Search results for "Condensed Matter - Statistical Mechanics"
showing 10 items of 508 documents
How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?
1998
Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.
The structural relaxation of molten sodium disilicate
2002
We use molecular dynamics computer simulations to study the relaxation dynamics of Na2O-2(SiO2) in its molten, highly viscous state. We find that at low temperatures the incoherent intermediate scattering function for Na relaxes about 100 times faster than the one of the Si and O atoms. In contrast to this all coherent functions relax on the same time scale if the wave-vector is around 1AA^-1. This anomalous relaxation dynamics is traced back to the channel-like structure for the Na atoms that have been found for this system. We find that the relaxation dynamics for Si and O as well as the time dependence of the coherent functions for Na can be rationalized well by means of mode-coupling th…
Microscopic theory of glassy dynamics and glass transition for molecular crystals.
2004
We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have …
Low-energy fixed points of random Heisenberg models
2002
The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent …
Numerical tests of conjectures of conformal field theory for three-dimensional systems
1999
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three-dimensional manifolds. Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three-dimensional, hyper-cylindr…
Universality in disordered systems: The case of the three-dimensional random-bond Ising model
2010
We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed by the same universality class as the site- and bond-diluted models, clearly distinct from that of the pure model, thus providing a complete set of universality in disordered systems.
Test of mode coupling theory for a supercooled liquid of diatomic molecules. II.q-dependent orientational correlators
1997
Using molecular dynamics computer simulations we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard- Jones interactions. The q-dependence of the static correlators S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are calculated for l=l'. A thorough test of the predictions of mode coupling theory (MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for l=1,..,6. We find a clear signature for the existence of a single temperature T…
The dynamics of sodium in sodium disilicate: Channel relaxation and sodium diffusion
2001
We use molecular dynamics computer simulations to study the dynamics of amorphous (Na_2O)2(SiO_2). We find that the Na ions move in channels embedded in a SiO_2 matrix. The characteristic distance between these channels gives rise to a prepeak in the structure factor at around q=0.95 A^-1. The dynamics of sodium is given by a fast process which can be seen in the incoherent scattering function and a slow process which is seen in the coherent function. The relaxation time of the latter coincides with the alpha-relaxation time of the matrix. The Kohlrausch exponent of the fast process for q>1.6 A^1 is the same as the von Schweidler exponent for the slow one, demonstrating that the two proc…
Vorticity Determines the Force on Bodies Immersed in Active Fluids
2021
When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by--but far away from--the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a non-vanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We …
Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators
2006
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several e…