Momentum Space Information Entropies Research Articles

Application of information theory in atoms, nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S = α + Μη Ν for the entropy as function of the number of particles Ν holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field.

Information entropies for the Morse potential using the J-matrix method

Information entropies, such as Shannon, Fisher and Rényi entropies, with their associated quantities, are calculated and discussed for the Morse potential in the position (r) and momentum (p) spaces using the J-matrix method. The entropies, for the s-wave, are numerically obtained for the diatomic molecules H2 and LiH. It is the first information entropy calculation for real diatomic molecules using the Morse potential. Interesting characteristic features of the entropy densities are shown, where the position and momentum space information entropies satisfy the uncertainty relations.

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as $ S_\mathrm{t}^{(D)} = N(a D - b \ln N) $ , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.

On the quantum information entropies and squeezing associated with the eigenstates of the isotonic oscillator

In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be compensated for by an increase in momentum entropy, such that the BBM inequality is guaranteed. To complete our study we investigate the amplitude squeezing in x and p-quadratures corresponding to the eigenstates of the isotonic oscillator and show that amplitude squeezing, again in x, will be revealed as expected, while the Heisenberg uncertainty relationship is also satisfied. Finally, our numerical calculations of the entropy densities will be presented graphically.

QUANTUM INFORMATION ENTROPIES OF THE EIGENSTATES OF THE MORSE POTENTIAL

The position and momentum space information entropies for the Morse potential are numerically obtained for different strengths of the potential. It is found to satisfy the bound obtained by Beckner, Bialynicki-Birula, and Mycielski. Interesting features of the entropy densities are graphically demonstrated.

Quantum-information entropies of the eigenstates and the coherent state of the Pöschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.

Universal property of the information entropy in atoms, nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S = a + bln N for the entropy as function of the number of particles N holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field.

Quantum Entropy for Nuclei

The position- and momentum-space information entropies of nuclei are calculated in the framework of two models of the nucleus, i.e. the harmonic oscillator shell model and a correlated model which takes into account short range correlations. It is found that for every nucleus the sum of position and momentum entropies is independent of the oscillator parameter and increases slightly by introducing short range correlations. Finally it turns out that the same functional form S =aN + bN ln N for the entropy as function of the number of particles N (electrons or nucleons) holds approximately for atomic and nuclear systems.