Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOlberts kappa Fermi and Bose distributions
71
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The quantum version of Olberts kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play, dominate the microscopic scale but may have macroscopic consequences.
rate research
Read More
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $kappa$-distributions) which are frequently observed particularly in high temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high energy truncation. We find the representation of the mean energy as function of probability, and provide the implicit form of Olbert (Lorentzian) entropy as well as its high temperature limit. The relation to phase space density of states is obtained. We then find the entropy as function of probability, an expression which is fundamental to statistical mechanics and here to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations which add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might at temperatures sufficiently far from zero.
We investigate magnetic properties and statistical effects in 1D strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization and susceptibility in the presence of an external magnetic field $H$ are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value $H^F_capprox frac{8}{gamma}E_F$, where $E_F$ is the Fermi energy and $gamma$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0 and the critical value $H=H^M_capprox frac{16}{gamma}E_F$. We find that a pure boson phase occurs in the absence of the external field, fully-polarized fermions and bosons coexist for $0<H<H^M_c$, and a fully-polarized fermion phase occurs for $Hge H_c^M$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.
The zero temperature phase diagram of binary boson-fermion mixtures in two-colour superlattices is investigated. The eigenvalue problem associated with the Bose-Fermi-Hubbard Hamiltonian is solved using an exact numerical diagonalization technique, supplemented by an adaptive basis truncation scheme. The physically motivated basis truncation allows to access larger systems in a fully controlled and very flexible framework. Several experimentally relevant observables, such as the matter-wave interference pattern and the condensatefraction, are investigated in order to explore the rich phase diagram. At symmetric half filling a phase similar to the Mott-insulating phase in a commensurate purely bosonic system is identified and an analogy to recent experiments is pointed out. Furthermore a phase of complete localization of the bosonic species generated by the repulsive boson-fermion interaction is identified. These localized condensates are of a different nature than the genuine Bose-Einstein condensates in optical lattices.
Recent progress in the field of ultracold gases has allowed the creation of phase-segregated Bose-Fermi systems. We present a theoretical study of their collective excitations at zero temperature. As the fraction of fermion to boson particle number increases, the collective mode frequencies take values between those for a fully bosonic and those for a fully fermionic cloud, with damping in the intermediate region. This damping is caused by fermions which are resonantly driven at the interface.
We study the effects of interaction between bosons and fermions in a Bose-Fermi mixtures loaded in an optical lattice. We concentrate on the destruction of a bosonic Mott phase driven by repulsive interaction between bosons and fermions. Once the Mott phase is destroyed, the system enters a superfluid phase where the movements of bosons and fermions are correlated. We show that this phase has simultaneously correlations reminiscent of a conventional superfluid and of a pseudo-spin density wave order.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
