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C. W. J. Beenakker

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

At least 289 records · Page 16Linked to original sources
arXiv1997

Thermopower of Single-Channel Disordered and Chaotic Conductors

We show (analytically and by numerical simulation) that the zero-temperature limit of the distribution of the thermopower S of a one-dimensional disordered wire in the localized regime is a Lorentzian, with a disorder-independent width of 4 pi^3 k_B^2 T/3eΔ(where T is the temperature and Δthe mean level spacing). Upon raising the temperature the distribution crosses over to an exponential form exp(-2|S|eT/Δ). We also consider the case of a chaotic quantum dot with two single-channel ballistic point contacts. The distribution of S then has a cusp at S=0 and a tail |S|^{-1-β} log|S| for large S (with β=1,2 depending on the presence or absence of time-reversal symmetry).

cond-mat.dis-nn↗
arXiv1997

Lasing Threshold and Mode Competition in Chaotic Cavities

The lasing threshold is studied of a multi-mode chaotic cavity (linear size D >> wavelength λ) coupled to the outside through a small hole (linear size d << λ). For sufficiently weak absorption by the boundaries, the statistical distribution of the threshold is wide, its mean value being much less than the pumping rate needed to compensate the average loss. The average number N_{nc} >> 1 of non-competing excited modes is proportional to the square root of the pumping rate. We use the classical model of spatial hole burning to account for mode competition and find a reduction in the average number of excited modes to N =3^{1/3} N_{nc}^{2/3}.

chao-dyn↗
arXiv1997

Reflection of light from a disordered medium backed by a phase-conjugating mirror

This is a theoretical study of the interplay of optical phase-conjugation and multiple scattering. We calculate the intensity of light reflected by a phase-conjugating mirror when it is placed behind a disordered medium. We compare the results of a fully phase-coherent theory with those from the theory of radiative transfer. Both methods are equivalent if the dwell time τ_{dwell} of a photon in the disordered medium is much larger than the inverse of the frequency shift 2Δωacquired at the phase-conjugating mirror. When τ_{dwell} Δω< 1, in contrast, phase coherence drastically affects the reflected intensity. In particular, a minimum in the dependence of the reflectance on the disorder strength disappears when Δωis reduced below 1/τ_{dwell}. The analogies and differences with Andreev reflection of electrons at the interface between a normal metal and a superconductor are discussed.

physics.optics↗
arXiv1997

Spontaneous Emission in Chaotic Cavities

The spontaneous emission rate Γof a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing N wavechannels, the distribution of Γis given by P(Γ) \propto Γ^{N/2-1}(Γ+Γ_0)^{-N-1}, where Γ_0 is the free-space rate. For small N the most probable value of Γis much smaller than the mean value Γ_0.

chao-dyn↗
arXiv1997

Quantum mechanical time-delay matrix in chaotic scattering

We calculate the probability distribution of the matrix Q = -i \hbar S^{-1} dS/dE for a chaotic system with scattering matrix S at energy E. The eigenvalues τ_j of Q are the so-called proper delay times, introduced by E. P. Wigner and F. T. Smith to describe the time-dependence of a scattering process. The distribution of the inverse delay times turns out to be given by the Laguerre ensemble from random-matrix theory.

chao-dyn↗
arXiv1997

Theory of directed localization in one dimension

We present an analytical solution of the delocalization transition that is induced by an imaginary vector potential in a disordered chain [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996), cond-mat/9603165]. We compute the relation between the real and imaginary parts of the energy in the thermodynamic limit, as well as finite-size effects. The results are in good agreement with numerical simulations for weak disorder (mean free path large compared to the wavelength).

cond-mat.mes-hall↗
arXiv1997

Distribution of parametric conductance derivatives of a quantum dot

The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX and $\sqrt{G(1-G)}$ is independent of G. Coulomb interactions change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can be tested in semiconductor microstructures or microwave cavities.

cond-mat.mes-hall↗
arXiv1996

Random-Matrix Theory of Quantum Transport

This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.

cond-mat.mes-hall↗
arXiv1996

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.

cond-mat.mes-hall↗
arXiv1996

Fluctuating "order parameter" for a quantum chaotic system with partially broken time-reversal symmetry

The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking time-reversal symmetry, the order parameter crosses over from one to zero. We compute its distribution in the crossover regime and find that it has large fluctuations around the ensemble average. These fluctuations imply long-range spatial correlations in the eigenfunction and non-Gaussian perturbations of eigenvalues, in precise agreement with results by Fal'ko and Efetov and by Taniguchi, Hashimoto, Simons, and Altshuler. As a third implication of the order-parameter fluctuations we find correlations in the response of an eigenvalue to independent perturbations of the system.

cond-mat↗
arXiv1996

Brightness of a phase-conjugating mirror behind a random medium

A random-matrix theory is presented for the reflection of light by a disordered medium backed by a phase-conjugating mirror. Two regimes are distinguished, depending on the relative magnitude of the inverse dwell time of a photon in the disordered medium and the frequency shift acquired at the mirror. The qualitatively different dependence of the reflectance on the degree of disorder in the two regimes suggests a distinctive experimental test for cancellation of phase shifts in a random medium.

cond-mat↗
arXiv1996

Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant $ε= ε'+iε''$. Depending on the sign of $ε''$, the medium is absorbing or amplifying. The transmitted intensity decays exponentially $\propto\exp(-L/ξ)$ as the waveguide length $L\to\infty$, regardless of the sign of $ε''$. The localization length $ξ$ is computed as a function of the mean free path $l$, the absorption or amplification length $|σ|^{-1}$, and the number of modes in the waveguide $N$. The method used is an extension of the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar to non-unitary scattering matrices. Asymptotically exact results are obtained for $N\gg1$ and $|σ|\gg1/N^2l$. An approximate interpolation formula for all $σ$ agrees reasonably well with numerical simulations.

cond-mat↗
arXiv1996

Reflectance Fluctuations in an Absorbing Random Waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $γ$ per mean free path. Two distinct regimes are identified. The regime $γN^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $γN^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-γN$.

cond-mat↗
arXiv1996

Phase-dependent magnetoconductance fluctuations in a chaotic Josephson junction

Motivated by recent experiments by Den Hartog et al., we present a random-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot which is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuations as a function of the magnetic field through the quantum dot and $2π$-periodic fluctuations as a function of the phase difference $ϕ$ of the superconductors. If the coupling to the superconductors is weak compared to the coupling to the normal metals, the $ϕ$-dependence of the conductance is harmonic, as observed in the experiment. In the opposite regime, the conductance becomes a random $2π$-periodic function of $ϕ$, in agreement with the theory of Altshuler and Spivak. The theoretical method employs an extension of the circular ensemble which can describe the magnetic field dependence of the scattering matrix.

cond-mat↗
arXiv1996

Superconductor-proximity effect in chaotic and integrable billiards

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.

cond-mat↗
arXiv1996

Induced superconductivity distinguishes chaotic from integrable billiards

Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for a non-chaotic rectangular billiard, and it is argued that this is generic for integrable systems.

cond-mat↗
arXiv1996

Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field

A theory is presented for the statistics of the excitation spectrum of a disordered metal grain in contact with a superconductor. A magnetic field is applied to fully break time-reversal symmetry in the grain. Still, an excitation gap of the order of $δ$ opens up provided $NΓ^2\gtrsim 1$. Here $δ$ is the mean level spacing in the grain, $Γ$ the tunnel probability through the contact with the superconductor, and $N$ the number of transverse modes in the contact region. This provides a microscopic justification for the new random-matrix ensemble of Altland and Zirnbauer.

cond-mat↗