A number-phase interaction is suggested that is analogous to the usual quadrature squeezing Hamiltonian for a mode of the electromagnetic field. Applied to an initial coherent state, it produces number-phase squeezed states. For moderate squeezing in either direction the result is close to a minimum uncertainty state. Two different ${\mathrm{\ensuremath{\chi}}}^{(3)}$ approximations to the ideal interaction are found, appropriate for the different directions of squeezing. Even with the approximate interaction, the fluctuations in photon number can be reduced to less than half a photon for an arbitrarily intense field.A number-phase interaction is suggested that is analogous to the usual quadrature squeezing Hamiltonian for a mode of the electromagnetic field. Applied to an initial coherent state, it produces number-phase squeezed states. For moderate squeezing in either direction the result is close to a minimum uncertainty state. Two different ${\mathrm{\ensuremath{\chi}}}^{(3)}$ approximations to the ideal interaction are found, appropriate for the different directions of squeezing. Even with the approximate interaction, the fluctuations in photon number can be reduced to less than half a photon for an arbitrarily intense field.

Physical Review LettersMay 31, 199321 citations

Off-site interaction effect in the Extended Hubbard Model with the SCRPA method

S Harir, Mohamed Bennai, Y. Boughaleb

The self consistent random phase approximation (SCRPA) and a direct analytical (DA) method are proposed to solve the Extended Hubbard Model (EHM) in one dimension (1D). We have considered an EHM including on-site and off-site interactions for closed chains in 1D with periodic boundary conditions. The comparison of the SCRPA results with the ones obtained by a DA approach shows that the SCRPA treats the problem of these closed chains in a rigorous manner. The analysis of the nearest–neighbour repulsion effect on the dynamics of our closed chains shows that this repulsive interaction between the electrons of the neighbouring atoms induces supplementary conductivity, since, the SCRPA energygap vanishes when these closed chains are governed by a strong repulsive on-site interaction and intermediate nearest–neighbour repulsion.The self consistent random phase approximation (SCRPA) and a direct analytical (DA) method are proposed to solve the Extended Hubbard Model (EHM) in one dimension (1D). We have considered an EHM including on-site and off-site interactions for closed chains in 1D with periodic boundary conditions. The comparison of the SCRPA results with the ones obtained by a DA approach shows that the SCRPA treats the problem of these closed chains in a rigorous manner. The analysis of the nearest–neighbour repulsion effect on the dynamics of our closed chains shows that this repulsive interaction between the electrons of the neighbouring atoms induces supplementary conductivity, since, the SCRPA energygap vanishes when these closed chains are governed by a strong repulsive on-site interaction and intermediate nearest–neighbour repulsion.

arXiv:0903.1347Physica ScriptaSep 14, 20073 citations

The average effective interaction

Philip R. Goode

Springer eBooksApr 6, 20080 citations

On point interactions

W.T.M. Caspers

Dec 17, 19924 citations

Anisotropic Ising model in a magnetic field: Effective-field theory analysis

Minos A. Neto, Rosana A. dos Anjos, J. Ricardo de Sousa

The anisotropic two-dimensional Ising model in the presence of a magnetic field is studied within two different approaches: the effective-field theory (EFT) with correlation and the Bethe-Peierls (BP) approximation. The model consists of ferromagnetic interaction $({J}_{x})$ in the $x$ direction and antiferromagnetic interaction $({J}_{y})$ in the $y$ direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case ${J}_{x}={J}_{y}$ . Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of $H∕J∊[0,2]$ , with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of $r={J}_{y}∕{J}_{x}$ , and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.The anisotropic two-dimensional Ising model in the presence of a magnetic field is studied within two different approaches: the effective-field theory (EFT) with correlation and the Bethe-Peierls (BP) approximation. The model consists of ferromagnetic interaction $({J}_{x})$ in the $x$ direction and antiferromagnetic interaction $({J}_{y})$ in the $y$ direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case ${J}_{x}={J}_{y}$. Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of $H∕J∊[0,2]$, with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of $r={J}_{y}∕{J}_{x}$, and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.

Physical Review BJun 23, 200632 citations

({J}_{x})

in the

x

direction and antiferromagnetic interaction

({J}_{y})

in the

y

direction. The phase diagram in the $T\text{\ensuremath{-}}H$ plane is obtained for the particular case

{J}_{x}={J}_{y}

. Special focus is given in the low-temperature region of the phase diagram, where a first-order phase transition is observed using the mean-field approximation, which is in disagreement with the linear chain approximation (LCA). Our results indicate a second-order phase transition for all values of

H∕J∊[0,2]

, with the presence of a reentrant behavior only observed in the BP approximation in accordance with the results of the LCA and exact solution. The null field critical temperature is an increasing function of

r={J}_{y}∕{J}_{x}

, and in the $r\ensuremath{\rightarrow}0$ limit we have found, using BP and EFT, the approximate form ${k}_{B}{T}_{N}∕{J}_{x}\ensuremath{\simeq}A∕\mathrm{ln}(1∕r)$ in accordance with the exact result of Onsager.