arXiv subjects

C. W. J. Beenakker

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

At least 271 records · Page 15Linked to original sources

arXiv1999

Effect of Dephasing on Charge-Counting Statistics in Chaotic Cavities

We calculate the cumulants of the charge transmitted through a chaotic cavity in the limit that the two openings have a large number of scattering channels. The shot noise, which is the second cumulant, is known to be insensitive to dephasing in this limit. Unexpectedly, the fourth and higher cumulants are found to depend on dephasing: A semiclassical theory and a quantum mechanical model with strong dephasing give a different result than a fully phase-coherent quantum mechanical theory.

cond-mat↗

arXiv1999

Radiative transfer theory for vacuum fluctuations

A semiclassical kinetic theory is presented for the fluctuating photon flux emitted by a disordered medium in thermal equilibrium. The kinetic equation is the optical analog of the Boltzmann-Langevin equation for electrons. Vacuum fluctuations of the electromagnetic field provide a new source of fluctuations in the photon flux, over and above the fluctuations due to scattering. The kinetic theory in the diffusion approximation is applied to the super-Poissonian noise due to photon bunching and to the excess noise due to beating of incident radiation with the vacuum fluctuations.

cond-mat.mes-hall↗

arXiv1999

Large Petermann factor in chaotic cavities with many scattering channels

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. The average Petermann factor $ $ in an ensemble of cavities with chaotic scattering and broken time-reversal symmetry is calculated non-perturbatively using random-matrix theory and the supersymmetry technique, as a function of the decay rate $Γ$ of the lasing mode and the number of scattering channels N. 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

High-frequency dynamics of wave localisation

We study the effect of localisation on the propagation of a pulse through a multi-mode disordered waveguide. The correlator of the transmitted wave amplitude u at two frequencies differing by delta_omega has for large delta_omega the stretched exponential tail ~exp(-sqrt{tau_D delta_omega/2}). The time constant tau_D=L^2/D is given by the diffusion coefficient D, even if the length L of the waveguide is much greater than the localisation length xi. Localisation has the effect of multiplying the correlator by a frequency-independent factor exp(-L/2xi), which disappears upon breaking time-reversal symmetry.

cond-mat.dis-nn↗

arXiv1999

Distribution of the reflection eigenvalues of a weakly absorbing chaotic cavity

The scattering-matrix product SS+ of a weakly absorbing medium is related by a unitary transformation to the time-delay matrix without absorption. It follows from this relationship that the eigenvalues of SS+ for a weakly absorbing chaotic cavity are distributed according to a generalized Laguerre ensemble.

cond-mat.dis-nn↗

arXiv1999

Shot-noise in non-degenerate semiconductors with energy-dependent elastic scattering

We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. The shot-noise power P is suppressed below the Poisson value P_{\rm Poisson}=2e\bar I (at mean current \bar I) by the Coulomb repulsion of the carriers. We consider a power-law dependence of the elastic scattering time τ\proptoε^α on kinetic energy εand present an exact solution of the non-linear kinetic equations in the regime of space-charge limited conduction. The ratio P/P_{\rm Poisson} decreases from 0.38 to 0 in the range -1/2 < α< 1.

cond-mat.mes-hall↗

arXiv1999

Photon shot noise

A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/I (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Buttiker's formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to 1 (as for a Poisson process). Absorption and amplification both increase the Fano factor above the Poisson value. For strong absorption P/I has the universal limit 1+3f/2 with f the Bose-Einstein function at the frequency of the incident radiation. This is the optical analogue of the one-third reduction factor of electronic shot noise in diffusive conductors. In the amplifying case the Fano factor diverges at the laser threshold, while the signal-to-noise ratio I^2/P reaches a finite, universal limit.

cond-mat.mes-hall↗

arXiv1999

Quantum-limited linewidth of a chaotic laser cavity

A random-matrix theory is presented for the linewidth of a laser cavity in which the radiation is scattered chaotically. The linewidth is enhanced above the Schawlow-Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. The factor K is expressed in terms of a non-Hermitian random matrix and its distribution is calculated exactly for the case that the cavity is coupled to the outside via a small opening. The average of K is found to depend non-analytically on the area of the opening, and to greatly exceed the most probable value.

chao-dyn↗

arXiv1999

Kinetic theory of shot noise in non-degenerate diffusive conductors

We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the non-linear kinetic equations in the regime of space-charge limited conduction, without resorting to the drift approximation of previous work. By including the effects of a finite voltage and carrier density in the contact region, a quantitative agreement is obtained with Monte Carlo simulations by Gonz{á}lez et al., for a model of an energy-independent elastic scattering rate. The shot-noise power $P$ is suppressed below the Poisson value $P_{Poisson}=2e\bar I$ (at mean current $\bar I$) by the Coulomb repulsion of the carriers. The exact suppression factor is close to 1/3 in a three-dimensional system, in agreement with the simulations and with the drift approximation. Including an energy dependence of the scattering rate has a small effect on the suppression factor for the case of short-range scattering by uncharged impurities or quasi-elastic scattering by acoustic phonons. Long-range scattering by charged impurities remains an open problem.

