Relation between Feynman cycles and off-diagonal long-range order

The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.     

Saddle-point energies and Monte Carlo simulation of the long-range order relaxation in CoPt

We present atomic-scale computer simulations in equiatomic L1₀-CoPt where Molecular Dynamics and Monte Carlo techniques have both been applied to study the vacancy-atom exchange and kinetics relaxation. The atomic potential is determined using a Tight-Binding formalism within the Second-Moment Approximation. It is used to evaluate the different saddle-point energies involved in a vacancy-atom exchange between nearest-neighbour sites. The potential and the saddle-point energies have been used to simulate the relaxation of the long-range order in CoPt using a Monte Carlo technique. A vacancy migration energy of 0.73±0.15 eV and an order-disorder transition temperature of 935 K have been found.     

Monte Carlo study of long-range chiral structure in QCD

Results of a Monte Carlo study of long-range chiral structure is massless 4-dimensional QCD are presented. The algorithm employed integrates fermion degrees of freedom exactly. The behavior of chiral correlations in both abelian and SU(2) color theories is compared. We find strong evidence for chiral breakdown, with a solution of the U(1) problem, in lattice QCD at large β.     

Segmental order in end-linked polymer networks: A Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.     

Local order parameter near the critical point: A Monte Carlo study

The probability distribution of the local magnetization in a Heisenberg ferromagnet has been investigated near the critical temperature. The distribution function depends strongly upon the number of atoms generating the local field. A cusp-like critical broadening is observed with different behavior above and below the critical temperature.     

Monte Carlo renormalization group study of first order phase transitions

The two-lattice matching MCRG method is used to study first order phase transitions. While the method gives the critical exponent in agreement with the predicted value 1/d, where d is the dimension of the system, it indicates discontinuous flows on the phase transition surface.     

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ _Q of the charge Q and the energy relaxation time τ _E . If τ _Q ? τ _E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid ⁴He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.     

Time-dependent concentration depolarization: A Monte Carlo study

The phenomenon of time-dependent concentration depolarization is examined by a Monte Carlo procedure. The method described is general and versatile, and allows one to arbitrarily choose absorption and emission molecular polarizations, energy transfer mechanisms, and radial and orientational distribution functions. Comparison is made with recent theoretical results on time-dependent depolarization, and with experimental results on the “steady-state” depolarization of the phosphorescence of phenanthrene-d₁₀. Good agreement is obtained for a wide range of concentrations.     

Two mutually-repelling self-avoiding walks: A Monte Carlo study

We consider two self-avoiding walks (SAWs) on a square lattice, beginning simultaneously from two arbitrary nearest neighbours. The walks cross neither themselves nor each other, and grow simultaneously. Using Monte Carlo technique we study the variation, with the length N of the walks, of the average end-to-end distance 〈R_N〉 of each walk and of their average separation 〈S_N〉. We find 〈R_N²〉∞N^2ν, 〈S_N²〉∞N^2λ, where ν ≈ λ ≈ 0.75 for two ordinary SAWs and ν ≈ λ ≈ 0.67 for two growing SAWs in two dimensions. For two directed SAWs, we find 〈R_N∥/⊥²〉 ∞ N^2ν∥/⊥ and 〈S_N∥/⊥² 〉 ∞ N^2λ_∥/⊥, where ν_∥ ≈ 1.00, ν_⊥ ≈ 0.56, λ_∥ ≈ 0.50 and λ_⊥ ≈ 0.59 in two dimensions. We thus find an indirect excluded volume effect on one directed SAW, due to the other.     

Reverse Monte Carlo study on structural order in liquid and glassy AlFe alloys

This paper reports that anomalous local order in liquid and glassy AlFeCe alloy has been detected by x-ray diffraction measurements. The addition of the element Ce has a great effect on this local structural order. The element Ce favours interpenetration of the icosahedra by sharing a common face and edges. It argues that frustration between this short-range order and the long-range crystalline order controls the glass-forming ability of these liquids. The obtained results suggest that a system having a stronger tendency to show local icosahedral order should be a better glass-former. This scenario also naturally explains the close relationship between the local icosahedral order in a liquid, glass-forming ability, and the nucleation barrier. Such topological local order has also been analysed directly using the reverse Monte Carlo method. It also estimated the fraction of local ordered and disordered structural units in a glassy AlFeCe alloy.