arXiv subjects

F. Schaefer

Publications and source records attributed to F. Schaefer.

12 recordsLinked to original sources

arXiv2011

PT symmetry and spontaneous symmetry breaking in a microwave billiard

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

quant-ph↗

arXiv2010

Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and non-symmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.

nlin.CD↗

arXiv2010

Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene

We present measurements of transmission and reflection spectra of a microwave photonic crystal composed of 874 metallic cylinders arranged in a triangular lattice. The spectra show clear evidence of a Dirac point, a characteristic of a spectrum of relativistic massless fermions. In fact, Dirac points are a peculiar property of the electronic band structure of graphene, whose properties consequently can be described by the relativistic Dirac equation. In the vicinity of the Dirac point, the measured reflection spectra resemble those obtained by conductance measurements in scanning tunneling microscopy of graphene flakes.

cond-mat.mes-hall↗

arXiv2009

Cross-Section Fluctuations in Chaotic Scattering

For the theoretical prediction of cross-section fluctuations in chaotic scattering, the cross-section autocorrelation function is needed. That function is not known analytically. Using experimental data and numerical simulations, we show that an analytical approximation to the cross-section autocorrelation function can be obtained with the help of expressions first derived by Davis and Boose. Given the values of the average S-matrix elements and the mean level density of the scattering system, one can then reliably predict cross-section fluctuations.

nlin.CD↗

arXiv2009

Quantum Chaotic Scattering in Microwave Resonators

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both, a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data.

nlin.CD↗

arXiv2009

Friedel Oscillations in Microwave Billiards

Friedel oscillations of electron densities near step edges have an analog in microwave billiards. A random plane wave model, normally only appropriate for the eigenfunctions of a purely chaotic system, can be applied and is tested for non-purely-chaotic dynamical systems with measurements on pseudo-integrable and mixed dynamics geometries. It is found that the oscillations in the pseudo-integrable microwave cavity matches the random plane-wave modeling. Separating the chaotic from the regular states for the mixed system requires incorporating an appropriate phase space projection into the modeling in multiple ways for good agreement with experiment.

nlin.CD↗

arXiv2009

Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances

We measure the complex scattering amplitudes of a flat microwave cavity (a "chaotic billiard"). Time-reversal T-invariance is partially broken by a magnetized ferrite placed within the cavity. We extend the random-matrix approach to T-violation in scattering, fit some of the properties of the scattering amplitudes, and then successfully predict others. Our work constitutes the most precise test of the theoretical approach to T-violation within the framework of random-matrix theory so far available.

nlin.CD↗

arXiv2008

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz.

nlin.CD↗

arXiv2007

Spectral properties of Bunimovich mushroom billiards

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the nearest-neighbor spacing distribution. Theoretical predictions for the quantum properties of mixed systems rely on the sharp separability of phase space - an unusual property met by mushroom billiards. We however find deviations which are ascribed to the presence of dynamic tunneling.

nlin.CD↗

arXiv2007

Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards

Using reciprocity, we investigate the breaking of time-reversal (T) symmetry due to a ferrite embedded in a flat microwave billiard. Transmission spectra of isolated single resonances are not sensitive to T-violation whereas those of pairs of nearly degenerate resonances do depend on the direction of time. For their theoretical description a scattering matrix model from nuclear physics is used. The T-violating matrix elements of the effective Hamiltonian for the microwave billiard with the embedded ferrite are determined experimentally as functions of the magnetization of the ferrite.

cond-mat.other↗

arXiv2006

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and - using the well known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard - their properties determined.

nlin.CD↗

arXiv1999

Theory for underdoped high-T_c superconductors: effects of phase fluctuations

In underdoped cuprates, T_c is thought to be determined by Cooper pair phase fluctuations because of the small superfluid density n_s. Experimentally, T_c is found to scale with n_s. The fluctuation-exchange approximation (FLEX) in its standard form fails to predict this behavior of T_c since it does not include phase fluctuations. We therefore extend the FLEX to include them selfconsistently. We present results for T_c[n_s,x], where x is the doping.

cond-mat.supr-con↗