scholarly journals Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 113
Author(s):  
Ignacio Baena ◽  
Pedro Pérez-Fernández ◽  
Manuela Rodríguez-Gallardo ◽  
José Miguel Arias
Keyword(s):  
Phase Transition ◽  
Ground State ◽  
Large Particle ◽  
State Energy ◽  
Particle Number ◽  
Diatomic Molecules ◽  
The Other ◽  
Abrupt Changes ◽  
Level Model ◽  
Two Level Model

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

Particle-number conservation in odd mass proton-rich nuclei in the isovector pairing case

2015 ◽  
Vol 24 (06) ◽  
pp. 1550042 ◽  
Author(s):  
M. Fellah ◽  
N. H. Allal ◽  
M. R. Oudih
Keyword(s):  
Ground State ◽  
State Energy ◽  
Particle Number ◽  
Mean Field ◽  
Expectation Values ◽  
Deformation Effect ◽  
Pairing Effect ◽  
Projection Effect ◽  
Particle Number Conservation ◽  
The One

An expression of a wave function which describes odd–even systems in the isovector pairing case is proposed within the BCS approach. It is shown that it correctly generalizes the one used in the pairing between like-particles case. It is then projected on the good proton and neutron numbers using the Sharp-BCS (SBCS) method. The expressions of the expectation values of the particle-number operator and its square, as well as the energy, are deduced in both approaches. The formalism is applied to study the isovector pairing effect and the number projection one on the ground state energy of odd mass N ≈ Z nuclei using the single-particle energies of a deformed Woods–Saxon mean-field. It is shown that both effects on energy do not exceed 2%, however, the absolute deviations may reach several MeV. Moreover, the np pairing effect rapidly diminishes as a function of (N - Z). The deformation effect is also studied. It is shown that the np pairing effect, either before or after the projection, as well as the projection effect, when including or not the isovector pairing, depends upon the deformation. However, it seems that the predicted ground state deformation will remain the same in the four approaches.

QUANTUM GLASSINESS AND SUPERCONDUCTIVITY IN DOPED LOW DIMENSIONAL ANTIFERROMAGNETS

2008 ◽  
Vol 22 (16) ◽  
pp. 2501-2516 ◽  
Author(s):  
CHRISTOS PANAGOPOULOS
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Direct Observation ◽  
Ground State ◽  
Glassy State ◽  
Quantum Critical Point ◽  
Intrinsic Property ◽  
Material Quality ◽  
Abrupt Changes ◽  
Low Dimensional

Following the direct observation of abrupt changes in the superconducting ground state in doped low dimensional antiferromagnets, we have identified a phase transition where superconductivity is optimal. The experiments indicate the presence of a putative quantum critical point associated with the emergence of a glassy state. This mechanism is argued to be an intrinsic property and as such, largely independent of material quality and the level of disorder.

Possible ferromagnetism of dense quark matter

2018 ◽  
Vol 96 (11) ◽  
pp. 1163-1172
Author(s):  
Kausik Pal
Keyword(s):  
Phase Transition ◽  
Magnetic Properties ◽  
Magnetic Susceptibility ◽  
Single Particle ◽  
Ground State ◽  
Quark Matter ◽  
State Energy ◽  
Magnetic Instability ◽  
Dense Quark Matter ◽  
Spin Polarized

The cardinal focus of the present review is to investigate the possibility of the para-ferro phase transition of dense quark matter. For these, the calculation of the single-particle energies, ground state energy (GSE) densities, and spin susceptibility χ of degenerate quark matter with one gluon exchange interaction in terms of spin-dependent Landau parameters (LPs) have been presented. The expressions for the GSE and χ of cold and dense spin-polarized quark matter have been derived with corrections due to correlation. Furthermore, the magnetic properties of spin polarized quark matter have been discussed by evaluating the magnetization ⟨M⟩ and magnetic susceptibility χM in terms of LPs. Finally, the possibility of magnetic instability has been revealed by studying the density dependence of ⟨M⟩ and χM.

Determination of the Recombination Processes in Copper Ternary Chalcopyrites by Phototransport Measurements

1996 ◽  
Vol 426 ◽  
Author(s):  
Y. Lubianmker ◽  
G. Bitton ◽  
I. Balberg ◽  
O. Resto ◽  
S. Z. Weisz
Keyword(s):  
Level Structure ◽  
Experimental Results ◽  
The Other ◽  
Recombination Level ◽  
Recombination Processes ◽  
General Recombination ◽  
Level Model ◽  
Ternary Chalcopyrites ◽  
Two Level Model

AbstractWe have measured the phototransport properties of CuGaSe2 films as a function of temperature. The simplest model which is consistent with all the experimental results consists of two recombination levels, one of which is donor-like and the other is acceptor-like. This model is similar to the symmetrical two-level model, which we have recently suggested for CuInS2 films. We thus conclude that this model, with slight variations, represents the general recombination level structure in all copper ternary chalcopyrites.

