A one dimensional experiment in granular dynamics is carried out to test the thermodynamic theory of weakly excited granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78, 2764(1997)] where granular particles are treated as spinless Fermions. The density profile is measured and then fit to the Fermi distribution function, from which the global temperature of the system, T , is determined. The...

Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einst...

Recent experiments have observed condensation behavior in a strongly interacting system of fermionic atoms. We interpret these observations in terms of a mean-field version of resonance superfluidity theory. We find that the objects condensed are not bosonic molecules composed of bound fermion pairs, but are rather spatially correlated Cooper pairs whose coherence length is comparable to the me...

Abstract A general method to construct basis functions for fermionic systems which account for the SU(2) symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system and it appears as a natural generalization of the Bethe Ansatz to the case of non integrable systems. As an example we present the block diagonalizati...

In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum dist...

2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....

2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....

2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....