An introduction to Bose-Einstein condensation and the $λ$-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.
An introduction to Bose-Einstein condensation and the λ-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.
Bose-Einstein condensation and the λ-transition are described in molecular detail for bosons interacting with a pair potential. New phenomena are identified that are absent in the usual ideal gas treatment. Monte Carlo simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons give a diverging heat capacity approaching the transition. Pure permutation loops give continuous growth in the occupancy of the ground momentum state. Mixed ground and excited momentum state permutation loops give a discontinuous transition to the condensed phase. The consequent latent heat for the λ-transition is 3\% of the total energy. The predicted critical velocity for superfluid flow is within a factor of three of the measured values over three orders of magnitude in pore diameter.
First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute Bose gas, where presence atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition is defined by a condition for the Bose-Einstein transition, which transforms reflected neutron pair modes to single neutron modes.
The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones 4He give the λ-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.
Abstract In this work, the authors show an apparent connection in the behaviors of superfluid Helium in its two stable isotopes, where the lambda transition to superfluidity is seen to correspond to a theoretical Bose–Einstein condensation temperature of the ideal parts of the two isotopes. A statistical model for the physical and thermodynamic behaviors is developed based on their known properties, where the equations of the partition function, entropy, and specific heat are constructed in such a way where one term applies to the ideal part of the fluid and the second to its interacting part. The calculated temperatures for the formation of a theoretical Bose–Einstein condensation in the ideal parts of both isotopes almost completely matches their lambda transition temperatures. The models of the two isotopes are very different due to the fermionic nature of Helium-3, for which the model is formed based on the Bardeen–Cooper–Schrieffer (BCS) theory of Cooper pairs of fermions. Using this formulation, the Bose–Einstein condensation temperature for the pairs of Helium-3 atoms is calculated, as opposed to the condensation temperature for Helium-4, which is directly derived from the bosonic atoms, leading to its much lower value than Helium-4.
Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statistics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discontinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.
Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.