Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Physical Review B

https://escholarship.org/content/qt7511z1pj/qt7511z1pj.pdf?t=p0uvj3

Quantum theory of nonequilibrium processes, I

https://hal.archives-ouvertes.fr/jpa-00239583/document

Il nuovo cimento

Many-fermion theory in expS- (or coupled cluster) form

The Galitskii-Feynman T matrix, which sums the infinite ladder series in a many-fermion system for both particle-particle and hole-hole scattering, is studied in detail for a family of realistic He-He interactions. The structure of the S-wave bound-state singularity, reported previously, and its dependence on the bare interaction are documented at length. Special attention is devoted to the T matrix in the scattering region, where the c.m. energy of the interacting pair is positive. In particular, the on-energy-shell T matrix in this region is parametrized in terms of real “effective” phase shifts incorporating many-body effects. The critical behavior discussed previously in the bound-state region manifests itself clearly in the zero-energy limit of these phase shifts for the S wave. Below (above) a certain critical density, which is a function of both temperature and c.m. momentum, this limit approaches the value 0(−π) radians. A generalized Levinson's theorem relates this behavior to the existence of fermion-fermion pairing. An especially striking feature of these many-body phase shifts is the cusp behavior exhibited at the Fermi surface in the lowtemperature limit, which turns out to arise essentially from the structure of the particle and hole occupation probabilities. Throughout this study the temperature dependence of the T matrix is particularly emphasized.

/pdf/a-study-of-the-galitskii-feynman-t-matrix-for-liquid-3-he-4eqzl2lt1p.pdf

A study of the Galitskii-Feynman T matrix for liquid 3 He

The low-energy atom-atom scattering properties are studied for various combinations of He isotopes interacting via a family of semiphenomenological potentials. Some of the potentials bind the (4He)2 molecule and some do not, and it is observed that molecular beam scattering measurements at energies currently accessible cannot resolve the difference between the two types of potentials. Our results are discussed within the framework of possible measurements to resolve this discrepancy. We present a method for solving the Schrodinger equation which is uniformly applicable for both bound and scattering state solutions and which is particularly suited to the types of potentials describing interactions for the rare gas atoms.

/pdf/low-energy-he-he-interactions-with-phenomenological-o5ypddf50b.pdf

Low-energy He-He interactions with phenomenological potentials

A general theory for solving the Hamilton-Jacobi partial differential equations for constrained Hamiltonian systems is proposed. The quantization of constrained systems is then applied using the WKB approximation. The constraints become conditions on the wave function to be satisfied in the semiclassical limit.

Quantization of constrained systems using the WKB approximation

/pdf/composite-pairs-and-effective-two-body-scattering-in-a-many-2n9deyl6dz.pdf

Composite pairs and effective two-body scattering in a many-body medium

The two-dimensional GaAs parabolic quantum dot (QD) is investigated in the static fluctuation approximation (SFA) where both the magnetic field and the electron–electron interaction are fully taken into account. The thermodynamic properties of the system are computed as functions of the temperature and magnetic field for different numbers of electrons ( N ). It is noted that the mean internal energy increases with increasing number of electrons and magnetic field. This increase is not smooth, and a sudden change in slope is observed at a certain value of magnetic field for N ≥4. It is found that the magnetization has sharp jumps for N ≥4; for N ≤3 a smooth monotonic diamagnetism is exhibited. A sharp peak is observed in the specific heat when the magnetic field is increased. It is found that the lowest-state transitions occur at a critical value of magnetic field. These transitions appear in the mean internal energy and magnetization.

Humam B. Ghassib

Papers

A study of the Galitskii-Feynman T matrix for liquid 3 He

Low-energy He-He interactions with phenomenological potentials

Quantization of constrained systems using the WKB approximation

Composite pairs and effective two-body scattering in a many-body medium

Thermodynamic properties of two-dimensional few-electrons quantum dot using the static fluctuation approximation (SFA)