Monte Carlo technique Hamiltonian system

In the investigation of Ortiz et al. [104], a stochastic method is presented which can handle complex Hermitian Hamiltonians where time-reversal invariance is broken explicitly. These workers fix the phase of the wave function and show that the equation for the modulus can be solved using quantum Monte Carlo techniques. Then, any choice for its phase affords a variational upper bound for the ground-state energy of the system. These authors apply this fixed phase method to the 2D electron fluid in an applied magnetic field with generalized periodic boundary conditions. 

The exponential in Eq. 2.14 represents the average over the system described by the hamiltonian Hx, and the corresponding series of conformers and configurational isomers is usually created by molecular dynamics or Monte Carlo methods. When the two systems X and Y are very similar, the exponential term vanishes, leading to a very slow convergence of the average in Eq. 2.14. A number of techniques have been described to overcome this problem 43 441. One of the few applications of this method to coordination compounds is the investigation of O2 and CO affinities to iron porphyrins[45]. 

Molecular level computer simulations based on molecular dynamics and Monte Carlo methods have become widely used techniques in the study and modeling of aqueous systems. These simulations of water involve a few hundred to a few thousand water molecules at liquid density. Because one can form statistical mechanical averages with arbitrary precision from the generated coordinates, it is possible to calculate an exact answer. The value of a given simulation depends on the potential functions contained in the Hamiltonian for the model. The potential describing the interaction between water molecules is thus an essential component of all molecular level models of aqueous systems. 

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