The quantum spectral analysis of the two-dimensional annular billiard system

Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.     

Experimental study of a Back Action Evading device for continuos measurements on a macroscopic harmonic oscillator at the quantum limit level

The Back Action Evading technique is a particular kind of quantum non demolition measurement, first proposed by Caves et al. in 1980 [3]. We present an experimental study to implement the Back Action Evading measurement scheme in monitoring the amplitude of an harmonic oscillator excited by a classical force. Results showing the agreement of our theoretical model with the experimental behaviour of our apparatus in the classical regime are presented. We discuss also the optimization of the performance of our set-up, which should allow to monitor our oscillator in quantum regime even below the standard quantum limit level. Received: 22 March 1996     

Femtosecond pump-probe fluorescence signals from classical trajectories: comparison with wave-packet calculations

A classical approach to simulate femtosecond pump-probe experiments is presented and compared to the quantum mechanical treatment. We restrict the study to gas-phase systems using the I₂ molecule as a numerical example. Thus, no relaxation processes are included. This allows for a direct comparison between purely quantum mechanical results and those obtained from classical trajectory calculations. The classical theory is derived from the phase-space representation of quantum mechanics. Various approximate quantum mechanical treatments are compared to their classical counterparts. Thereby it is demonstrated that the representation of the radial density as prepared in the pump-process is most crucial to obtain reliable signals within the classical approach. Received 28 March 2001     

Coherent resonant transport through a mesoscopic system with quantum ac microwave field

The time-dependent transport through an ultrasmall quantum dot coupling to two electron reservoirs is investigated. The quantum dot is perturbed by a quantum microwave field (QMF) through gate. The tunneling current formulae are obtained by taking expectation values over coherent state (CS), and SU(1,1) CS. We derive the transport formulae at low temperature by employing the nonequilibrium Green function technique. The currents exhibit coherent behaviors which are strongly associated with the applied QMF. The time-dependent currents appear compound effects of resonant tunneling and time-oscillating evolution. The time-averaged current and differential conductance are calculated, which manifest photon-assisted behaviors. Numerical calculations reveal the similar properties as those in classical microwave field (CMF) perturbed system for the situations concerning CS and squeezed vacuum SU(1,1) CS. But for other squeezed SU(1,1) CS, the tunneling behavior is quite different from the system perturbed by a single CMF through gate. Due to the quantum signal perturbation, the measurable quantities fluctuate fiercely. Received 28 May 1998     

Semiclassical theory of integrable and rough Andreev billiards

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations. Received 21 August 1999 and Received in final form 21 March 2001     

Low-temperature resistance of DNA-templated nanowires

We present low-temperature measurements of the electrical conductivity of metallic nanowires assembled on single DNA molecules by chemical deposition of a thin continuous palladium film. The investigated nanowires exhibit ohmic transport behaviour at room temperature. At low temperature we observe an increase of resistance with decreasing temperature that follows a logarithmic dependence. This behaviour can be described with quantum effects in a disordered metallic film. Received: 4 October 2001 / Accepted: 12 December 2001 / Published online: 20 March 2002     

Atomic reflection from a magnetic mirror: Beyond the adiabatic approximation

We present theoretical calculations for the reflection of atoms from a magnetic surface with a sinusoidal magnetization. A fully quantum mechanical treatment is possible because the problem may be reduced to an effective one-dimensional one. Results of numerical wave-packet calculations are presented and compared with an analytical model in which the atoms separate into different internal state components which follow classical paths in different potentials. Received 21 October 1999 and Received in final form 18 January 2000     

Model calculations of diffusion limited trapping dynamics in quantum well laser structures

We present a phenomenological theoretical model to treat the trapping of carriers into quantum wells of semiconductor laser structures. We consider explicitely the transport within the barrier layers by solving the continuity equation with the appropriate boundary conditions taking into account surface recombination, radiative and nonradiative recombination in the barrier layers and trapping of carriers into the quantum wells. The experimental findings for the trapping dynamics in GaAs/AlGaAs quantum well structures can be consistently interpreted by the model calculations.     

