It is established that for finite number of electrons, N ∞, and in the limit T = 0, the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, Ev[N], of an interacting N-particle system under an external single-particle potential, v(r), is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.It is established that for finite number of electrons, N ∞, and in the limit T = 0, the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, Ev[N], of an interacting N-particle system under an external single-particle potential, v(r), is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.

World Journal of Condensed Matter PhysicsJan 1, 20149 citations

Ground State Theory of Many-Particle Systems

Léon Van Hove

Elsevier eBooksJan 1, 19619 citations

Ground State of Systems of Three Particles with Coulomb Interaction

W Kołos, Clemens C. J. Roothaan, R. A. Sack

Reviews of Modern PhysicsApr 1, 1960148 citations

Conduction in correlated one-dimensional electronic systems

Shubha Tewari

Motivated by the observation of periodic conductance oscillations in narrow channels, we study finite one-dimensional electronic systems with the following interactions: (i) an exactly solvable 1/ ${\mathit{x}}^{2}$ potential and (ii) the Coulomb potential with a cutoff, 1/ \ensuremath{\surd} ${\mathit{x}}^{2}$ +${\mathrm{\ensuremath{\delta}}}^{2}$ . The study of the 1/ ${\mathit{x}}^{2}$ model shows that at T=0, d〈N〉/d\ensuremath{\mu} exhibits sharp peaks as a function of chemical potential \ensuremath{\mu}, where 〈N〉 is the average number of particles in the channel. At finite temperatures, the peaks are broadened, but their spacings remain unchanged. We establish that the peaks are equally spaced for a model whose many-particle ground-state energy is quadratic in N, the particle number. We discuss our results for the ground-state energy of the Coulomb potential obtained from a Monte Carlo simulation at T=0 in this context.Motivated by the observation of periodic conductance oscillations in narrow channels, we study finite one-dimensional electronic systems with the following interactions: (i) an exactly solvable 1/${\mathit{x}}^{2}$ potential and (ii) the Coulomb potential with a cutoff, 1/ \ensuremath{\surd}${\mathit{x}}^{2}$+${\mathrm{\ensuremath{\delta}}}^{2}$ . The study of the 1/${\mathit{x}}^{2}$ model shows that at T=0, d〈N〉/d\ensuremath{\mu} exhibits sharp peaks as a function of chemical potential \ensuremath{\mu}, where 〈N〉 is the average number of particles in the channel. At finite temperatures, the peaks are broadened, but their spacings remain unchanged. We establish that the peaks are equally spaced for a model whose many-particle ground-state energy is quadratic in N, the particle number. We discuss our results for the ground-state energy of the Coulomb potential obtained from a Monte Carlo simulation at T=0 in this context.

Physical review. B, Condensed matterSep 15, 199211 citations

Path-integral approach to the ground-state energy of a homogeneous polaron gas

F. Brosens, Serghei N. Klimin, J. T. Devreese

The ground-state energy of an $N$ -polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed- and open-shell systems. The average fermion density in the neutral spherical dot is characterized by the Wigner-Seitz parameter ${r}_{s}$ . For a sufficiently large but finite number of polarons, the dependency of the ground-state energy on ${r}_{s}$ is very similar to that for a polaron gas in bulk. From this, we can conclude that the ground-state energy of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a neutralizing background charge.The ground-state energy of an $N$-polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed- and open-shell systems. The average fermion density in the neutral spherical dot is characterized by the Wigner-Seitz parameter ${r}_{s}$. For a sufficiently large but finite number of polarons, the dependency of the ground-state energy on ${r}_{s}$ is very similar to that for a polaron gas in bulk. From this, we can conclude that the ground-state energy of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a neutralizing background charge.

Physical Review BFeb 11, 20083 citations

Ground state energy of a many-particle boson system

M. E. Grypeos

International Journal of Theoretical PhysicsDec 1, 19721 citation

Motivated by the observation of periodic conductance oscillations in narrow channels, we study finite one-dimensional electronic systems with the following interactions: (i) an exactly solvable 1/

{\mathit{x}}^{2}

potential and (ii) the Coulomb potential with a cutoff, 1/ \ensuremath{\surd}

{\mathit{x}}^{2}

+${\mathrm{\ensuremath{\delta}}}^{2}$ . The study of the 1/

{\mathit{x}}^{2}

model shows that at T=0, d〈N〉/d\ensuremath{\mu} exhibits sharp peaks as a function of chemical potential \ensuremath{\mu}, where 〈N〉 is the average number of particles in the channel. At finite temperatures, the peaks are broadened, but their spacings remain unchanged. We establish that the peaks are equally spaced for a model whose many-particle ground-state energy is quadratic in N, the particle number. We discuss our results for the ground-state energy of the Coulomb potential obtained from a Monte Carlo simulation at T=0 in this context.

The ground-state energy of an

N

-polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed- and open-shell systems. The average fermion density in the neutral spherical dot is characterized by the Wigner-Seitz parameter

{r}_{s}

. For a sufficiently large but finite number of polarons, the dependency of the ground-state energy on

{r}_{s}

is very similar to that for a polaron gas in bulk. From this, we can conclude that the ground-state energy of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a neutralizing background charge.