Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

Free space excitation of novel “Fractional” whispering gallery mode dielectric resonators

Solutions to the main problems that limit the sensitivity of an electron magnetic resonance (EMR) spectrometer on the basis of a whispering gallery mode dielectric resonator (WGMDR) are presented. The electromagnetic losses in the transition regions between the overmoded metallic waveguide, the overmoded dielectric waveguide and the mono-mode dielectric waveguide can be avoided by the free space excitation of the resonator that is proved to be very effective for suitably designed resonators. The EMR measurements on high-dielectric-loss samples can be safely developed employing the novel class of “fractional” WGMDRs, in which the usual traveling wave resonator is modified in a structurally stationary wave resonator. Several peculiarities of a fractional WGMDR, investigated both theoretically and experimentally, evidence the advantages of the application of this class of WGMDRs to EMR spectroscopy.     

Controlled dumping of pulses of laser radiation ranging from MIR to the MM by means of optical semiconductor switching

A simple method to produce sub-ns pulses of laser radiation with wavelength ranging from middle infrared (MIR) to millimeter (MM) is experimentally demonstrated. The system operates with a single OSS (optical semiconductor switching) driven by a ns Nd laser. Pulse control is produced by varying the distance of a mirror from an OSS used as a cavity dumping. The effectiveness of this sub-ns MM pulse generation is larger than the one observed in other schemes. Pulses with 500-ps FWHM and 15-W power were produced at 2.65 mm with a time compression compared to the 2-ns FWHM of the 1.06-μm driving laser. Received: 30 October 2000 / Revised version: 26 January 2001 / Published online: 9 May 2001     

Evaluation of the Antioxidant Activity of Nigella sativa L. and Allium ursinum Extracts in a Cellular Model of Doxorubicin-Induced Cardiotoxicity

Natural products black cumin—Nigella sativa (N. sativa) and wild garlic—Allium ursinum (AU) are known for their potential role in reducing cardiovascular risk factors, including antracycline chemotherapy. Therefore, this study investigates the effect of N. sativa and AU water and methanolic extracts in a cellular model of doxorubicin (doxo)-induced cardiotoxicity. The extracts were characterized using Ultraviolet-visible (UV-VIS) spectroscopy, Fourier-transform infrared (FT-IR) spectroscopy, Liquid Chromatography coupled with Mass Spectrometry (LC-MS) and Gas Chromatography coupled with Mass Spectrometry (GC-MS) techniques. Antioxidant activity was evaluated on H9c2 cells. Cytosolic and mitochondrial reactive oxygen species (ROS) release was evaluated using 2′,7′-dichlorofluorescin-diacetate (DHCF-DA) and mitochondria-targeted superoxide indicator (MitoSOX red), respectively. Mitochondrial membrane depolarization was evaluated by flow cytometry. LC-MS analysis identified 12 and 10 phenolic compounds in NSS and AU extracts, respectively, with flavonols as predominant compounds. FT-IR analysis identified the presence of carbohydrates, amino acids and lipids in both plants. GC-MS identified the sulfur compounds in the AU water extract. N. sativa seeds (NSS) methanolic extract had the highest antioxidant activity reducing both intracellular and mitochondrial ROS release. All extracts (excepting AU methanolic extract) preserved H9c2 cells viability. None of the investigated plants affected the mitochondrial membrane depolarization. N. sativa and AU are important sources of bioactive compounds with increased antioxidant activities, requiring different extraction solvents to obtain the pharmacological effects.     

Electroproduction of supersymmetric particles and gauge bosons

The electroproduction of scalar leptons and gauginos at HERA and at supercollider energies is studied. In particular, the channel $\text{ep}\text{→}\text{e}\text{(→}\text{e}\text{+}\text{γ}\text{)}\text{γ}\text{X}$ is analyzed in full detail. The exa analytic expressions for the cross section and the spectrum of the final electron are derived and evaluated for $\text{√s ? 0.15?3}\text{TeV}$ and different values of the scalar electron and photino masses. Since the exact formulae are relatively complicated, simplified expressions in the Weizsäcker-Williams approximation are also given and their accuracy is discussed by comparison with the exact formulae. The standard processes $\text{ep}\text{→}\text{Z}\text{(→ v}\text{v}\text{)}\text{eX and ep}\text{→}\text{W}\text{(→}\text{e}\text{v}\text{)v}\text{X}$ which also lead to one final electron and two invisible particles are considered in parallel. The corresponding cross sections and distributions are discussed in comparison with the supersymmetric signal. The Z⁰ cross section is found to be quite smaller than was reported previously. To clarify this point the Z⁰ production at the leptonic vertex was computed both exactly and in the Weizsäcker-Williams approximation with quite consistent results.     

Type-II Matrices Attached to Conference Graphs

We determine the Nomura algebras of the type-II matrices belonging to the Bose-Mesner algebra of a conference graph.     

Low threshold voltage asymmetric antiferroelectric liquid crystal cells

Asymmetric antiferroelectric liquid crystal displays (AAFLCD) are attractive since they show a very well defined off state and fast switching time. Moreover, they can be driven by a simple biasless DC compensated waveform. The electrooptical response of an AAFLCD allows for new addressing modes, including quasi-static intermediate greyscales maintained without applying a field and passively addressed multiplexed high-frequency displays and spatial light modulators. A new kind of asymmetric cells have been obtained by using fluorinated block copolymer (FBC) alignment, which enhances surface segregation and provides a low energy surface. In this work we combine FBC alignment with antiferroelectric liquid crystal mixtures containing strongly electronegative fluorinated components. Threshold voltages for the antiferroelectric-ferroelectric phase transition as low as 3 volts are observed. We report the time evolution of the shift of the electro-optical response.     

Small random perturbations of dynamical systems: Exponential loss of memory of the initial condition

We consider Markov processes arising from small random perturbations of non-chaotic dynamical systems. Under rather general conditions we prove that, with large probability, the distance between two arbitrary paths starting close to a same attractor of the unperturbed system decreases exponentially fast in time. The case of paths starting in different basins of attraction is also considered as well as some applications to the analysis of the invariant measure and to elliptic problems with small parameter in front to the second derivatives. The proof is based on a multiscale analysis of the typical trajectories of the Markov process; this analysis is done using techniques involved in the proof of Anderson localization for disordered quantum systems.     

Some new results on the two-dimensional kinetic Ising model in the phase coexistence region

We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature . We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scalet _even, much smaller than the global relaxation timet _rel, such that, with large probability, any initial configuration first relaxes to one of the two phases in a time scale of ordert _even and only after a time scale of the order oft _rel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.