arXiv subjects

C. W. J. Beenakker

Publications and source records attributed to C. W. J. Beenakker.

At least 253 records · Page 14Linked to original sources

arXiv2001

Can mesoscopic fluctuations reverse the supercurrent through a disordered Josephson junction?

We calculate the Josephson coupling energy $U_J(ϕ)$ (related to the supercurrent $I=(2e/\hbar) dU_J/dϕ$) for a disordered normal metal between two superconductors with a phase difference $ϕ$. We demonstrate that the symmetry of the scattering matrix of non-interacting quasiparticles in zero magnetic field implies that $U_J(ϕ)$ has a minimum at $ϕ=0$. A maximum (that would lead to a $π$-junction or negative superfluid density) is excluded for any realization of the disorder.

cond-mat.mes-hall↗

arXiv2001

Andreev levels in a single-channel conductor

We calculate the subgap density of states of a disordered single-channel normal metal connected to a superconductor at one end (NS junction) or at both ends (SNS junction). The probability distribution of the energy of a bound state (Andreev level) is broadened by disorder. In the SNS case the two-fold degeneracy of the Andreev levels is removed by disorder leading to a splitting in addition to the broadening. The distribution of the splitting is given precisely by Wigner's surmise from random-matrix theory. For strong disorder the mean density of states is largely unaffected by the proximity to the superconductor, because of localization, except in a narrow energy region near the Fermi level, where the density of states is suppressed with a log-normal tail.

cond-mat.mes-hall↗

arXiv2001

Effect of inelastic scattering on the average Coulomb-blockade peak height in quantum dots

The average height of the Coulomb-blockade conductance peaks for chaotic elastic scattering is known to increase by a factor of 4/3 upon breaking time-reversal symmetry. We calculate the temperature dependence of this factor in the regime that the inelastic scattering rate Gamma_in is greater than the mean tunneling rate Gamma_el, which itself is less than the mean level spacing Delta. Comparison with recent experimental data by Folk et al. (cond-mat/0008052) demonstrates that Gamma_in lies below Gamma_el and hence also below Delta, consistent with the low-energy suppression of inelastic electron-electron scattering in quantum dots.

cond-mat.mes-hall↗

arXiv2000

Limits to error correction in quantum chaos

We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy (B) and spin-spin interaction energy (J). A non-degenerate code with error rate kappa can recover the original state with high fidelity within a time kappa^1/2 / max(B,J) -- independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.

quant-ph↗

arXiv2000

Dynamics of localization in a waveguide

This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of a reflected pulse. The long-time dynamics is dominated by resonant transmission over length scales much larger than the localization length. The corresponding distribution of the Wigner-Smith delay times is the Laguerre ensemble of random-matrix theory. In the power spectrum the resonances show up as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode delay times the resonances introduce a dynamic coherent backscattering effect, that provides a way to distinguish localization from absorption.

cond-mat.dis-nn↗

arXiv2000

Counting statistics of photons produced by electronic shot noise

A theory is presented for the photodetection statistics of radiation produced by current fluctuations in a phase-coherent conductor. Deviations are found from the Poisson statistics that would result from a classical current. For detection in a narrow frequency interval, the photocount distribution has the negative-binomial form of black-body radiation if this frequency interval is less than the mean current in the conductor. When electronic localization sets in, a different type of super-Poissonian photon statistics results.

cond-mat.mes-hall↗

arXiv2000

Single-mode delay time statistics for scattering by a chaotic cavity

We investigate the low-frequency dynamics for transmission or reflection of a wave by a cavity with chaotic scattering. We compute the probability distribution of the phase derivative phi'=d phi/d omega of the scattered wave amplitude, known as the single-mode delay time. In the case of a cavity connected to two single-mode waveguides we find a marked distinction between detection in transmission and in reflection: The distribution P(phi') vanishes for negative phi' in the first case but not in the second case.

cond-mat.dis-nn↗

arXiv2000

Localization-induced coherent backscattering effect in wave dynamics

We investigate the statistics of single-mode delay times of waves reflected from a disordered waveguide in the presence of wave localization. The distribution of delay times is qualitatively different from the distribution in the diffusive regime, and sensitive to coherent backscattering: The probability to find small delay times is enhanced by a factor close to sqrt(2) for reflection angles near the angle of incidence. This dynamic effect of coherent backscattering disappears in the diffusive regime.

