Confining potential

From the starting structures (PDB file), the full complement of hydrogens is added using a utility within CHARMM. The entire protein is then solvated within a sphere of TIP3P model waters, with radius such that all parts of the protein were solvated to a depth of at least 5 A. A quartic confining potential localized on the surface of the spherical droplet prevented evaporation of any of the waters during the course of the trajectory. The fully solvated protein structure is energy minimized and equilibrated before the production simulation. 

Figure 8. Histograms of the nearest-neighbor spacing distribution for the nucleon (left plots) and the delta (right plots). The data is for Goldstone-boson exchange and for one-gluon exchange compared to a pure linear confinement potential of the same strength. Curves represent the Poisson and the GOE-Wigner distributions.

Quarkonium in a monochromatic field can be considered as an analog of the hydrogen atom in a monochromatic field, in which Coulomb potential is replaced by Coulomb plus confining potential. 

Figure 2(a)-(d) displays the PECs of several electronic states of H2 and of the ground state of the Hj ion in the presence of a confining potential. Several features may be observed when compared to the situation where no potential is applied. Firstly, the energy corresponding to a dissociation limit, Enm—E(r 00), shifts up for all the states when the strength of the potential increases. For instance, in the dissociation channel for the X and b (channel I), Fiim= —1.0000 a.u. for w O.OO a.u. 

Note that the potential energy V(x) rises to infinite values at sufficiently large displacement. One should expect this boundary condition to mean that the vibrational wavefunction will fall to zero amplitude at large displacement (as in the square well case, but less abruptly). One should also expect that the confining potential well would lead to quantized solutions, as is indeed the case ... 

In previous papers [10,11] we have formulated a procedure for splitting the ground-state energy of a multifermionic system into an averaged, structure-less part, E, and a residual, shell-structure part, 8E. The latter originates from quantum interference effects of the one-particle motion in the confining potential [12] and has the form of a shell-correction expansion 5E = It was also shown [11] that the first-order corrective term,... 

Fig. 5. The differential conductance interference pattern near the lower crossing point calculated using a smooth confining potential for the upper wire. vc = IAvf, vs = vf, and AUf = lOiv/L.

There is a general statement [17] that spin-orbit interaction in ID systems with Aharonov-Bohm geometry produces additional reduction factors in the Fourier expansion of thermodynamic or transport quantities. This statement holds for spin-orbit Hamiltonians for which the transfer matrix is factorized into spin-orbit and spatial parts. In a pure ID case the spin-orbit interaction is represented by the Hamiltonian //= a so)pxaz, which is the product of spin-dependent and spatial operators, and thus it satisfies the above described requirements. However, as was shown by direct calculation in Ref. [4], spin-orbit interaction of electrons in ID quantum wires formed in 2DEG by an in-plane confinement potential can not be reduced to the Hamiltonian H s. Instead, a violation of left-right symmetry of ID electron transport, characterized by a dispersion asymmetry parameter Aa, appears. We show now that in quantum wires with broken chiral symmetry the spin-orbit interaction enhances persistent current. 

In quantum wires formed in a two-dimensional electron gas (2DEG) by lateral confinement the Rashba spin-orbit interaction is not reduced to a pure ID Hamiltonian H[s = asopxaz. As was shown in Ref. [4] the presence of an inplane confinement potential qualitatively modifies the energy spectrum of the ID electrons so that a dispersion asymmetry appears. As a result the chiral symmetry is broken in quantum wires with Rashba coupling. Although the effect was shown [4] not to be numerically large, the breakdown of symmetry leads to qualitatively novel predictions. 

For neutral doped fullerene onions A C6o C24o, A C6o C24o Cs4o, etc., the confining potential Vn of a multiwalled cage is replaced by a linear combination of corresponding single-walled potentials V [32]... 

The anharmonicity of the confining potential can be controlled by changing the depth of the Gaussian potential D with respect to >z and ojxy, respectively. The parameters coz and coxy represent the frequency of the harmonic-oscillator potential characterizing the strength of confinement of... 

Introducing anharmonicity is important for simulating realistic confining potentials [23,24]. 

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