Microwave Studies of Billiard Green Functions and Propagators

Stein, J.; Stöckmann, H.-J.; Stoffregen, U.

doi:10.1103/physrevlett.75.53

Cited by 114 publications

(121 citation statements)

References 11 publications

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“…The quantity directly accessible in the experiment is the scattering matrix [21]. From a reflection measurement as a function of the antenna position a mapping of the modulus of the wave function can be obtained; to get the sign as well, the transmission between two antennas is needed.…”

Section: Methodsmentioning

confidence: 99%

Current and vortex statistics in microwave billiards

Barth

Stöckmann

2002

Phys. Rev. E

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Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system probability densities and currents were studied in a microwave billiard with a ferrite insert as well as in an open billiard. Distribution functions were obtained for probability densities, currents and vorticities. In addition the vortex pair correlation function could be extracted. For all studied quantities a complete agreement with the predictions from the random-superposition-of-plane-waves approach was obtained.

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Section: Methodsmentioning

confidence: 99%

Current and vortex statistics in microwave billiards

Barth

Stöckmann

2002

Phys. Rev. E

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“…With increasing frequency one typically observes a transition from localized to delocalized wave functions, depending on the number of scatterers and the strength of the scattering potential. Pulse propagation can be studied as well by microwave techniques as has been shown by Stein et al (1995). All quantities of interest are thus experimentally accessible in disordered systems, including conductivity, localizationdelocalization transitions, pulse propagation, transition from the ballistic to the diffusive regime, and so on.…”

Section: Motivationmentioning

confidence: 99%

A supersymmetry approach to billiards with randomly distributed scatterers

Stoeckmann¹

2002

J. Phys. A: Math. Gen.

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Abstract. The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N ×N matrix, an explicit analytic expression is obtained for the case of broken time-reversal symmetry, depending on rank N of the matrix, number L of scatterers, and strength of the scattering potential. In the strong coupling limit a discontinuous change is observed in the density of states as soon as L exceeds N .

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“…The distnbution of dG/3E (grand-canomcal ensemble) also has an algebraic tail [°c (dG/dE)~ß~2], while the distnbution of 8G/8Q (canomcal ensemble) is identically zero for |öG/ö<2l > π In both ensembles, the second moment of the conductance velocities is fimte for β = 2 and 4, but infinite for β = l [33] In conclusion, we have calculated the jomt distnbution of the conductance G and its parametric derivatives for a chaotic cavity, coupled to electron reservoirs by two smgle-mode balhstic point contacts The distnbution is fundamentally different from the multimode case, being highly non-Gaussian and with correlated deiivatives (Correlations between G and the parametric derivatives can be transfoimed away by a change of variables ) We account toi Coulomb mteractions by usmg a canomcal ensemble mstead of a grand-canomcal ensemble Our results foi the canomcal ensemble are relevant for the analysis of recent experiments on chaotic quantum dots, where the conductance G is measured äs a function of both the magnetic field and the shape of the quantum dot [8] The grand canomcal results are relevant for experiments on microwave cavities [34,35] …”

Section: Distribution Of Parametric Conductance Derivatives Of a Quanmentioning

confidence: 99%

Distribution of Parametric Conductance Derivatives of a Quantum Dot

et al. 1997

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The conductance G of a quantum dot with single-mode ballistic pomt contacts depends sensitively on external parameters X such äs gate voltage and magnetic field We calculate the jomt distnbution of G and dG/dX by relating it to the distnbution of the Wigner Smith time delay matnx of a chaotic System The distnbution of dG/dX has a smgularity at zero and algebraic tails While G and dG/dX are correlated, the ratio of dG/dX and -jG(l -G) is independent of G Coulomb interactions change the distnbution of dG/dX by mducing a transition from the grand canonical to the canonical ensemble All these piedictions can be tested in semiconductor microstiuctures or microwave cavities [S0031 9007(97) The mterest m this problem was stimulated by expenments on semiconductor microstructures known äs quantum dots, m which the election motion is ballistic and chaotic [5] A typical quantum dot is confined by gate electrodes, and connected to two election reservoirs by bal hstic pomt contacts, thiough which only a few modes can propagate at the Fermi level The parametnc dependence of the conductance has been measured by several groups [6][7][8] In the single-mode hmit, parametnc fluctuations are of the same ordei äs the aveiage, so that one needs the complete distnbution of G and dG/dX to character ize the System Knowing the average and vanance is not sufficient Analytical results are available for pomt con tacts with a large number of modes [9][10][11][12][13][14][15] In this paper, we present the complete distnbution in the opposite hmit of two single-mode pomt contacts and show that it differs stnkmgly from the multimode case consideied previouslyThe mam differences which we have found are the following We consider the jomt distnbution of the conductance G and the derivatives 3G/3V, dG/dX with respect to the gate voltage V and an external parameter X (typically the magnetic field) If the pomt contacts contain a large number of modes, P(G, 3G/3V, dG/dX) factonzes mto three independent Gaussian distnbutions [9][10][11][12] In the single-mode case, in contrast, we find that this distnbution does not factonze and decays algebraically rather than exponentially By integratmg out G and one of the two derivatives, we obtain the conductance velocity distnbutions P(dG/dV) and P(dG/dX) plotted m Fig l Both distubutions have a smgularity at zero velocity, and alge braic tails A remaikable piediction of our theory is that the correlations between G, on the one hand, and dG/dV and dG/dX, on the other hand, can be transformed away by the change of variables G = (2e 2 /h) sin 2 Θ, where θ is the polar coordmate mtroduced in Ref [13] The derivatives dO/dV and 3Θ/ΘΧ are statistically independent of θ Theie exists no change of variables that transforms away the correlations between dG/dV and 3G/dX Anothei new feature of the smgle mode case concerns the effect of Coulomb mtei actions [16,17] In the simplest model, the strength of the Coulomb repulsion is measured by the ratio of the chaiging eneigy e 1 /C (with C the capacitance of the quantum dot) and...

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Microwave Studies of Billiard Green Functions and Propagators

Cited by 114 publications

References 11 publications

Current and vortex statistics in microwave billiards

Current and vortex statistics in microwave billiards

A supersymmetry approach to billiards with randomly distributed scatterers

Distribution of Parametric Conductance Derivatives of a Quantum Dot

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