cond-mat.dis-nn↗

arXiv2000

Signature of wave localisation in the time dependence of a reflected pulse

The average power spectrum of a pulse reflected by a disordered medium embedded in an N-mode waveguide decays in time with a power law t^(-p). We show that the exponent p increases from 3/2 to 2 after N^2 scattering times, due to the onset of localisation. We compare two methods to arrive at this result. The first method involves the analytic continuation to imaginary absorption rate of a static scattering problem. The second method involves the solution of a Fokker-Planck equation for the frequency dependent reflection matrix, by means of a mapping onto a problem in non-Hermitian quantum mechanics.

cond-mat.dis-nn↗

arXiv2000

Universal gap fluctuations in the superconductor proximity effect

Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal function in rescaled units. Our analytical prediction for the gap distribution agrees well with exact diagonalization of a model Hamiltonian.

cond-mat.mes-hall↗

arXiv2000

Coherent backscattering effect on wave dynamics in a random medium

A dynamical effect of coherent backscattering is predicted theoretically and supported by computer simulations: The distribution of single-mode delay times of waves reflected by a disordered waveguide depends on whether the incident and detected modes are the same or not. The change amounts to a rescaling of the distribution by a factor close to $\sqrt{2}$. This effect appears only if the length of the waveguide exceeds the localization length; there is no effect of coherent backscattering on the delay times in the diffusive regime.

cond-mat.dis-nn↗

arXiv2000

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (``grey body'') and of an amplifying medium (``random laser'') are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold.

cond-mat.mes-hall↗

arXiv2000

Photonic excess noise and wave localization

This is a theory for the effect of localization on the super-Poissonian noise of radiation propagating through an absorbing disordered waveguide. Localization suppresses both the mean photon current I and the noise power P, but the Fano factor P/I is found to remain unaffected. For strong absorption the Fano factor has the universal value 1+3f/2 (with f the Bose-Einstein function), regardless of whether the waveguide is long or short compared to the localization length.

cond-mat.dis-nn↗

arXiv1999

Scaling at the chaos threshold in an interacting quantum dot

The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated numerically and compared with analytical predictions. Two distinct regimes are found in the dependence of the inverse participation ratio in Fock space I on the dimensionless conductance of the quantum dot g and the excitation energy E. In both regimes I>>1, but only the small-g regime is described by the golden rule. The crossover region is characterized by a maximum in a scaling function that becomes more pronounced with increasing excitation energy. The scaling parameter that governs the transition is (E/g)ln g.

cond-mat.mes-hall↗

arXiv1999

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.

cond-mat.dis-nn↗

arXiv1999

Quantum limit of the laser linewidth in chaotic cavities and statistics of residues of scattering matrix poles

The quantum-limited linewidth of a laser cavity is enhanced above the Schawlow-Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. We derive the relation between the Petermann factor and the residues of poles of the scattering matrix and investigate the statistical properties of the Petermann factor for cavities in which the radiation is scattered chaotically. For a single scattering channel we determine the complete probability distribution of K and find that the average Petermann factor $ $ depends non-analytically on the area of the opening, and greatly exceeds the most probable value. For an arbitrary number N of scattering channels we calculate $ $ as a function of the decay rate $Γ$ of the lasing mode. We find for $N\gg 1$ that for typical values of $Γ$ the average Petermann factor $ \propto \sqrt{N}\gg 1$ is parametrically larger than unity.

chao-dyn↗

arXiv1999

Search for two-scale localization in disordered wires in a magnetic field

The supersymmetry technique [A. V. Kolesnikov and K. B. Efetov, Phys. Rev. Lett. 83, 3689 (1999)] predicts a two-scale behavior of wavefunction decay in disordered wires in the crossover regime from preserved to broken time-reversal symmetry. We have tested this prediction by a transmission approach, relying on the Borland conjecture that relates the decay length of the transmittance to the decay length of the wavefunctions. Our numerical simulations show no indication of two-scale behavior.

cond-mat.dis-nn↗

arXiv1999

Propagation of squeezed radiation through amplifying or absorbing random media

We analyse how nonclassical features of squeezed radiation (in particular the sub-Poissonian noise) are degraded when it is transmitted through an amplifying or absorbing medium with randomly located scattering centra. Both the cases of direct photodetection and of homodyne detection are considered. Explicit results are obtained for the dependence of the Fano factor (the ratio of the noise power and the mean current) on the degree of squeezing of the incident state, on the length and the mean free path of the medium, the temperature, and on the absorption or amplification rate.

quant-ph↗