Path-integral study of a two-dimensional Lennard-Jones glass

The glass transition in a quantum Lennard-Jones mixture is investigated by constant-volume path-integral simulations. Particles are assumed to be distinguishable, and the strength of quantum effects is varied by changing h from zero (the classical case) to one (corresponding to a highly quantum-mechanical regime). Quantum delocalization and zero point energy drastically reduce the sensitivity of structural and thermodynamic properties to the glass transition. Nevertheless, the glass transition temperature T-g can be determined by analyzing the phase space mobility of path-integral centroids. At constant volume, the T-g of the simulated model increases monotonically with increasing h. Low temperature tunneling centers are identified, and the quantum versus thermal character of each center is analyzed. The relation between these centers and soft quasilocalized harmonic vibrations is investigated. Periodic minimizations of the potential energy with respect to the positions of the particles are performed to determine the inherent structure of classical and quantum glassy samples. The geometries corresponding to these energy minima are found to be qualitatively similar in all cases. Systematic comparisons for ordered and disordered structures, harmonic and anharmonic dynamics, classical and quantum systems show that disorder, anharmonicity, and quantum effects are closely interlinked.

Simultaneous histories, path sums, and measurements for noncommuting variables

We analyze von Neumann-like quantum measurements in terms of simultaneous virtual paths constructed for two noncommuting variables. The approach is applied to measurements of operator functions of conjugate variables and to the joint measurements of such variables. The limits of applicability of the restricted phase space path integral are studied. We demonstrate that, for a simple joint measurement, using entangled meter states allows one to manipulate the order in which the measurements are conducted. The effects of '' weakening '' a measurement by choosing unsharp meter states are also discussed.

Quantum annealing of an ising spin-glass by Green's function Monte Carlo

We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

Monte Carlo studies of quantum and classical annealing on a double well

We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the path integral Monte Carlo approach is found to yield nontrivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a "relativistic" kinetic energy form, leading to a higher probability of long real-space jumps, can be considerably more effective than the standard nonrelativistic one.

Path-Dependency, Stocks, Switching Points, Flows: Reflections on Long-term Global Change and Local Opportunities

This paper examines the possibilities for peripheral localities to achieve upward mobility in the world-system by “hooking on” to larger processes of world-system accumulation. In particular, is it possible for economies that are dependent on foreign investment to receive a flow of investments that is high enough to overcome the negative impacts of a high stock of foreign investment, thus enabling them to cross a threshold and achieve upward mobility in the world-system? An analysis of therecent experience of the southern Irish “Celtic Tiger” economy during 1990-2000 indicates that such an upward movement is possible on the basis of massive foreign investment inflows. On closer examination, however, the Irish-type model appears to be highly deficient, because a high proportion of growth is illusionary and also on grounds of social desirability and lack of generalizability.