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

Transmission in waveguides with compositional and structural disorder: experimental effects of disorder cross-correlations

We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterised by random heights and positions, corresponding to compositional and structural disorder. We measure the effects of cross-correlations between two kinds of disorder, showing how they enhance or attenuate the experimentally found transmission gaps generated by long-range self-correlations. The results agree with the theoretical predictions obtained for the aperiodic Kronig-Penney model and prove that self- and cross-correlations have relevant effects also in finite disordered samples of small size.Comment: 15 pages, 8 figure

Fermi's golden rule and exponential decay as a RG fixed point

We discuss the decay of unstable states into a quasicontinuum using models of the effective Hamiltonian type. The goal is to show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. We use random matrices for the interaction, and show that the ensemble fluctuations vanish in the scaling limit. Thus the limit is the same for every model in the ensemble with probability one.Comment: 20 pages, 1 figur

Can billiard eigenstates be approximated by superpositions of plane waves?

The plane wave decomposition method (PWDM) is one of the most popular strategies for numerical solution of the quantum billiard problem. The method is based on the assumption that each eigenstate in a billiard can be approximated by a superposition of plane waves at a given energy. By the classical results on the theory of differential operators this can indeed be justified for billiards in convex domains. On the contrary, in the present work we demonstrate that eigenstates of non-convex billiards, in general, cannot be approximated by any solution of the Helmholtz equation regular everywhere in $\R^2$ (in particular, by linear combinations of a finite number of plane waves having the same energy). From this we infer that PWDM cannot be applied to billiards in non-convex domains. Furthermore, it follows from our results that unlike the properties of integrable billiards, where each eigenstate can be extended into the billiard exterior as a regular solution of the Helmholtz equation, the eigenstates of non-convex billiards, in general, do not admit such an extension.Comment: 23 pages, 5 figure

Strong anisotropy of superexchange in the copper-oxygen chains of La_{14-x}Ca_{x}Cu_{24}O_{41}

Electron spin resonance data of Cu^{2+} ions in La_{14-x}Ca_{x}Cu_{24}O_{41} crystals (x=9,11,12) reveal a very large width of the resonance line in the paramagnetic state. This signals an unusually strong anisotropy of ~10% of the isotropic Heisenberg superexchange in the Cu-O chains of this compound. The strong anisotropy can be explained by the specific geometry of two symmetrical 90 degree Cu-O-Cu bonds, which boosts the importance of orbital degrees of freedom. Our data show the apparent limitations of the applicability of an isotropic Heisenberg model to the low dimensional cuprates.Comment: 14 pages, 3 figures included, to be published in Phys. Rev. Let

Quasiclassical Random Matrix Theory

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail [email protected]

Spectral Duality for Planar Billiards

For a bounded open domain $\Omega$ with connected complement in ${\bf R}^2$ and piecewise smooth boundary, we consider the Dirichlet Laplacian $-\Delta_\Omega$ on $\Omega$ and the S-matrix on the complement $\Omega^c$. We show that the on-shell S-matrices ${\bf S}_k$ have eigenvalues converging to 1 as $k\uparrow k_0$ exactly when $-\Delta_\Omega$ has an eigenvalue at energy $k_0^2$. This includes multiplicities, and proves a weak form of ``transparency'' at $k=k_0$. We also show that stronger forms of transparency, such as ${\bf S}_{k_0}$ having an eigenvalue 1 are not expected to hold in general.Comment: 33 pages, Postscript, A

Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots

A new theoretical survey of proteins' resistance to constant speed stretching is performed for a set of 17 134 proteins as described by a structure-based model. The proteins selected have no gaps in their structure determination and consist of no more than 250 amino acids. Our previous studies have dealt with 7510 proteins of no more than 150 amino acids. The proteins are ranked according to the strength of the resistance. Most of the predicted top-strength proteins have not yet been studied experimentally. Architectures and folds which are likely to yield large forces are identified. New types of potent force clamps are discovered. They involve disulphide bridges and, in particular, cysteine slipknots. An effective energy parameter of the model is estimated by comparing the theoretical data on characteristic forces to the corresponding experimental values combined with an extrapolation of the theoretical data to the experimental pulling speeds. These studies provide guidance for future experiments on single molecule manipulation and should lead to selection of proteins for applications. A new class of proteins, involving cystein slipknots, is identified as one that is expected to lead to the strongest force clamps known. This class is characterized through molecular dynamics simulations.Comment: 40 pages, 13 PostScript figure

Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard

We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only a few families of nongeneric periodic orbits. We introduce an analytic method for their treatment. The length spectrum can be understood in terms of the nongeneric and unstable periodic orbits. For unequal radii of the quarter cylinders the level statistics agree well with predictions from random matrix theory. For equal radii the billiard exhibits an additional symmetry. We investigated the effects of symmetry breaking on spectral properties. Moreover, for equal radii, we observe a small deviation of the level statistics from random matrix theory. This led to the discovery of stable and marginally stable orbits, which are absent for un equal radii.Comment: 11 pages, 10 eps figure

Cultural and Media Identity Among Latvian Migrants in Germany

This chapter explores how transnational media and culture impacts on the identity formation of recent Latvian migrants in Germany. In the context of the EU, Germany opened its labour market to the new EU countries rather late, when compared to other ‘old’ EU countries. This has had an effect on the composition of the group of Latvian migrants going to Germany, and their identities. In the light of this, this chapter examines how Latvian migrants in Germany feel and experience their belonging to Latvia and its culture. It analyses the social and communicative practices crucial for the development of belonging, including the rootedness in the country where they live and the cultural references that are important for them. The evidence for the analysis in this chapter comes from in-depth interviews, open media diaries and network maps of Latvian migrants in Germany. The chapter situates the description of evidence in the framework of cultural identity concepts and discusses the role of culture and media in the process of building migrant identity. The chapter argues that culture is shaping the transnational self-perception of Latvian migrants in Germany – as it provides collective narratives of imagined common frames of references, and confirms feelings of belonging and distinction