Fritz Haake - Academia.edu (original) (raw)
Papers by Fritz Haake
Europhysics Letters (EPL), 1989
Recent experiments on superfluorescence from O2- centres in KCl host crystals, with quasi-one-dim... more Recent experiments on superfluorescence from O2- centres in KCl host crystals, with quasi-one-dimensional active volumes, have shown identically shaped and perfectly synchronized forward and backward pulses in each run. This is in blatant contrast to previous experiments on atomic beams and gases in which no forward-backward correlation beyond energy conservation had been found. We argue that a linear coupling due
Physica B+C, 1982
ABSTRACT
Journal of Physics a Mathematical and General, Mar 17, 2006
We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predic... more We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a semiclassical approach we evaluate the contributions of quadruplets of classical trajectories to shot noise. Our approach can be extended to a variety of transport phenomena as illustrated for the crossover between symmetry classes in the presence of a weak magnetic field. 72.20.My, 72.15.Rn, 05.45.Mt, 03.65.Sq Ballistic chaotic cavities have universal transport properties, just as do disordered conductors. The explanation of such universality cannot rely on any disorder average but must make do with chaos in an individual clean cavity. We shall present here the semiclassical explanation of shot noise, relating the quantum properties of chaotic cavities to the interference between contributions of mutually close classical trajectories. Similar methods have recently been used for explaining universal spectral fluctuations of chaotic quantum systems [1, 2], and to calculate the universal mean conductance in .
We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical... more We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a “quantum smoothened” approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.
J Math Phys, 1996
For a simple model describing the S-matrices of open resonators the statistical properties of the... more For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator.
Phys Rev a, 1995
We discuss the fate of initial states of the Schrödinger cat type for the damped harmonic oscilla... more We discuss the fate of initial states of the Schrödinger cat type for the damped harmonic oscillator, mostly employing a linear version of the stochastic Schrödinger equation. We also comment on how such cat states might be prepared and on the relation of single realizations of the noise to single runs of experiments.
A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonaliz... more A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonalizing the semiclassically approximated Floquet matrix. Classical orbits between prescribed initial and final points, real or of the ghost type, were incurred for the matrix elements rather than periodic orbits which arise in the Gutzwiller approach. In lowest order in ħ an accuracy of roughly 3% of the mean spacing was obtained for the quasienergies. We here extend the analysis to the next-to-leading order in ħ for the Floquet matrix. The accuracy for the quasienergy spectrum improves accordingly. Moreover, we thus explain why the previous leading-order treatment gave the mentioned 3% accuracy.
A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonaliz... more A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonalizing the semiclassically approximated Floquet matrix. Classical orbits between prescribed initial and final points, real or of the ghost type, were incurred for the matrix elements rather than periodic orbits which arise in the Gutzwiller approach. In lowest order in ħ an accuracy of roughly 3% of the mean spacing was obtained for the quasienergies. We here extend the analysis to the next-to-leading order in ħ for the Floquet matrix. The accuracy for the quasienergy spectrum improves accordingly. Moreover, we thus explain why the previous leading-order treatment gave the mentioned 3% accuracy.
Phys Rev a, 1989
The problem of reducing the contributions of pump and spontaneous-emission noise to the output no... more The problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field is studied. Two models based on an atomic medium are considered, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation, the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Dec 1, 2003
We investigate the correspondence between the decay of correlation in classical systems, governed... more We investigate the correspondence between the decay of correlation in classical systems, governed by Ruelle-Pollicott resonances, and the properties of the corresponding quantum systems. For this purpose we construct classical dynamics with controllable resonances together with their quantum counterparts. As an application of such tunable resonances we reveal the role of Ruelle-Pollicott resonances for the localization properties of quantum energy eigenstates.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Dec 1, 2003
We investigate the correspondence between the decay of correlation in classical systems, governed... more We investigate the correspondence between the decay of correlation in classical systems, governed by Ruelle-Pollicott resonances, and the properties of the corresponding quantum systems. For this purpose we construct classical dynamics with controllable resonances together with their quantum counterparts. As an application of such tunable resonances we reveal the role of Ruelle-Pollicott resonances for the localization properties of quantum energy eigenstates.
