Search results for " statistical mechanics"
showing 10 items of 557 documents
Cooperative motion and growing length scales in supercooled confined liquids
2002
Using molecular dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as close to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance from the wall whereas in the second case they strongly decrease. We use this dependence to extract various dynamical length scales and show that they grow with decreasing temperature. By calculating the frequency dependent average susceptibility of such confined systems we show that the experimental interpretation of such data is very difficult.
Fluctuation dissipation ratio in an aging Lennard-Jones glass
1998
By using extensive Molecular Dynamics simulations, we have determined the violation of the fluctuation-dissipation theorem in a Lennard-Jones liquid quenched to low temperatures. For this we have calculated $X(C)$, the ratio between a one particle time-correlation function $C$ and the associated response function. Our results are best fitted by assuming that $X(C)$ is a discontinuous, piecewise constant function. This is similar to what is found in spin systems with one step replica symmetry breaking. This strengthen the conjecture of a similarity between the phase space structure of structural glasses and such spin systems.
Microscopic theory for the glass transition in a system without static correlations
2002
We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in t…
Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model
2014
As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin film geometry $L_x \times L_y \times L_z$ with periodic boundary conditions along the z-axis and two free $L_x \times L_y$ surfaces at which opposing surface fields $\pm H_{1}$ act, under conditions of partial wetting, a single planar interface inclined under a contact angle $\theta < \pi/2$ relative to the yz-plane is stabilized. In the y-direction, a generaliza…
Ideal glass transitions for hard ellipsoids
2000
For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X$_0$. With increasing aspect ratio we find the idealized glass transition to become primarily be driven by orientational degrees of freedom. For needle or plate like systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition lines. The first one ($\phi_c^{(B)}$) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one ($\phi_c^{(B')}$) which oc…
Quantum effects on the herringbone ordering ofN2on graphite
1993
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
Test of the semischematic model for a liquid of linear molecules
1998
We apply to a liquid of linear molecules the semischematic mode-coupling model, previously introduced to describe the center of mass (COM) slow dynamics of a network-forming molecular liquid. We compare the theoretical predictions and numerical results from a molecular dynamics simulation, both for the time and the wave-vector dependence of the COM density-density correlation function. We discuss the relationship between the presented analysis and the results from an approximate solution of the equations from molecular mode-coupling theory [R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
2005
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the ch…
Some aspects of the nonperturbative renormalization of the phi^4 model
2007
A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamiltonian under the integration over a shell Lambda - d Lambda < k < Lambda, where d Lambda -> 0. We show that the known Wegner--Houghton equation is consistent with the assumption of a simple superposition of the integration results for +/- q. The renormalized action can be expanded in powers of the phi^4 coupling constant u in the high temperature phase at u -> 0. We compare the expansion coefficients with those exactly calculated by the…
Theory of bound polarons in oxide compounds
2001
We present a multilateral theoretical study of bound polarons in oxide compounds MgO and \alpha-Al_2O_3 (corundum). A continuum theory at arbitrary electron-phonon coupling is used for calculation of the energies of thermal dissociation, photoionization (optically induced release of an electron (hole) from the ground self-consistent state), as well as optical absorption to the non-relaxed excited states. Unlike the case of free strong-coupling polarons, where the ratio \kappa of the photoionization energy to the thermal dissociation energy was shown to be always equal to 3, here this ratio depends on the Froehlich coupling constant \alpha and the screened Coulomb interaction strength \beta.…