scholarly journals $$\mu PT$$ statistical ensemble: systems with fluctuating energy, particle number, and volume

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ugo Marzolino
Keyword(s):  
Partition Function ◽  
Particle Number ◽  
Mean Field ◽  
Statistical Ensemble ◽  
Energy Particle ◽  
Ensemble Equivalence ◽  
Ideal Gases ◽  
Model Independent ◽  
Independent Features ◽  
Ensemble Systems

AbstractWithin the theory of statistical ensemble, the so-called $$\mu PT$$ μ P T ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number statistics are derived. Non-analytic points of the partition function are discussed in connection with divergent fluctuations and ensemble equivalence. Quantum and classical ideal gases, and a model of Bose gas with mean-field interactions are discussed as examples of the above considerations.

scholarly journals Rotation as an origin of high energy particle collisions

2016 ◽  
Vol 31 (04) ◽  
pp. 1650029 ◽  
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Center Of Mass ◽  
High Energy ◽  
High Energy Particle ◽  
Particle Collisions ◽  
Energy Particle ◽  
Relativistic Stars ◽  
Mass Frame ◽  
Model Independent

We consider collision of two particles in rotating spacetimes without horizons. If the metric coefficient responsible for rotation of spacetime is big enough, the energy of collisions in the center of mass frame can be as large as one likes. This can happen in the ergoregion only. The results are model-independent and apply both to relativistic stars and wormholes.

NEUTRON–PROTON PAIRING EFFECT ON ONE-PROTON AND TWO-PROTON SEPARATION ENERGIES IN RARE-EARTH PROTON-RICH NUCLEI

2012 ◽  
Vol 21 (12) ◽  
pp. 1250100 ◽  
Author(s):  
F. HAMMACHE ◽  
N. H. ALLAL ◽  
M. FELLAH
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Particle Number ◽  
Good Description ◽  
Mean Field ◽  
Pairing Effect ◽  
Pairing Correlations ◽  
The One ◽  
Proton Pairing ◽  
Realistic Choice

The one-proton and two-proton separation energies are studied for "ordinary" and rare-earth proton-rich nuclei by including the isovector neutron–proton (np) pairing correlations using the BCS approximation. Even–even as well as odd nuclei are considered. In the latter case, the wave function is defined using the blocked-level technique. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the np isovector pairing effects on the one-proton and two-proton separation energies are non-negligible. However, the only isovector BCS approximation seems to be inadequate for a good description of these quantities when including the np pairing effects: either a particle-number projection or the inclusion of the isoscalar pairing effect seems to be necessary. Another possible improvement would be a more realistic choice of the pairing strengths.

SUPERHEAVY NUCLEI IN DIFFERENT PAIRING MODELS

2006 ◽  
Vol 15 (02) ◽  
pp. 452-456 ◽  
Author(s):  
ANDRZEJ BARAN ◽  
ZDZISŁAW ŁOJEWSKI ◽  
KAMILA SIEJA
Keyword(s):  
Spontaneous Fission ◽  
Particle Number ◽  
Mean Field ◽  
Projection Methods ◽  
Bcs Theory ◽  
Microscopic Description ◽  
Fission Process ◽  
State Dependent ◽  
Fission Barriers ◽  
Inertia Parameters

Pairing plays an important role in both mean-field and macroscopic-microscopic description of the fission process. We discuss two kinds of pairing models: monopole (g = const ) and state dependent (δ-type force). As is known the BCS theory leads to the particle number symmetry braking. To restore the symmetry one uses a projection methods (projection before- or after variation) or one solves the Lipkin-Nogami equations. We apply all these methods in the case of monopole pairing. Fission barriers, inertia parameters and spontaneous fission half-lives are studied in the case of Z = 112 isotopes.

scholarly journals Mean-field evolution of open quantum systems: an exactly solvable model

2012 ◽  
Vol 468 (2147) ◽  
pp. 3398-3412 ◽  
Author(s):  
M. Merkli ◽  
G. P. Berman
Keyword(s):  
Particle Number ◽  
Open Quantum Systems ◽  
Mean Field ◽  
Solvable Model ◽  
Direct Interaction ◽  
Quantum Particles ◽  
Exactly Solvable ◽  
Energy Conserving ◽  
Markovian Approximations ◽  
The Mean

We consider quantum particles coupled to local and collective thermal quantum environments. The coupling is energy conserving, and the collective coupling is scaled in the mean-field way. There is no direct interaction between the particles. We show that an initially factorized state of the particles remains factorized at all times, in the limit of large particle number. Each single-particle factor evolves according to an explicit, nonlinear, dissipative and time-dependent Hartree–Lindblad equation. The model is exactly solvable; we do not make any weak coupling or any Markovian approximations, and our results are mathematically rigorous.

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.

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