# Tobias Kramer

## Contact Details

NameTobias Kramer |
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## Pubs By Year |
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## Pub CategoriesQuantum Physics (19) Physics - Mesoscopic Systems and Quantum Hall Effect (16) Physics - Chemical Physics (5) Physics - Biological Physics (4) Physics - Atomic Physics (3) Mathematics - Mathematical Physics (3) Mathematical Physics (3) Earth and Planetary Astrophysics (3) Physics - Other (1) |

## Publications Authored By Tobias Kramer

We have performed time-dependent wave packet simulations of realistic Aharonov-Bohm (AB) devices with a quantum dot embedded in one of the arms of the interferometer. The AB ring can function as a measurement device for the intrinsic transmission phase through the quantum dot, however, care has to be taken in analyzing the influence of scattering processes in the junctions of the interferometer arms. We consider a harmonic quantum dot and show how the Darwin-Fock spectrum emerges as a unique pattern in the interference fringes of the AB oscillations. Read More

The Rosetta probe around comet 67P/Churyumov-Gerasimenko (67P) reveals an anisotropic dust distribution of the inner coma with jet-like structures. The physical processes leading to jet formation are under debate, with most models for cometary activity focusing on localised emission sources, such as cliffs or terraced regions. Here we suggest, by correlating high-resolution simulations of the dust environment around 67P with observations, that the anisotropy and the background dust density of 67P originate from dust released across the entire sunlit surface of the nucleus rather than from few isolated sources. Read More

Dust transport and deposition behind larger boulders on the comet 67P/Churyumov-Gerasimenko (67P/C-G) have been observed by the Rosetta mission. We present a mechanism for dust transport vectors based on a homogenous surface activity model incorporating in detail the topography of 67P/C-G. The combination of gravitation, gas drag, and Coriolis force leads to specific dust transfer pathways, which for higher dust velocities fuel the near nucleus coma. Read More

We compute trajectories of dust grains starting from a homogeneous surface activity-profile on a irregularly shaped cometary nucleus. Despite the initially homogeneous dust distribution a collimation in jet-like structures becomes visible. The fine structure is caused by concave topographical features with similar bundles of normal vectors. Read More

We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and center-of-mass coordinates we obtain an analytical identification of all spurious center-of-mass states of the Coulomb-interacting electrons. We find a substantial reduction in the basis set used for numerical computations. Read More

The theoretical and experimental study of energy transfer in photosynthesis has revealed an interesting transport regime, which lies at the borderline between classical transport dynamics and quantum-mechanical interference effects. Dissipation is caused by the coupling of electronic degrees of freedom to vibrational modes and leads to a directional energy transfer from the antenna complex to the target reaction-center. The dissipative driving is robust and does not rely on fine-tuning of specific vibrational modes. Read More

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte-Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. Read More

The prevalence of long-lasting oscillatory signals in the 2d echo-spectroscopy of light-harvesting complexes has led to a search for possible mechanisms. We investigate how two causes of oscillatory signals are intertwined: (i) electronic coherences supporting delocalized wave-like motion, and (ii) narrow bands in the vibronic spectral density. To disentangle the vibronic and electronic contributions we introduce a time-windowed Fourier transform of the signal amplitude. Read More

Solving the quantum-mechanical many-body problem requires scalable computational approaches, which are rooted in a good understanding of the physics of correlated electronic systems. Interacting electrons in a magnetic field display a huge variety of eigenstates with different internal structures, which have been probed experimentally in the Hall effect. The advent of high-performing graphics processing units has lead to a boost in computational speed in particular for classical systems. Read More

The observed prevalence of oscillatory signals in the spectroscopy of biological light-harvesting complexes at ambient temperatures has led to a search for mechanisms supporting coherent transport through larger molecules in noisy environments. We demonstrate a generic mechanism supporting long-lasting electronic coherence up to 0.3 ps at a temperature of 277 K. Read More

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential. Read More

Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question whether coherence and wave-like behaviour plays a significant role in photosynthesis. We perform a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which account for the pigments electronic and vibrational excitations respectively. Read More

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require to consider time non-local propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments (J. Read More

Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized wave-packet reveals the eigenstates and eigenvalues of the system under consideration. We discuss applications of the wave-packet method in atomic, molecular, and mesoscopic systems and point out specific advantages of the time-dependent approach. Read More

The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane, which is commonly the case in nanodevices. Read More

Quantum coherent properties of electrons can be studied in Aharonov-Bohm (AB) interferometers. We investigate both experimentally and theoretically the transmission phase evolution in a four-terminal quasi-one-dimensional AlGaAs/GaAs-based waveguide AB ring. As main control parameter besides the magnetic field, we tune the Fermi wave number along the pathways using a top-gate. Read More

