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## RECENT RESEARCH HIGHLIGHTS

An effective series expansion to the equation of state of unitary Fermi gases (

Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first

For details see:

*J. Phys. B: At. Mol. Opt. Phys.***49**225301 2016).Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first

*three*virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity*z*= 18, which is a vast improvement over the other analytical equations of state available where the agreements is*only*up to z =7. Second, by truncating our series solution to four terms again using first*four*virial coefficients, we find the Bertsch parameter \xi =0.35, which is in good agreement with the direct experimental measurement of \xi =0.37. This second form of equation of state shows a good agreement with self-consistent*T*-matrix calculations in the normal phase.For details see:

*J. Phys. B: At. Mol. Opt. Phys.***49**225301 2016.An effective mean-field theory for the coexistence of anti-ferromagnetism and superconductivity: Applications to Iron-based superconductors and cold Bose-Fermi atomic mixtures (Physics Letters A 380 (2016) 3421-3429).

We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose-Einstein condensation (BEC) in electronic systems and Bose-Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study the model within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.

For details see: Physics Letters A380 (2016) 3421-3429.

We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose-Einstein condensation (BEC) in electronic systems and Bose-Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study the model within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.

For details see: Physics Letters A380 (2016) 3421-3429.

Phase diagram of strongly attractive

We examine a system of doubly degenerate

For details see: Physics Letters A 379 (2015) 2715–2722.

*p*-orbital fermions on optical lattices (Physics Letters A 379 (2015) 2715–2722).We examine a system of doubly degenerate

*p*-orbital polarized fermions on a two-dimensional square lattice with a strong on-site interaction. We consider the system density at the half filling limit and tackle the strong attractive interaction using a perturbation theory. We treat the four-site square plaquette interaction term generated from the directional tunneling dependence of*p*-orbitals using the fourth order in perturbation theory. We map the strong coupling particle Hamiltonian into an effective spin-Hamiltonian and then use a variational mean field approach and a linear spin-wave theory to study the phase diagram. Further, we discuss the experimental signatures of these phases within the context of current cold-atom experimental techniques.For details see: Physics Letters A 379 (2015) 2715–2722.

Polarization-induced phase separation and re-entrant transition of two-component fermions in a one-dimensional lattice (Phys. Rev. A 91, 053627, 2015)

By investigating the compressibility of one-dimensional lattice fermions at various filling factors, we study the phase separation and re-entrant transition within the framework of the Bethe ansatz method. We model the system using the repulsive Hubbard model and calculate compressibility as a function of polarization for arbitrary values of chemical potential, temperature, and interaction strength. For filling factors 0<n<1, compressibility is a nonmonotonic function of polarization at all thermodynamic parameters. The compressibility reveals a phase transition into a phase-separated state for both low and intermediate temperatures at intermediate interactions as one increases the polarization. For certain filling factors, we find the re-entrant transition into the mixed phase at a higher polarization.

For details see: Physical Review A Phys. Rev. A 91, 053627 (2015).

By investigating the compressibility of one-dimensional lattice fermions at various filling factors, we study the phase separation and re-entrant transition within the framework of the Bethe ansatz method. We model the system using the repulsive Hubbard model and calculate compressibility as a function of polarization for arbitrary values of chemical potential, temperature, and interaction strength. For filling factors 0<n<1, compressibility is a nonmonotonic function of polarization at all thermodynamic parameters. The compressibility reveals a phase transition into a phase-separated state for both low and intermediate temperatures at intermediate interactions as one increases the polarization. For certain filling factors, we find the re-entrant transition into the mixed phase at a higher polarization.

For details see: Physical Review A Phys. Rev. A 91, 053627 (2015).

Evidence for the breakdown of momentum independent many-body t-matrix approximation in the normal phase of Bosons (

We revisit the momentum independent many-body t-matrix approach for boson systems developed by Shi and Griffin and Bijlsma and Stoof. Despite its popularity, simplicity, and expected advantage of being its applicability to both normal and superfluid phases, we find that the theory breaks down in the normal phase of bosons. We conjecture that this failure is due to neglecting of momentum dependence on the t-matrix.

For details see: Frontiers of Physics

*Front. Phys*. 2, 78, 2014)We revisit the momentum independent many-body t-matrix approach for boson systems developed by Shi and Griffin and Bijlsma and Stoof. Despite its popularity, simplicity, and expected advantage of being its applicability to both normal and superfluid phases, we find that the theory breaks down in the normal phase of bosons. We conjecture that this failure is due to neglecting of momentum dependence on the t-matrix.

For details see: Frontiers of Physics

*Front. Phys*. 2:78. doi: 10.3389/fphy.2014.00078.