Quantum force

The quintessence hypothesis was proposed by J. P. Ostriker and Steinhardt (2001). The authors use the term quintessence ( fifth substance ) to describe a quantum force field which is gravitationally repulsive. It has a certain similarity to an electrical or magnetic field and could lead to an invisible energy field which accelerates cosmic expansion. 

T. Hagler, Derivation of class II force fields. 1. Methodology and quantum force field for the alkyl functional group and alkane molecules, J. Comput. Chem. 15 162 (1994). 

This formulation results very insightful according to Equation 8.30, particles move under the action of an effective force — We , i.e., the nonlocal action of the quantum potential here is seen as the effect of a (nonlocal) quantum force. From a computational viewpoint, these formulation results are very interesting in connection to quantum hydrodynamics [21,27]. Thus, Equations 8.27 can be reexpressed in terms of a continuity equation and a generalized Euler equation. As happens with classical fluids, here also two important concepts that come into play the quantum pressure and the quantum vortices [28], which occur at nodal regions where the velocity field is rotational. 

In TD-DFT, the wave function is antisymmetrized and therefore, nonfactorizable or entangled. However, as said above, it is not entangled from a dynamical point of view because the quantum forces originated from a nonseparable quantum potential as in Equation 8.34 are not taken into account. 

Hagler, ]. Comput. Chem., 15, 162 (1994). Derivation of Class II Force Fields. I. Methodology and Quantum Force Field for the Alkyl Functional Group and Alkane Molecules. 

Laboratory. During the period 19191922, Langmuir developed what he called a "deductive chemistry" using the electron-pair theory of valency and the quantum hypothesis. However, physicists rejected the premises and methodology of Langmuir s theory, which proposed the existence of a "quantum force" to counterbalance Coulombic attraction and which used the notion of principal quantum number but deduced positions of equilibrium rather than quantum jumps for electrons. 12... 

Quantum Force Regno di Piacere Event o Rituale Pietra Stagione Senso... 

Any stationary state is seen to be brought about by the force balance W = —Wq. The quantum force is a function of the pressure potential, or stress tensor, f dp/p that produces inner forces in the continuum. At equilibrium, in stationary states, the potential energy remains constant, i.e. 

Monard G, M Loos, V Thery, K Baka, and JL Rivail (1996) Hybrid classical quantum force field for modeling very large molecules. Int. J. Quantum Chem. 58 (2) 153-159... 

In the oxygen VER experiments (3) the n = 1 vibrational state of a given oxygen molecule is prepared with a laser, and the population of that state, probed at some later time, decays exponentially. Since in this case tiojo kT, we are in the limit where the state space can be truncated to two levels, and 1/Ti k, 0. Thus the rate constant ki o is measured directly in these experiments. Our starting point for the theoretical discussion is then Equation (14). For reasons discussed in some detail elsewhere (6), for this problem we use the Egelstaff scheme in Equation (19) to relate the Fourier transform of the quantum force-force time-correlation function to the classical time-correlation function, which we then calculate from a classical molecular dynamics computer simulation. The details of the simulation are reported elsewhere (4) here we simply list the site-site potential parameters used therein e/k = 38.003 K, and a = 3.210 A, and the distance between sites is re = 0.7063 A. 

It is noted that a system of particles reaches equilibrium when the resulting forces on them are zero, and hence the quantum force on a free particle must be perceived to vanish. This requires the quantum potential to be either zero or a constant, independent of position. The first condition relates to a classical particle, whereas the second condition implies... 

This equation shows that in addition to the classical force — W acting on the particle there is also the quantum force —Wq. 

Here the velocity V is a function (not an operator), often referred to in the literature as the quantum force, and is given by... 

As for the classical potential, the gradient of quantum potential energy defines a quantum force. A quantum object therefore has an equation of motion, m x= —VH — VV. For an object in uniform motion (constant potential) the quantum force must vanish, which requires = 0 or a constant, —k say. 

The unexpected conclusion is that a real wave function, d o = implies S o(a ) = 0 and hence the momentum VS = p = 0 and E = V + Vg. Those states with m = 0 all have real wave functions, which therefore means that such electrons have zero kinetic energy and are therefore at rest. The classical (electrostatic) and quantum forces on electrons in such stationary states are therefore balanced and so stabilize the position of the electron with respect to the nucleus. 

The first and last terms on the right hand side are diffusion and first order terms. The middle term corresponds to what is called drift or quantum force. In every iteration, this term forces each random walker into regions of higher trial wavefunction density, in much the same way that classical forces move atoms in MD simulations. This adds a degree of controllability that allows systems with at least several hundred particles to be treated the more closely the trial wavefunction resembles the true wavefunction, the faster the calculation will converge. 

A Modified Divide-and-Conquer Linear-Scaling Quantum Force Field with Multipolar Charge Densities... 

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