Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions

We discuss a general form of the exchange energy for a homogeneous system of interacting electrons in two spatial dimensions which is particularly suited in the presence of a generic spin-orbit interaction. The theory is best formulated in terms of a generalized fractional electronic polarization. Remarkably we find that a net generalized polarization does not necessarily translate into an increase in the magnitude of the exchange energy, a fact that in turn favors unpolarized states. Our results account qualitatively for the findings of recent experimental investigations

Detection of Tiny Mechanical Motion by Means of the Ratchet Effect

We propose a position detection scheme for a nanoelectromechanical resonator based on the ratchet effect. This scheme has an advantage of being a dc measurement. We consider a three-junction SQUID where a part of the superconducting loop can perform mechanical motion. The response of the ratchet to a dc current is sensitive to the position of the resonator and the effect can be further enhanced by biasing the SQUID with an ac current. We discuss the feasibility of the proposed scheme in existing experimental setups.Comment: 8 pages, 9 figure

Mechanical effects of optical resonators on driven trapped atoms: Ground state cooling in a high finesse cavity

We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics are a competition of the mechanical effects of the cavity and of the laser photons, which may mutually interfere. We focus onto the good-cavity limit and identify novel cooling schemes, which are based on quantum interference effects and lead to efficient ground state cooling in experimentally accessible parameter regimes.Comment: 17 pages, 6 figure

Early-type Galaxies in the Hubble Deep Field. The <mu_e>-r_e relation and the lack of large galaxies at high redshift

We present the results of the detailed surface photometry of a sample of early-type galaxies in the Hubble Deep Field. Effective radii, surface brightnesses and total V_606 magnitudes have been obtained, as well as U_300, B_450, I_814, J, H and K colors, which are compared with the predictions of chemical-spectrophotometric models of population synthesis. Spectroscopic redshifts are available for 23 objects. For other 25 photometric redshifts are given. In the -r_e plane the early-type galaxies of the HDF, once the appropriate K+E corrections are applied, turn out to follow the `rest frame' Kormendy relation. This evidence, linked to the dynamical information gathered by Steidel et al.(1996), indicates that these galaxies, even at z~2-3, lie in the Fundamental Plane, in a virial equilibrium condition. At the same redshifts a statistically significant lack of large galaxies [i.e. with Log r_e(kpc) > 0.2] is observed.Comment: 30 pages, LaTeX with aasms4.sty macros, 9 embedded postscript figures + 1 postscript Table. To appear in the Astronomical Journa

Kovacs effects in an aging molecular liquid

We study by means of molecular dynamics simulations the aging behavior of a molecular model of ortho-terphenyl. We find evidence of a a non-monotonic evolution of the volume during an isothermal-isobaric equilibration process, a phenomenon known in polymeric systems as Kovacs effect. We characterize this phenomenology in terms of landscape properties, providing evidence that, far from equilibrium, the system explores region of the potential energy landscape distinct from the one explored in thermal equilibrium. We discuss the relevance of our findings for the present understanding of the thermodynamics of the glass state.Comment: RevTeX 4, 4 pages, 5 eps figure

Hawking-like radiation does not require a trapped region

We discuss the issue of quasi-particle production by ``analogue black holes'' with particular attention to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: We show that in order to obtain a stationary and Planckian emission of quasi-particles, it is not necessary to create a trapped region in the acoustic spacetime (corresponding to a supersonic regime in the fluid flow). It is sufficient to set up a dynamically changing flow asymptotically approaching a sonic regime with sufficient rapidity in laboratory time.Comment: revtex4, 4 pages, 1 figur

Crack roughness and avalanche precursors in the random fuse model

We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents ($\zeta$, $\zeta_{loc}$) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as $s_0 \sim L^D$, with a universal fractal dimension $D$, the distribution exponent $\tau$ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value $\tau=5/2$

Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential

Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer subjected to a potential layer with alternating (attractive and repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon request at [email protected] . Physical Review Letter

Optimized Dynamical Decoupling for Time Dependent Hamiltonians

The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $\pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.Comment: 5 pages, no figure

Quantum Fluctuations of the Gravitational Field and Propagation of Light: a Heuristic Approach

Quantum gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, like gamma ray bursters and active galactic nuclei, and also in earth-based interferometers, like those used for gravitational wave detection. Here we describe a simple heuristic picture of the quantum fluctuations of the gravitational field that we have proposed recently, and show how to use it to estimate quantum gravity effects in interferometers.Comment: LaTeX2e, 8 pages, 2 eps figures: Talk presented at QED2000, 2nd Workshop on Frontier Tests of Quantum Electrodynamics and Physics of the Vacuum; included in conference proceeding