Search results for "Abstract algebra"
showing 10 items of 452 documents
Four-time rotational correlation functions
1998
A scheme to analyze four-time rotational correlation functions of any rank is developed and details for rank L = 1 and 2 are given. The scheme provides a transparent way for identifying deviations from simple Markovian dynamics as observed, e.g., in complex liquids close to the glass transition. The method should be applicable to NMR and optical multiple-pulse techniques as well as to photon correlation spectroscopy. Results are given for 2H-NMR multiple-pulse data in supercooled glycerol. We identify and analyze the dynamical heterogeneity of molecular reorientation in a range of 205 − 215 K close to the glass temperature Tg = 190 K.
Dimensional Regularization. Ultraviolet and Infrared Divergences
2015
The cornerstone of Quantum Field Theory is renormalization. We shall speak more about in the next chapters. Before, it is necessary to discuss the method. The best and most simple is, of course, dimensional regularization (doesn’t break the symmetries, doesn’t violate the Ward Identities, preserves Lorentz invariance, etc.). When explained consistently, it becomes very simple and clear. Here, we shortly discuss ultraviolet (UV) and infrared (IR) divergences with a few examples. However, in Chap. 8, we shall extensively treat one-loop two and three-point functions and analyse many more examples of IR and UV divergences.
ELASTIC WAVES: MENTAL MODELS AND TEACHING/LEARNING SEQUENCES
2006
In last years many research studies have pointed out relevant student difficulties in understanding the physics of mechanical waves. Moreover, it has been reported that these difficulties deal with some fundamental concepts as the role of the medium in wave propagation, the superposition principle and the mathematical description of waves involving the use of functions of two variables. In the context of pre-service courses for teacher preparation a teaching/learning (T/L) sequence based on using simple RTL experiments and interactive simulation environments aimed to show the effect of medium properties on the propagation speed of a wave pulse, has been experimented. Here, preliminary resul…
Intraenvironmental correlations in the ground state of a nonisolated two-state particle
1996
The existence of entanglement in the ground state of a two-level particle coupled to a bosonic environment is proved. The quantum covariances of pairs of simple dynamical variables relative to different subsystems are explicitly shown to be bounded. Physically interpretable conditions for the occurrence of weak intraenvironmental correlations are reported and discussed. The potentialities of our treatment are briefly put into evidence.
Calculation of local pressure tensors in systems with many-body interactions
2005
Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4,) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infinitesim…
Constraints on Area Variables in Regge Calculus
2000
We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.
Spectral analysis of two-dimensional Bose-Hubbard models
2016
One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.
Simultaneous recording of true and random coincidences using a two-parameter analyzer system
1971
Abstract A description is given of a simple fast coincidence method which allows the simultaneous recording of coincidence and random coincidence spectra. The method is based on the properties of a standard two-parameter pulse-height analyzer system, and no special electronics is required.
Nonlinear response of superparamagnets with finite damping: an analytical approach
2004
The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modelling of the experimental data and the determination of the damping coefficient in superparamagnets.
Quantitative tests of mode-coupling theory for fragile and strong glass-formers
2001
We calculate for a binary mixture of Lennard-Jones particles the time dependence of the solution of the mode-coupling equations in which the full wave vector dependence is taken into account. In addition we also take into account the short time dynamics, which we model with a simple memory kernel. We find that the so obtained solution agrees very well with the time and wave vector dependence of the coherent and incoherent intermediate scattering functions as determined from molecular dynamics computer simulations. Furthermore we calculate the wave vector dependence of the Debye-Waller factor for a realistic model of silica and compare these results with the ones obtained from a simulation o…