Zeitschrift für Physik B Condensed Matter
We discuss a top undergoing constant precession around a magnetic field and suffering a periodic ... more We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.
We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) pro... more We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) propagator for phase-space (quasi-)probability densities in a Hamiltonian system displaying a mix of regular and chaotic behavior. We focus on common resonances of these operators which we determine by blurring phase-space resolution. We demonstrate that classical and quantum time evolution look alike if observed with a resolution much coarser than a Planck cell and explain how this similarity arises for the propagators as well as their spectra. The indistinguishability of blurred quantum and classical evolution implies that classical resonances can conveniently be determined from quantum mechanics and in turn become effective for decay rates of quantum correlations.
Physical Review Letters
We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid... more We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid under conditions of both regular and chaotic classical motion. In contrast to conventional periodic-orbit theory we implement the semiclassical limit for each matrix element of the Floquet operator rather than for the trace of the propagator. Even though a classical looking action is involved, the approximate matrix elements are specified in terms of complex ghost trajectories instead of real classical orbits. Our mean error for the quasienergies is a surprisingly small 3% of the mean spacing.
Physical Review Letters
We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid... more We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid under conditions of both regular and chaotic classical motion. In contrast to conventional periodic-orbit theory we implement the semiclassical limit for each matrix element of the Floquet operator rather than for the trace of the propagator. Even though a classical looking action is involved, the approximate matrix elements are specified in terms of complex ghost trajectories instead of real classical orbits. Our mean error for the quasienergies is a surprisingly small 3% of the mean spacing.
Physical Review Letters
Feshbach's projector technique is employed to quantize the electromagnetic field in optical reson... more Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.
Physical Review Letters
Feshbach's projector technique is employed to quantize the electromagnetic field in optical reson... more Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.
Europhysics Letters (EPL), 1989
Recent experiments on superfluorescence from O2- centres in KCl host crystals, with quasi-one-dim... more Recent experiments on superfluorescence from O2- centres in KCl host crystals, with quasi-one-dimensional active volumes, have shown identically shaped and perfectly synchronized forward and backward pulses in each run. This is in blatant contrast to previous experiments on atomic beams and gases in which no forward-backward correlation beyond energy conservation had been found. We argue that a linear coupling due
Physica B+C, 1982
ABSTRACT
Journal of Physics a Mathematical and General, Mar 17, 2006
We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predic... more We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a semiclassical approach we evaluate the contributions of quadruplets of classical trajectories to shot noise. Our approach can be extended to a variety of transport phenomena as illustrated for the crossover between symmetry classes in the presence of a weak magnetic field. 72.20.My, 72.15.Rn, 05.45.Mt, 03.65.Sq Ballistic chaotic cavities have universal transport properties, just as do disordered conductors. The explanation of such universality cannot rely on any disorder average but must make do with chaos in an individual clean cavity. We shall present here the semiclassical explanation of shot noise, relating the quantum properties of chaotic cavities to the interference between contributions of mutually close classical trajectories. Similar methods have recently been used for explaining universal spectral fluctuations of chaotic quantum systems [1, 2], and to calculate the universal mean conductance in .
We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical... more We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a “quantum smoothened” approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.
J Math Phys, 1996
For a simple model describing the S-matrices of open resonators the statistical properties of the... more For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator.
Phys Rev a, 1995
We discuss the fate of initial states of the Schrödinger cat type for the damped harmonic oscilla... more We discuss the fate of initial states of the Schrödinger cat type for the damped harmonic oscillator, mostly employing a linear version of the stochastic Schrödinger equation. We also comment on how such cat states might be prepared and on the relation of single realizations of the noise to single runs of experiments.