Two-level model for near saturated fluorescence in diatomic molecules

1979 ◽  
Vol 18 (6) ◽  
pp. 856 ◽  
Author(s):  
R. P. Lucht ◽  
N. M. Laurendeau
Keyword(s):  
Diatomic Molecules ◽  
Level Model ◽  
Two Level Model

scholarly journals Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator

2021 ◽  
Author(s):  
Junjun Xu
Keyword(s):  
Critical Point ◽  
Particle Number ◽  
Entanglement Entropy ◽  
Common Belief ◽  
Number Partition ◽  
Level Model ◽  
The Common ◽  
Adiabatic Dynamics ◽  
Symmetry Protected ◽  
Two Level Model

Abstract We study the non-adiabatic dynamics of a typical symmetry-protected topological phase-the Haldane insulator phase with broken bond-centered inversion. By continuously breaking the middle chain, we find the gap closes at a critical point in the deep Haldane insulator regime with a change of particle number partition of the left or right system. The adiabatic evolution fails at this critical point and we show how to predict the dynamics of the entanglement entropy near this point using a two-level model. These results show that one can find a critical regime where the entanglement measurement is relatively robust against perturbation that breaks the protecting symmetries in the Haldane insulator. This is in contrast to the common belief that the symmetry-protected topological phases are fragile without the protecting symmetries.

THE ELECTRONIC CORRELATION EFFECT FROM WEAK TO STRONG IN THE THREE DIMENSIONAL ELECTRON GAS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250065 ◽  
Author(s):  
ZHI-MING YU ◽  
QING-WEI WANG ◽  
YU-LIANG LIU
Keyword(s):  
Phase Transition ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electron Gas ◽  
Three Dimensional ◽  
Positive Function ◽  
Correlation Effect ◽  
Electronic Correlation ◽  
The Difference

Based on the success of the eigenfunctional theory ( EFT) in the one-dimensional model,16,24,51 we apply it to the three-dimensional homogeneous electron gas. By EFT, we first present a rigorous expression of the pair distribution function g(r) of the electron gas. This expression effectively solves the negative problem of g(r) that when electronic correlation effect is strong, the previous theories give a negative g(r),9 while g(r) is strictly a positive function. From this reasonable g(r), we estimate and establish a newly effective fitting expression of the ground state energy of electron gas. The new fitting expression presents a similar result with present theories when rs is small, since only in the limit of rs is small, present theories estimate a exact ground state energy. When rs increases, the difference between EFT and other theories becomes more and more remarkable. The difference is expected as EFT estimates a reasonable g(r) and would effectively amend the overestimate of previous theories in the ground state energy. In addition, by the ground state energy, we estimate the phase transition derived by the strong correlation effect. When the density decreases, the electronic correlation effect changes from weak to strong and we observe a sudden phase transition from paramagnetic to full spin polarization occurring at rs = 31 ± 4.

Particle-number conservation in quasiparticle representation in the isovector neutron–proton pairing case

2015 ◽  
Vol 24 (12) ◽  
pp. 1550097 ◽  
Author(s):  
M. Fellah ◽  
N. H. Allal ◽  
Faiza Hammache ◽  
M. R. Oudih
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Number Operator ◽  
Expectation Values ◽  
Total Particle Number ◽  
Total Particle ◽  
Level Model ◽  
Particle Number Conservation ◽  
The One ◽  
Proton Pairing

Until now, the Sharp-Bardeen–Cooper–Schrieffer (SBCS) particle-number projection method, in the isovector neutron–proton pairing case, has been developed in the particle representation. However, this formalism is sometimes complicated and cumbersome. In this work, the formalism is developed in the quasiparticle representation. An expression of the projected ground state wave function is proposed. Expressions of the energy as well as the expectation values of the total particle-number operator and its square are deduced. It is shown that these expressions are formally similar to their homologues in the pairing between like-particles case. They are easier to handle than the ones obtained using the particle representation and are more adapted to numerical calculations. The method is then numerically tested within the schematic one-level model, which allows comparisons with exact results, as well as in the case of even–even nuclei within the Woods–Saxon model. In each case, it is shown that the particle-number fluctuations that are inherent to the BCS method are completely eliminated by the projection. In the framework of the one-level model, the values of the projected energy are clearly closer to the exact values than the BCS ones. In realistic cases, the relative discrepancies between projected and unprojected values of the energy are small. However, the absolute deviations may reach several MeV.

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