cond-mat.mes-hall↗

arXiv1999

Excess noise for coherent radiation propagating through amplifying random media

A general theory is presented for the photodetection statistics of coherent radiation that has been amplified by a disordered medium. The beating of the coherent radiation with the spontaneous emission increases the noise above the shot-noise level. The excess noise is expressed in terms of the transmission and reflection matrices of the medium, and evaluated using the methods of random-matrix theory. Inter-mode scattering between $N$ propagating modes increases the noise figure by up to a factor of $N$, as one approaches the laser threshold. Results are contrasted with those for an absorbing medium.

quant-ph↗

arXiv1998

Sub-Poissonian shot noise in non-degenerate diffusive conductors

A theory is presented for the universal reduction of shot noise by Coulomb repulsion, which was observed in computer simulations of a disordered non-degenerate electron gas by Gonzalez et al. (cond-mat/9803372). The universality of the reduction below the uncorrelated value is explained as a feature of the high-voltage regime of space-charge limited conduction. The reduction factor depends on the dimensionality d of the density of states, being close but not quite equal to 1/d in two and three dimensions.

cond-mat.mes-hall↗

arXiv1998

Non-Cayley-tree model for quasiparticle decay in a quantum dot

The decay of a quasiparticle in a confined geometry, resulting from electron-electron interactions, has been mapped onto the single-electron problem of diffusion on a Cayley tree by Altshuler et al. [Phys.Rev.Lett. 78, 2803 (1997)]. We study an alternative model, that captures the strong correlations between the self-energies of different excitations with the same number of quasiparticles. The model has a recursion relation for the single-particle density of states that is markedly different from the Cayley tree. It remains tractable enough that sufficiently large systems can be studied to observe the localization transition in Fock space predicted by Altshuler et al.

cond-mat.mes-hall↗

arXiv1998

Excitation spectrum of Andreev billiards with a mixed phase space

We present a semiclassical theory for the excitation spectrum of a ballistic quantum dot weakly coupled to a superconductor, for the generic situation that the classical motion gives rise to a phase space containing islands of regularity in a chaotic sea. The density of low-energy excitations is determined by quantum energy scales that are related in a simple way to the morphology of the mixed phase space. An exact quantum mechanical computation for the annular billiard shows good agreement with the semiclassical predictions, in particular for the reduction of the excitation gap when the coupling to the regular regions is maximal.

cond-mat.mes-hall↗

arXiv1998

Long-range correlation of thermal radiation

A general theory is presented for the spatial correlations in the intensity of the radiation emitted by a random medium in thermal equilibrium. We find that a non-zero correlation persists over distances large compared to the transverse coherence length of the thermal radiation. This long-range correlation vanishes in the limit of an ideal black body. We analyze two types of systems (a disordered waveguide and an optical cavity with chaotic scattering) where it should be observable.

quant-ph↗

arXiv1998

Distribution of the quantum mechanical time-delay matrix for a chaotic cavity

We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-i\hbar S^{-1} \partial S/\partial ε$ and the scattering matrix $S$ for scattering from a chaotic cavity with ideal point contacts. Hereto we prove a conjecture by Wigner about the unitary invariance property of the distribution functional $P[S(ε)]$ of energy dependent scattering matrices $S(ε)$. The distribution of the inverse of the eigenvalues $τ_1,...,τ_N$ of $Q$ is found to be the Laguerre ensemble from random-matrix theory. The eigenvalue density $ρ(τ)$ is computed using the method of orthogonal polynomials. This general theory has applications to the thermopower, magnetoconductance, and capacitance of a quantum dot.

cond-mat.mes-hall↗

arXiv1998

Photon statistics of a random laser

A general relationship is presented between the statistics of thermal radiation from a random medium and its scattering matrix S. Familiar results for black-body radiation are recovered in the limit S to 0. The mean photocount is proportional to the trace of 1-SS^dagger, in accordance with Kirchhoff's law relating emissivity and absorptivity. Higher moments of the photocount distribution are related to traces of powers of 1-SS^dagger, a generalization of Kirchhoff's law. The theory can be applied to a random amplifying medium (or "random laser") below the laser threshold, by evaluating the Bose-Einstein function at a negative temperature. Anomalously large fluctuations are predicted in the photocount upon approaching the laser threshold, as a consequence of overlapping cavity modes with a broad distribution of spectral widths.

quant-ph↗

arXiv1998

Thermal radiation and amplified spontaneous emission from a random medium

We compute the statistics of thermal emission from systems in which the radiation is scattered chaotically, by relating the photocount distribution to the scattering matrix - whose statistical properties are known from random-matrix theory. We find that the super-Poissonian noise is that of a black body with a reduced number of degrees of freedom. The general theory is applied to a disordered slab and to a chaotic cavity, and is extended to include amplifying as well as absorbing systems. We predict an excess noise of amplified spontaneous emission in a random laser below the laser threshold.

quant-ph↗

arXiv1998

Berry phase and adiabaticity of a spin diffusing in a non-uniform magnetic field

An electron spin moving adiabatically in a strong, spatially non-uniform magnetic field accumulates a geometric phase or Berry phase, which might be observable as a conductance oscillation in a mesoscopic ring. Two contradicting theories exist for how strong the magnetic field should be to ensure adiabaticity if the motion is diffusive. To resolve this controversy, we study the effect of a non-uniform magnetic field on the spin polarization and on the weak-localization effect. The diffusion equation for the Cooperon is solved exactly. Adiabaticity requires that the spin-precession time is short compared to the elastic scattering time - it is not sufficient that it is short compared to the diffusion time around the ring. This strong condition severely complicates the experimental observation.

cond-mat.mes-hall↗