Pseudo-ensemble methods

C. Pseudo-Ensemble Methods Histogram Reweighting Conclusion... 

There are many different routes for calculating phase equilibria that are covered in detail in other chapters of this volume thermodynamic scaling Monte Carlo (chapter by Valleau), Gibbs-Duhem integration along coexistence lines (chapter by Kofke), and pseudo-ensemble methods (chapter by de Pablo and Escobedo). Thus these methods are not discussed here. 

The same pseudo-ensemble concept has been used by Camp and Allen [44] to obtain a pseudo-Gibbs method in which particle transfers are substituted by volume fluctuations of the two phases. The volume fluctuations are unrelated to the ones required for pressure equality (10.7) but are instead designed to correct imbalances in the chemical potentials of some of the components detected, for example, by test particle insertions. 

III. THE NPT+ TEST PARTICLE METHOD, GIBBS-DUHEM INTEGRATION AND PSEUDO-ENSEMBLES... 

The same pseudo-ensemble concept has been used by Camp and Allen [53] to obtain a pseudo jibbs method in which particle transfers are substituted by volume fluctuations of the two phases. The volume... 

Interesting connections between many of the methods discussed in the present chapter have been pointed out by Escobedo [54,55]. In particular, Escobedo suggests that Gibbs-Duhem integration, pseudo-ensembles, and the NPT + test particle method can be considered as low-order approximations of a histogram reweighting approach. 

Because Newton s equations of motion are conservative, the natural ensemble is NVE (micro-canonical), Aat is one in which the internal energy rather than the temperature is held constant. This is inconvenient if one wishes to compare with experiment where it is the temperature that is generally controlled. In order to perform molecular dynamics in the canonical ensemble, a thermostat must be applied to the system. This is accomplished by constructing a pseudo-Lagrangian. Many forms for temperature-conserving Lagrangians have been proposed, most of which can be written in a form that adds a frictional (velocity-dependent) term to the equations of motion (Allen and Tildesley 1989). Physically, the thermostat can be thought of as a heat bath to which the system is coupled. In the NPT ensemble, in which the pressure is held constant, the cell size and shape fluctuates. The choice of dynamical variables is critical. If the lattice parameters are chosen as in the method of Parrinello and Rahman (1981), the time evolution may depend on the chosen size or shape of the supercell. This difficulty is... 

Conventional NMR deals with a large ensemble of spins. It means that the state of the system is in a statistical mixture, which is obviously inadequate for QIP. However, the NMR ability for manipulating spins states worked out by Cory et al. [24] and Chuang et al. [23] resulted in elegant methods for creating the so called effectively pure or pseudo-pure states. Behind the idea of the pseudo-pure states is the fact that NMR experiments are only sensitive to the traceless deviation density matrix. Thus, we might search for transformations that, applied to the thermal equilibrium density matrix, produce a deviation density matrix with the same form as a pure state density matrix. Once such state is created, all remaining unitary transformations will act only on such a deviation density matrix, which will transform as a true pure state. 

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