one single mean-field trajectory and taking into account the quantization of the density by a modified integer Gross-Pitaevskii equation...

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 dyna...

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi d...

A useful semiclassical method to calculate eigenfunctions of the Schrödinger equation is the mapping to a well-known ordinary differential equation, such as for example Airy's equation. In this paper, we generalize the mapping procedure to the nonlinear Schrödinger equation or Gross–Pitaevskii equation describing the macroscopic wavefunction of a B...

A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of the mean-field Gross-Pitaevskii equation and is expected to be valid for large N. We demonstrate the possibili...

We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schroedinger equation). An importan...

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.

We consider the dynamics of a quantum particle in a one-dimensional periodic potential (lattice) under the action of a static and time-periodic field. The analysis is based on a nearest-neighbor tight-binding model which allows a convenient closed form description of the transport properties in terms of generalized Bessel functions. The case of bic...

The diabolic crossing scenario of two-state quantum systems can be generalized to a non-Hermitian case as well as to a nonlinear one. In the non-Hermitian case two different crossing types appear, distinguished according to the crossing or anticrossing of real parts or imaginary parts of the eigenvalues. In the nonlinear case additional stationary...

A useful semiclassical method to calculate eigenfunctions of the Schroedinger equation is the mapping to a well-known ordinary differential equation, as for example Airy's equation. In this paper we generalize the mapping procedure to the nonlinear Schroedinger equation or Gross-Pitaevskii equation describing the macroscopic wave function of a Bose...

It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub-bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands,...

We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well as in the mean-field approximation. Novel nonlinear eigen-states emerge in the mean-field description, which leads to a breakdown of adiabaticity: The Landau-Zener transition probability does not vani...

We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well and in the mean-field approximation. The many-particle problem can be solved approximately within an independent crossings approximation, which yields an explicit Landau-Zener formula.

The semiclassical quantization of complex energy resonance poles of the S-matrix is reviewed. The method leads to closed form results, which are valid also for broad shape resonances in the vicinity or above potential barriers. The theory is extended to various Feshbach-type resonances in curve crossing systems. The results are in very good agreeme...

We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parame...

We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the transport properties of the system analytically in terms of ingoing and outgoing waves. Resonances and bound s...

The nonlinear Schrödinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schrödinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary sta...

Quantum decay in an ac driven biased periodic potential modeling cold atoms in optical lattices is studied for a symmetry broken driving. For the case of fully chaotic classical dynamics the classical exponential decay is quantum mechanically suppressed for a driving frequency \omega in resonance with the Bloch frequency \omega_B, q\omega=r\omega_B...

We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable mod...

We investigate the dynamics of Bose-Einstein condensates (BEC) in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrab...

The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schroedinger equation....

A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the dynamics shows a much richer behaviour. The Bloch oscillations are discussed using analytical expressions for...

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correl...

Bloch oscillations in a two-dimensional periodic potential under a (relatively weak) static force are studied for separable and non-separable potentials. The dynamics depends sensitively on the direction of the static field with respect to the lattice. Almost dispersionless periodic motion of the wavepackets is observed, as well as breathing modes....

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correl...

We study the dynamics of Bloch oscillations in a one-dimensional periodic potential plus a (relatively weak) static force. The tight-binding and single-band approximations are analysed in detail, and also in a classicalized version. A number of numerically exact results obtained from wavepacket propagation are analysed and interpreted in terms of t...

Quantum diffusion in a biased kicked Harper system, modeling field-induced transport in superlattices, is studied for fully chaotic dynamics of the underlying classical system. Under these conditions, the classical transport is diffusive whereas the quantum diffusion can be either enhanced or suppressed for commensurable or incommensurable ratio of...

The dynamics of the driven single band tight binding model for Wannier–Stark systems is formulated and solved using a dynamical algebra. This Lie algebraic approach is very convenient for evaluating matrix elements and expectation values. A classicalization of the tight binding model is discussed as well as some illustrating examples of Bloch oscil...

In two recent papers (Baranger et al 2001 J. Phys. A: Math. Gen. 34 7227; 2002 J. Phys. A: Math. Gen. 35 9493) co-authored by us, we mentioned the work of Dr Kenneth G Kay (Kay 1994 J. Chem. Phys. 100(6) 4377; 100 4432) in an unfavourable light. In this comment we correct this impression, as it was based on a misunderstanding of his work. The point...

For high electric fields, the lifetime of Wannier-Stark ladder states in a periodic potential is reduced by the fundamental process of Zener tunneling. We report on the analysis of the coherence lifetime of such states in semiconductor superlattices by interband spectroscopy. The reduction of lifetime by strong coupling between bands can only in th...

Bloch oscillations of cold atoms in two-dimensional optical lattices are studied. The cases of separable and nonseparable potentials are compared by simulating the wave-packet dynamics. For these two classes of optical potential, the Bloch oscillations were found to be qualitatively the same in the case of a weak static field but fundamentally diff...

The complex energy resonances of a double δ potential well in a constant (Stark) field are studied. Varying the two system parameters (well distance and field strength) we investigate the behaviour of the resonance energies and wavefunctions both analytically and numerically. Different crossing scenarios for the real and imaginary parts of two reso...

The typical avoided crossings for Hermitian quantum systems depending on parameters, the diabolic crossing scenario, are generalized to the non-Hermitian case, e.g. for resonances. Two types of crossings appear: for type I, the real parts show an avoided and the imaginary parts a true crossing of the eigenenergies, and for type II the opposite is f...

The optical properties of an electrically biased semiconductor superlattice are strongly influenced by coupling to other bands. As these coupling mechanisms depend on the strength of the applied electric field, we find a distinct variation in transition line broadening, dephasing time and spatial extension of the wavefunction. The fundamental Bloch...

The Herman–Kluk (HK) formula was shown in (Baranger et al J. Phys. A: Math. Gen. 34 7227 ) not to be a correct semiclassical limit of an exact quantum mechanical formula. Two previous attempts to derive it using semiclassical arguments contain serious errors. These statements are left totally untouched by Herman and Grossmann's comment. They argue...

The pulsed output from a Bose-Einstein condensate can be described using ordinary one-particle quantum mechanics. The initial state is described in terms of Stark resonances truncated in momentum space. The states obtained in this way resemble the normalizable scattering states defined in terms of Moshinsky functions. The validity of this approach...

It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of t...

An exact dynamical parametrization of pulse-induced transition amplitudes in a Rosen–Zener- or Nikitin-type two-level system is constructed. The three dynamical parameters are closely related to the shape of the interaction pulse and are convenient to calculate. The Milne equation with a complex coefficient function is essential for these calculati...

The quantum and classical dynamics in a two-dimensional (2D) periodic potential influenced by a constant force is discussed and compared. Classically, the dynamics is chaotic. A branched flow of the particles similar but more structured than the coherent branched flow in a 2D electron gas is observed. In the classical case, the formation of separat...

The rapid delocalization of chaotic Hamiltonian dynamics can be described by a local measure on phase space, the microscopic heterogeneity, both for classical and quantum systems. The properties of this new measure are discussed and studied numerically for a one-dimensional nonlinearly driven oscillator. An intricate and highly structured phase spa...

An extremely simple and convenient method is presented for computing eigenvalues in quantum mechanics by representing position and momentum operators in matrix form. The simplicity and success of the method is illustrated by numerical results concerning eigenvalues of bound systems and resonances for Hermitian and non-Hermitian Hamiltonians as well...