Seismic Waveguide of Metamaterials

We have developed a new method of an earthquake-resistant design to support conventional aseismic designs using acoustic metamaterials. We suggest a simple and practical method to reduce the amplitude of a seismic wave exponentially. Our device is an attenuator of a seismic wave. Constructing a cylindrical shell-type waveguide that creates a stop-band for the seismic wave, we convert the wave into an evanescent wave for some frequency range without touching the building we want to protect.Comment: 4 pages, 4 figure

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states

Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed state concept proposed in [Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The first and second order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states.Comment: New section IV, new figure, journal ref adde

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Soldered Bundle Background for the De Sitter Top

We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.Comment: 12 pages, Latex; some improvements introduced, reference added, typos correcte

Calmodulin affects sensitization of Drosophila melanogaster odorant receptors

Flying insects have developed a remarkably sensitive olfactory system to detect faint and turbulent odor traces. This ability is linked to the olfactory receptors class of odorant receptors (ORs), occurring exclusively in winged insects. ORs form heteromeric complexes of an odorant specific receptor protein (OrX) and a highly conserved co-receptor protein (Orco). The ORs form ligand gated ion channels that are tuned by intracellular signaling systems. Repetitive subthreshold odor stimulation of olfactory sensory neurons sensitizes insect ORs. This OR sensitization process requires Orco activity. In the present study we first asked whether OR sensitization can be monitored with heterologously expressed OR proteins. Using electrophysiological and calcium imaging methods we demonstrate that D. melanogaster OR proteins expressed in CHO cells show sensitization upon repeated weak stimulation. This was found for OR channels formed by Orco as well as by Or22a or Or56a and Orco. Moreover, we show that inhibition of calmodulin (CaM) action on OR proteins, expressed in CHO cells, abolishes any sensitization. Finally, we investigated the sensitization phenomenon using an ex vivo preparation of olfactory sensory neurons (OSNs) expressing Or22a inside the fly's antenna. Using calcium imaging, we observed sensitization in the dendrites as well as in the soma. Inhibition of calmodulin with W7 disrupted the sensitization within the outer dendritic shaft, whereas the sensitization remained in the other OSN compartments. Taken together, our results suggest that CaM action is involved in sensitizing the OR complex and that this mechanisms accounts for the sensitization in the outer dendrites, whereas further mechanisms contribute to the sensitization observed in the other OSN compartments. The use of heterologously expressed OR proteins appears to be suitable for further investigations on the mechanistic basis of OR sensitization, while investigations on native neurons are required to study the presently unknown additional mechanisms involved in OSN sensitization

Non-classical Photon Statistics For Two-mode Optical Fields

The non-classical property of subpoissonian photon statistics is extended from one to two-mode electromagnetic fields, incorporating the physically motivated property of invariance under passive unitary transformations. Applications to squeezed coherent states, squeezed thermal states, and superposition of coherent states are given. Dependences of extent of non-classical behaviour on the independent squeezing parameters are graphically displayed.Comment: 15 pages, RevTex, 5 figures, available by sending email to [email protected]

Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light

Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well

Characterisations of Classical and Non-classical states of Quantised Radiation

A new operator based condition for distinguishing classical from non-classical states of quantised radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalisation of the notion of subpoissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuations in quadratic combinations of mode annihilation and creation operators conserving the total photon number. This generalisation is nontrivial and intrinsically two-mode as it goes beyond all possible single mode projections of the two-mode field. The nonclassicality of pair coherent states, squeezed vacuum and squeezed thermal states is analysed and contrasted with one another, comparing the generalised subpoissonian statistics with extant signatures of nonclassical behaviour.Comment: 16 pages, Revtex, One postscript Figure compressed and uuencoded Replaced, minor changes in eq 4.30 and 4.32. no effect on the result

Geometric Phase in Entangled Bipartite Systems

The geometric phase (GP) for bipartite systems in transverse external magnetic fields is investigated in this paper. Two different situations have been studied. We first consider two non-interacting particles. The results show that because of entanglement, the geometric phase is very different from that of the non-entangled case. When the initial state is a Werner state, the geometric phase is, in general, zero and moreover the singularity of the geometric phase may appear with a proper evolution time. We next study the geometric phase when intra-couplings appear and choose Werner states as the initial states to entail this discussion. The results show that unlike our first case, the absolute value of the GP is not zero, and attains its maximum when the rescaled coupling constant $J$ is less than 1. The effect of inhomogeneity of the magnetic field is also discussed.Comment: 5 pages and to be published in Euro. Phys. J.