LMC complexity for the ground states of different quantum systems

Abstract Lower bound for the shape complexity measure of Lopez-Ruiz–Mancini–Calbet (LMC), C LMC is studied. Analytical relations for simple examples of the harmonic oscillator, the hydrogen atom and two-electron ‘entangled artificial’ atom proposed by Moshinsky are derived. Several numerical examples of the spherically confined model systems are presented as the test cases. For the homogeneous potential, C LMC is found to be independent of the parameters in the potential which is not the case for the non-homogeneous potentials.

[1]  M. Moshinsky.  How Good is the Hartree-Fock Approximation , 1968 .

[2]  J. Garza,et al.  Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model. , 2006, The Journal of chemical physics.

[3]  S. Patil,et al.  Characteristic features of net information measures for constrained Coulomb potentials , 2007 .

[4]  Ricardo López-Ruiz,et al.  Features of the extension of a statistical measure of complexity to continuous systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  K. Sen.  Shell-confined hydrogen atom. , 2005, The Journal of chemical physics.

[6]  J. D. Boer,et al.  Remarks concerning molecural interaction and their influence on the polarisability , 1937 .

[7]  K. Sen,et al.  Information entropies for eigendensities of homogeneous potentials. , 2006, The Journal of chemical physics.

[8]  J. S. Dehesa,et al.  Information entropies of many‐electron systems , 1995 .

[9]  Jaime Sanudo,et al.  Some features of the statistical complexity, Fisher–Shannon information and Bohr-like orbits in the quantum isotropic harmonic oscillator , 2008, 0803.2968.

[10]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[11]  J. S. Shiner,et al.  Disorder and complexity in an ideal non-equilibrium Fermi gas , 1998 .

[12]  Pair function at coincidence and ground-state energy for interacting systems of two fermions with isotropic harmonic confinement and antiparallel spins , 2001 .

[13]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.