Scaled Hamiltonians

Errington, J. R. Panagiotopoulos, A. Z., Phase equilibria of the modified Buckingham exponential-6 potential from Hamiltonian scaling grand canonical Monte Carlo, J. Chem. Phys. 1998,109, 1093-1100... 

Hcs determines the isotropic chemical shift Hamiltonian scaled by a... 

One nice thing about H in mass-scaled coordinates is that it is identical to the Hamiltonian of a mass point movmg in two dimensions. This is convenient for visualizing trajectory motions or wavepackets, so the mass-scaled coordinates are commonly used for plotting data from scattering calculations. 

Iterative approaches, including time-dependent methods, are especially successfiil for very large-scale calculations because they generally involve the action of a very localized operator (the Hamiltonian) on a fiinction defined on a grid. The effort increases relatively mildly with the problem size, since it is proportional to the number of points used to describe the wavefiinction (and not to the cube of the number of basis sets, as is the case for methods involving matrix diagonalization). Present computational power allows calculations... 

An alternate and fonnally very powerfiil approach to resonance extraction is complex scaling [7, 101. 102. 103. 104. 105. 106 and 107] whereby a new Hamiltonian is solved. In this Hamiltonian, tlie grid s multidimensional coordinate (e.g., x) is multiplied by a complex constant a. The kinetic energy gains a constant complex factor > (1/a )(d /dx )), while the potential needs to be evaluated at points with a complex... 

Chu S I 1991 Complex quasivibrational energy formalism for intense-field multiphoton and above-threshold dissociation—complex-scaling Fourier-grid Hamiltonian method J. Chem. Phys. 94 7901... 

If one is only interested in the properties of the interface on scales much larger than the width of the intrinsic profiles, the interface can be approximated by an infinitely thin sheet and the properties of the intrinsic profiles can be cast into a few effective parameters. Using only the local position of the interface, effective interface Hamiltonians describe the statistical mechanics of fluctuating interfaces and membranes. 

The limit equation governing limj -,o qc can be motivated by referring to the quantum adiabatic theorem which originates from work of Born and FOCK [4, 20] The classical position g influences the Hamiltonian very slowly compared to the time scale of oscillations of in fact, infinitely slowly in the limit e — 0. Thus, in analogy to the quantum adiabatic theorem, one would expect that the population of the energy levels remain invariant during the evolution ... 

The total space of system coordinates consists of a tagged coordinate Q (conjugate momentum P) and a set of mass-scaled bath coordinates q (conjugate momenta p). The Hamiltonian reads... 

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