Wave packets provide a well established and versatile tool for studying time-dependent effects in molecular physics. Here, we demonstrate the application of wave packets to mesoscopic nanodevices at low temperatures. The electronic transport in the devices is expressed in terms of scattering and transmission coefficients, which are efficiently obtained by solving an initial value problem (IVP) using the time-dependent Schroedinger equation. Read More

Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential, which resembles results obtained by conformal-mapping methods. As shown by a microscopic model of the current injection, the Hall effect is linked to specific boundary conditions at the particle reservoirs. Read More

We investigate the propagation of wave-packets on graphene in a perpendicular magnetic field and the appearance of collapses and revivals in the time-evolution of an initially localised wave-packet. The wave-packet evolution in graphene differs drastically from the one in an electron gas and shows a rich revival structure similar to the dynamics of highly excited Rydberg states. We present a novel numerical wave-packet propagation scheme in order to solve the effective single-particle Dirac-Hamiltonian of graphene and show how the collapse and revival dynamics is affected by the presence of disorder. Read More

We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. Read More

Low frequency AC-measurements are commonly used to determine the voltage and currents through mesoscopic devices. We calculate the effect of the alternating Hall voltage on the recorded time-averaged voltage in the presence of a top-gate covering a large part of the device. The gate is kept on a constant voltage, while the Hall voltage is recorded using an integrating alternating-current lock-in technique. Read More

We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics. Read More

The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and involve assumptions about disorder, localized states, extended states, edge states, Fermi levels pinned by Landau levels, etc. These standard narratives give plausible reasons for the existence of the plateaus, but provide little in the way of even a qualitative understanding of the shape and width of the Hall plateaus, much less a first principles calculation. Read More

We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. Read More

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results and a variety of numerical methods have been developed to solve the time-dependent Schroedinger equation. Read More

Progress in manufacturing technology has allowed us to probe the behavior of devices on a smaller and faster scale than ever before. With increasing miniaturization, quantum effects come to dominate the transport properties of these devices, between collisions, carriers undergo ballistic motion under the influence of local electric and magnetic fields. The often surprising propertiesof quantum ballistic transport are currently elucidated in clean atomic physics experiments. Read More

We present a 3D quantum mechanical theory of radio-frequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio-frequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field. Read More

I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic fields is employed to construct a non-linear transport theory. Another important ingredient of the alternative theory is the coupling of the two-dimensional electron gas to the leads and the applied voltages. Read More

Atoms and negative ions interacting with laser photons yield a coherent source of photoelectrons. Applying external fields to photoelectrons gives rise to interesting and valuable interference phenomena. We analyze the spatial distribution of the photocurrent using elementary quantum methods. Read More

The classical drift motion of electrons in crossed electric and magnetic fields provides an interesting example of a system with an on average constant velocity -- despite the presence of an electric field. This drift-velocity depends solely on the ratio of the electric and magnetic fields and not on the initial momentum of the electron. The present work describes the quantum-mechanical version of this drift-motion, which differs drastically from the classical result: The drift becomes dependent on the energy and a quantization of the transport occurs. Read More

We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the classical motion of the electrons: For instance, the number of interfering trajectories can be adjusted in this system, and the turning surfaces of classical motion contain a complex array of singularities. We perform a comprehensive analysis of both the semiclassical approximation and the quantum solution, and we make predictions that should serve as a guide for future photodetachment experiments. Read More

Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the quantum current through a Hall device that does not invoke disorder or interactions as the cause of the integer quantum Hall effect (QHE), but is based on a proper quantization of the classical electron drift motion. The theory yields a quantitative description of the breakdown of the QHE at high current densities that is in agreement with experimental data. Read More

**Category:**Quantum Physics

Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent Hamiltonians which are not higher than quadratic in the position operator, like i.e the driven harmonic oscillator with time-dependent frequency. Read More

The propagation of electrons in static and uniform electromagnetic fields is a standard topic of classical electrodynamics. The Hamilton function is given by a quadratic polynomial in the positions and momenta. The corresponding quantum-mechanical problem has been analyzed in great detail and the eigenfunctions and time evolution operators are well-known. Read More

Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a coherent source (atom laser). We introduce the energy-dependent Green function as a suitable tool to calculate the arising currents. Read More

Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. Read More

We investigate photodetachment from negative ions in a homogeneous 1.0-T magnetic field and a parallel electric field of approximately 10 V/cm. A theoretical model for detachment in combined fields is presented. Read More

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely propagating particles. Read More

Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are introduced into the Schr\"odinger equation. The source formalism yields direct access to the scattering wave function, particle distribution, and total current. Read More

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. Read More

Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices. Scenarios of positive and negative energy are distinguished. Read More