Electrical transport measurements on single-walled carbon nanotubes

We review transport measurements on single-walled carbon nanotubes contacted by metal electrodes. At room temperature some devices show transistor action similar to that of p-channel field effect transistors, while others behave as gate-voltage independent wires. At low temperatures transport is usually dominated by Coulomb blockade. In this regime the quantum eigenstates of the finite-length tubes can be studied. At higher temperatures power law behaviour is observed for the temperature and bias dependence of the conductance. This is consistent with tunneling into a one-dimensional Luttinger liquid in a nanotube. We also discuss recent developments in contacting nanotubes which should soon allow study of their intrinsic transport properties. Received: 17 May 1999 / Accepted 18 May 1999 / Published online: 4 August 1999     

Two-dimensional electron systems in inversion layers of p-type Hg0.8Zn0.2Te metal-insulator-semiconductor structures

Strong oscillations on capacitance and conductance have been observed in p-type Hg0.8Zn0.2Te metal-insulator-semiconductor structures, made by using a recent process for the interface passivation. This behaviour is attributed to a two-dimensional electron gas in the n-inversion layer and the variation of the conductance maximums with temperature indicates that the dominant perpendicular transport mechanism for electrons is an incoherent two-step tunnelling through deep levels in the gap. Three models have been used to describe the quantum confinement: the simple variational method, the triangular potential approximation and the propagation matrix method. The later approach takes into account the non parabolicity of the conduction band structure and uses a finite height barrier at the insulator-semiconductor interface. A very good agreement between experimental and calculated values for the two lowest subband energy is obtained. Received 9 February 1999     

Molecular fusion of fullerenes

New experimental data is reported for the absolute cross sections for the fusion reaction channel in single gas-phase collisions between fullerenes. The experimental data is compared with the results of quantum mechanical and classical molecular dynamics simulations as well as with simple models. Quantum molecular dynamics simulations are in very good quantitative agreement with the experimental data. The overall dynamical behaviour can be well-described qualitatively in the framework of simple models. Received 2 October 2000     

Interpretation of the magnetoresistance in doped magnetic tunnel junctions

We present a quantum mechanical model of the magnetoresistance in ferromagnetic tunnel junctions artificially doped by the introduction of layers of impurities in the middle of the barrier. The electron transport across the barrier is described by a combination of direct tunneling, tunneling assisted by spin-conserving scattering and tunneling assisted by spin-flip scattering. With this model, we interpret recent experimental results concerning the dependence of the TMR amplitude on the amount of impurities in the barrier and on temperature. Received 1st February 2001 and Received in final form 14 June 2001     

Macroscopic quantum coherence of the Neel vector in antiferromagnetic system without Kramers' degeneracy

At low temperatures the Neel vector in a small antiferromagnetic particle can possess quantum coherence between the classically degenerate minima. In some cases, the topological term in the magnetic action can lead to destructive interference between the symmetry-related trajectories for the half-integer excess spin antiferromagnetic particle. By studying a macroscopic quantum coherence problem of the Neel vector with biaxial crystal symmetry and a weak magnetic field applied along the hard axis, we find that the quenching of tunnel splitting could take place in the system without Kramers' degeneracy. Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factors are found exactly for the tunnel splitting. Results show that the tunnel splitting oscillates with the weak applied magnetic field for both the integer and half-integer excess spin antiferromagnetic particles, and vanishes at certain values of the field. All the calculations are performed based on the two sublattices model and the instanton method in spin-coherent-state path integral. Received: 24 July 1997 / Accepted: 30 September 1997     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Complex-Domain Semiclassical Theory: Application to Time-Dependent Barrier Tunneling Problems

Semiclassical theory based upon complexified classical mechanics is developed for periodically time-dependent scattering systems, which are minimal models of multi-dimensional systems. Semiclassical expression of the wave-matrix is derived, which is represented as the sum of the contributions from classical trajectories, where all the dynamical variables as well as the time are extended to the complex-domain. The semiclassical expression is examined by a periodically perturbed 1D barrier system and an excellent agreement with the fully quantum result is confirmed. In a stronger perturbation regime, the tunneling component of the wave-matrix exhibits a remarkable interference fringes, which is clarified by the semiclassical theory as an interference among multiple complex tunneling trajectories. It turns out that such a peculiar behavior is the manifestation of an intrinsic multi-dimensional effect closely related to a singular movement of singularities possessed by the complex classical trajectories.     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Smoothed wave functions of chaotic quantum systems

It is shown that wave functions of quantum systems as ħ → 0 have an extra density near unstable periodic trajectories of the classical problem. The averaged wave function square is represented as the sum over a finite number of periodic trajectories. The contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory. The results are compared with the numerical calculations of the wave functions for the stadium billiard.