Thermal energies of classical and quantum damped oscillators coupled to reservoirs

We consider the global thermal state of classical and quantum harmonic oscillators that interact with a reservoir. Ohmic damping of the oscillator can be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic damping is conveniently treated with a continuum reservoir of harmonic oscillators. Using the diagonalized Hamiltonian of the total system, we calculate a number of thermodynamic quantities for the damped oscillator: the mean force internal energy, mean force free energy, and another internal energy based on the free-oscillator Hamiltonian. The classical mean force energy is equal to that of a free oscillator, for both Ohmic and non-Ohmic damping and no matter how strong the coupling to the reservoir. In contrast, the quantum mean force energy depends on the details of the damping and diverges for strictly Ohmic damping. These results give additional insight into the steady-state thermodynamics of open systems with arbitrarily strong coupling to a reservoir, complementing results for energies derived within dynamical approaches (e.g. master equations) in the weak-coupling regime.Comment: 13 page

Studies of an Off-Lattice Model for Protein Folding: Sequence Dependence and Improved Sampling at Finite Temperature

We study the thermodynamic behavior of a simple off-lattice model for protein folding. The model is two-dimensional and has two different ``amino acids''. Using numerical simulations of all chains containing eight or ten monomers, we examine the sequence dependence at a fixed temperature. It is shown that only a few of the chains exist in unique folded state at this temperature, and the energy level spectra of chains with different types of behavior are compared. Furthermore, we use this model as a testbed for two improved Monte Carlo algorithms. Both algorithms are based on letting some parameter of the model become a dynamical variable; one of the algorithms uses a fluctuating temperature and the other a fluctuating monomer sequence. We find that by these algorithms one gains large factors in efficiency in comparison with conventional methods.Comment: 17 pages, 9 Postscript figures. Combined with chem-ph/950500

Monte Carlo Study of the Phase Structure of Compact Polymer Chains

We study the phase behavior of single homopolymers in a simple hydrophobic/hydrophilic off-lattice model with sequence independent local interactions. The specific heat is, not unexpectedly, found to exhibit a pronounced peak well below the collapse temperature, signalling a possible low-temperature phase transition. The system size dependence at this maximum is investigated both with and without the local interactions, using chains with up to 50 monomers. The size dependence is found to be weak. The specific heat itself seems not to diverge. The homopolymer results are compared with those for two non-uniform sequences. Our calculations are performed using the methods of simulated and parallel tempering. The performances of these algorithms are discussed, based on careful tests for a small system.Comment: 13 pages LaTeX, 6 Postscript figures, References adde

Education and family background: Mechanisms and policies.

In every society for which we have data, people’s educational achievement is positively correlated with their parents’ education or with other indicators of their parents’socioeconomic status. This topic is central in social science, and there is no doubt that research has intensified during recent decades, not least thanks to better data having become accessible to researchers. The purpose of this chapter is to summarize and evaluate recent empirical research on education and family background. Broadly speaking, we focus on two related but distinct motivations for this topic. The first is equality of opportunity. Here, major the research issues are: How important a determinant of educational attainment is family background, and is family background—in the broad sense that incorporates factors not chosen by the individual—a major, or only a minor, determinant of educational attainment? What are the mechanisms that make family background important? Have specific policy reforms been successful in reducing the impact of family background on educational achievement? The second common starting point for recent research has been the child development perspective. Here, the focus is on how human-capital accumulation is affected by early childhood resources. Studies with this focus address the questions: what types of parental resources or inputs are important for children’s development, why are they important and when are they important? In addition, this literature focuses on exploring which types of economic policy, and what timing of the policy in relation to children’s social and cognitive development, are conducive to children’s performance and adult outcomes. The policy interest in this research is whether policies that change parents’ resources and restrictions have causal effects on their children.Intergenerational mobility; Sibling correlations; Education; Education reform.

Plasmonic metagratings for simultaneous determination of Stokes parameters

Measuring light's state of polarization is an inherently difficult problem, since the phase information between orthogonal polarization states is typically lost in the detection process. In this work, we bring to the fore the equivalence between normalized Stokes parameters and diffraction contrasts in appropriately designed phase-gradient birefringent metasurfaces and introduce a concept of all-polarization birefringent metagratings. The metagrating, which consists of three interweaved metasurfaces, allows one to easily analyze an arbitrary state of light polarization by conducting simultaneous (i.e., parallel) measurements of the correspondent diffraction intensities that reveal immediately the Stokes parameters of the polarization state under examination. Based on plasmonic metasurfaces operating in reflection at the wavelength of 800 nm, we design and realize phase-gradient birefringent metasurfaces and the correspondent metagrating, while experimental characterization of the fabricated components convincingly demonstrates the expected functionalities. We foresee the use of the metagrating in compact polarimetric setups at any frequency regime of interest

N-body simulations of star clusters

Two aspects of our recent N-body studies of star clusters are presented: (1) What impact does mass segregation and selective mass loss have on integrated photometry? (2) How well compare results from N-body simulations using NBODY4 and STARLAB/KIRA?Comment: 2 pages, 1 figure with 4 panels (in colour, not well visible in black-and-white; figures screwed in PDF version, ok in postscript; to see further details get the paper source). Conference proceedings for IAUS246 'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief Editor), M. Giersz, A. Sills, Capri, Sept. 2007; v2: references correcte

Education and Family Background: Mechanisms and Policies

In every society for which we have data, people’s educational achievement is positively correlated with their parents’ education or with other indicators of their parents’ socioeconomic status. This topic is central in social science, and there is no doubt that research has intensified during recent decades, not least thanks to better data having become accessible to researchers. The purpose of this chapter is to summarize and evaluate recent empirical research on education and family background. Broadly speaking, we focus on two related but distinct motivations for this topic. The first is equality of opportunity. Here, major the research issues are: How important a determinant of educational attainment is family background, and is family background – in the broad sense that incorporates factors not chosen by the individual – a major, or only a minor, determinant of educational attainment? What are the mechanisms that make family background important? Have specific policy reforms been successful in reducing the impact of family background on educational achievement? The second common starting point for recent research has been the child development perspective. Here, the focus is on how human-capital accumulation is affected by early childhood resources. Studies with this focus address the questions: what types of parental resources or inputs are important for children's development, why are they important and when are they important? In addition, this literature focuses on exploring which types of economic policy, and what timing of the policy in relation to children's social and cognitive development, are conducive to children's performance and adult outcomes. The policy interest in this research is whether policies that change parents' resources and restrictions have causal effects on their children.intergenerational mobility, sibling correlations, education, education reform

Master equation approach to computing RVB bond amplitudes

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes are radially symmetric and fall off as 1/r^3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.Comment: 8 pages, 7 figure