A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonaliz... more A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonalizing the semiclassically approximated Floquet matrix. Classical orbits between prescribed initial and final points, real or of the ghost type, were incurred for the matrix elements rather than periodic orbits which arise in the Gutzwiller approach. In lowest order in ħ an accuracy of roughly 3% of the mean spacing was obtained for the quasienergies. We here extend the analysis to the next-to-leading order in ħ for the Floquet matrix. The accuracy for the quasienergy spectrum improves accordingly. Moreover, we thus explain why the previous leading-order treatment gave the mentioned 3% accuracy.
A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonaliz... more A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonalizing the semiclassically approximated Floquet matrix. Classical orbits between prescribed initial and final points, real or of the ghost type, were incurred for the matrix elements rather than periodic orbits which arise in the Gutzwiller approach. In lowest order in ħ an accuracy of roughly 3% of the mean spacing was obtained for the quasienergies. We here extend the analysis to the next-to-leading order in ħ for the Floquet matrix. The accuracy for the quasienergy spectrum improves accordingly. Moreover, we thus explain why the previous leading-order treatment gave the mentioned 3% accuracy.
Phys Rev a, 1989
The problem of reducing the contributions of pump and spontaneous-emission noise to the output no... more The problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field is studied. Two models based on an atomic medium are considered, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation, the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Dec 1, 2003
We investigate the correspondence between the decay of correlation in classical systems, governed... more We investigate the correspondence between the decay of correlation in classical systems, governed by Ruelle-Pollicott resonances, and the properties of the corresponding quantum systems. For this purpose we construct classical dynamics with controllable resonances together with their quantum counterparts. As an application of such tunable resonances we reveal the role of Ruelle-Pollicott resonances for the localization properties of quantum energy eigenstates.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Dec 1, 2003
We investigate the correspondence between the decay of correlation in classical systems, governed... more We investigate the correspondence between the decay of correlation in classical systems, governed by Ruelle-Pollicott resonances, and the properties of the corresponding quantum systems. For this purpose we construct classical dynamics with controllable resonances together with their quantum counterparts. As an application of such tunable resonances we reveal the role of Ruelle-Pollicott resonances for the localization properties of quantum energy eigenstates.
Zeitschrift für Physik B Condensed Matter
We discuss a top undergoing constant precession around a magnetic field and suffering a periodic ... more We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.
We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) pro... more We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) propagator for phase-space (quasi-)probability densities in a Hamiltonian system displaying a mix of regular and chaotic behavior. We focus on common resonances of these operators which we determine by blurring phase-space resolution. We demonstrate that classical and quantum time evolution look alike if observed with a resolution much coarser than a Planck cell and explain how this similarity arises for the propagators as well as their spectra. The indistinguishability of blurred quantum and classical evolution implies that classical resonances can conveniently be determined from quantum mechanics and in turn become effective for decay rates of quantum correlations.
Physical Review Letters
We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid... more We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid under conditions of both regular and chaotic classical motion. In contrast to conventional periodic-orbit theory we implement the semiclassical limit for each matrix element of the Floquet operator rather than for the trace of the propagator. Even though a classical looking action is involved, the approximate matrix elements are specified in terms of complex ghost trajectories instead of real classical orbits. Our mean error for the quasienergies is a surprisingly small 3% of the mean spacing.
Physical Review Letters
We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid... more We present anh ! 0 approximation for the quasienergy spectrum of a periodically kicked top, valid under conditions of both regular and chaotic classical motion. In contrast to conventional periodic-orbit theory we implement the semiclassical limit for each matrix element of the Floquet operator rather than for the trace of the propagator. Even though a classical looking action is involved, the approximate matrix elements are specified in terms of complex ghost trajectories instead of real classical orbits. Our mean error for the quasienergies is a surprisingly small 3% of the mean spacing.
Physical Review Letters
Feshbach's projector technique is employed to quantize the electromagnetic field in optical reson... more Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.
Physical Review Letters
Feshbach's projector technique is employed to quantize the electromagnetic field in optical reson... more Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.