Narrow Results

An analytical and nonperturbative approach to SU(2) and SU(3) Yang–Mills thermodynamics is developed and applied. Each theory comes in three phases: A deconfining, a preconfining, and a confining one. We show how macroscopic and inert scalar fields emerge in each phase and how they determine the ground-state physics and the properties of the excitations. While the excitations in the deconfining and preconfining phases are massless or massive gauge modes the excitations in the confining phase are massless or massive spin-1/2 fermions. The nature of the two phase transitions is investigated for each theory. We compute the temperature evolution of thermodynamical quantities in the deconfining and preconfining phase and estimate the density of states in the confining phase. Some implications for particle physics and cosmology are discussed.

Interacting Bose gas confined by an external potential is studied using Green functions in spectral representation. The calculation is presented transparently using the equation of motion method. With this, the interplay between the condensed and the non-condensed atoms is inevitably seen. An expression for the condensate number at finite temperature is obtained in the lowest and first orders, from which depletion of bosons from the ground state is qualitatively analyzed. Finally, we discuss the behaviour of the specific heat of a trapped interacting Bose gas in the quasi-continuum limit.

The doping dependence of the bose condensation energy is investigated by using our SU(2) holon-pair boson theory. It is shown that the bose condensation energy U results from the interplay between the charge and spin degrees of freedom and that the doping dependence of U at T=0K is well fit by the relation, with Δ₀, the spin gap at 0K; x, the hole doping concentration and α, a constant.

Extensive Path Integral Monte Carlo simulations of two-dimensional para-Hydrogen embedded in a crystalline matrix of Alkali atoms, show no evidence of superfluid behavior at low temperature. Rather, the system is observed to form a commensurate (non superfluid) crystal.

We have studied the thermodynamic properties of noninteracting gases in periodic lattice potential at arbitrary integer fillings and compared them with that of ideal homogeneous gases. By deriving explicit expressions for the thermodynamic quantities and performing exact numerical calculations, we have found that the dependence of e.g., entropy and energy on the temperature in the normal phase is rather weak especially at large filling factors. In the Bose condensed phase, their power dependence on the reduced temperature is nearly linear, which is in contrast to that of ideal homogeneous gases. We evaluated the discontinuity in the slope of the specific heat which turned out to be approximately the same as that of the ideal homogeneous Bose (IHB) gas for filling factor ν = 1. The discontinuity i.e. the jump in the heat capacity per particle linearly decreases with increasing ν. These results may serve as a checkpoint for various experiments on optical lattices as well as theoretical studies of weakly interacting Bose systems in periodic potentials being a starting point for perturbative calculations.

The ground-state properties in one-dimensional Hubbard model with on-site attraction and repulsion of electrons in the presence of magnetic field h are calculated by means of the exact Bethe-ansatz formalism and the generalized self-consistent field (GSCF) approach for general electron concentrations n and arbitrary interaction strength. The ground-state properties, including the energy, the average spin (magnetization) and the kinetic energy are compared over a wide range of parameter space. The GSCF theory is in qualitative and in some cases in good quantitative agreement with the exact results. The GSCF theory at U≤0 (or U≥0) differentiates the spin (or charge) energy gap from the BCS (or antiferromagnetic) order parameter and suggests a smooth crossover from the phase with the itinerant BCS-like behavior to the Bose condensation regime of the local pairs.

Atomic vapors can be prepared and manipulated at very low densities and temperatures. When they are rotating, they can reach a quantum Hall regime in which there should be manifestations of the fractional quantum Hall effect. We discuss the appearance of the principal sequence of fractions ν=p/(p±1) for bosonic atoms. The termination point of this series is the paired Moore–Read Pfaffian state. Exotic states fill the gap between the paired state and the vortex lattice expected at high filling of the lowest Landau level. In fermionic vapors, the p-wave scattering typical of ultralow energy collisions leads to the hard-core model when restricted to the lowest Landau level.

The Bose–Einstein condensates of the alkali atomic gases trapped in magnetic traps are spinor fields with local "spin-gauge" symmetry.⁵ Here we show that there is fundamental difference in the manifestation of spin-gauge effects between two low-field-seeking states: |F=2,m_F=2〉 and |1,-1〉.

Interacting Bose gas confined by an external potential is studied using Green functions in spectral representation. The calculation is presented transparently using the equation of motion method. With this, the interplay between the condensed and the non-condensed atoms is inevitably seen. An expression for the condensate number at finite temperature is obtained in the lowest and first orders, from which depletion of bosons from the ground state is qualitatively analyzed. Finally, we discuss the behaviour of the specific heat of a trapped interacting Bose gas in the quasi-continuum limit.

Extensive Path Integral Monte Carlo simulations of two-dimensional para-Hydrogen embedded in a crystalline matrix of Alkali atoms, show no evidence of superfluid behavior at low temperature. Rather, the system is observed to form a commensurate (non superfluid) crystal.