Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.Comment: Expanded version of Proceedings StatPhys-Kolkata V

Topological delocalization in the completely disordered two-dimensional quantum walk

We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time evolution of the wave functions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization and finding signatures of the delocalization in the finite-size scaling of transmission. We show criticality of the Haar random quantum walk by calculating the critical exponent $\eta$ in three different ways and find $\eta$ $\approx$ 0.52 as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.Comment: 18 pages, 18 figures. Similar to the published version. Comments are welcom

On the Real Spectra of Calogero Model with Complex Coupling

We study the eigenvalue problem of the rational Calogero model with the coupling of the inverse-square interaction as a complex number. We show that although this model is manifestly non-invariant under the combined parity and time-reversal symmetry ${\cal{PT}}$, the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.Comment: revtex4 8 pages, 2 figure

Detection of MicroRNAs in Dried Serum Blots

MicroRNAs are short RNAs which can be utilized as biomarkers for a variety of conditions. They are detectable in serum, and changes in the levels of circulating microRNAs have been associated with different diseases. We tested for the presence of microRNAs in serum that is dried on paper and stored unrefrigerated instead of being kept frozen. MicroRNAs were readily detectable in such blots, and their detectability was improved by using paper made of cellulose instead of glass fiber, and by re-hydrating dried blots with Trizol™ instead of water, phosphate-buffered saline, or guanidine hydrochloride before RNA extraction. MicroRNA preservation was not diminished by drying of blots at 37, 45 or 60 ºC instead of room temperature or by storage of blots at 37, 45 or 60 ºC instead of room temperature, but was worse when blots were dried incompletely or exposed to high humidity during storage. Preservation of microRNAs in serum was not adversely affected if instead of being kept frozen at -80 ºC it was stored as dried blots at room temperature or 37 ºC for ten or eight and a half months, respectively. In a group of ten individuals, microRNA quantifications of -80 ºC-frozen or dried sera stored at room temperature correlated well. Dried blots may thus be a convenient and safer way to save, transport, and store serum without refrigeration for microRNA assays