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Register a new userQuantum Monte Carlo study of spin-polarized deuterium
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The ground state properties of spin-polarized deuterium (D$downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$downarrow$ species have been investigated (D$downarrow_1$, D$downarrow_2$, D$downarrow_3$), corresponding respectively to one, two and three equally occupied nuclear spin states. Influence of the backflow correlations on the ground state energy of the systems is explored. The equilibrium densities for D$downarrow_2$ and D$downarrow_3$ liquids are obtained and compared with ones obtained in previous approximate prediction. The density and the pressure at which the gas-liquid phase transition occurs at $T$=0 is obtained for D$downarrow_1$.
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This work expands recent investigations in the field of spin-polarized tritium (T$downarrow$) clusters . We report the results for the ground state energy and structural properties of large T$downarrow$ cl usters consisting of up to 320 atoms. All calculations have been performed with variational and diffusi on Monte Carlo methods, using an accurate {it ab initio} interatomic potential. Our results for $N le q 40$ are in good agreement with results obtained by other groups. Using a liquid-drop expression for t he energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T$downarrow$. In addition, the calculations of the energy for larg e clusters have allowed for an estimation of the surface tension. From the mean-square radius of the dr op, determined using unbiased estimators, we determine the dependence of the radii on the size of the c luster and extract the unit radius of the T$downarrow$ liquid.
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks (Gross-Pitaevskii, Bethe ansatz, local density approximation, etc.) the main tool of the study is the Quantum Monte Carlo method in different modifications (variational Monte Carlo, diffusion Monte Carlo, fixed-node Monte Carlo methods). We benchmark our Monte Carlo calculations by recovering known analytical results (perturbative theories in dilute limits, exactly solvable models, etc.) and extend calculations to regimes, where the results are so far unknown. In particular we calculate the equation of state and correlation functions for gases in various geometries and with various interatomic interactions.
The ground-state properties of spin-polarized tritium T$downarrow$ at zero temperature are obtained by means of diffusion Monte Carlo calculations. Using an accurate {em ab initio} T$downarrow$-T$downarrow$ interatomic potential we have studied its liquid phase, from the spinodal point until densities above its freezing point. The equilibrium density of the liquid is significantly higher and the equilibrium energy of $-3.664(6)$ K significantly lower than in previous approximate descriptions. The solid phase has also been studied for three lattices up to high pressures, and we find that hcp lattice is slightly preferred. The liquid-solid phase transition has been determined using the double-tangent Maxwell construction; at zero temperature, bulk tritium freezes at a pressure of $P=9(1)$ bar.
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density $n_B$ is smaller than the fermion density $n_F$, for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing $n_B$.
We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T$downarrow$ atoms and the mixtures of T$downarrow$ with spin-polarized deuterium D$downarrow$ and hydrogen H$downarrow$ atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D$downarrow$ atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T$downarrow$ clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T$downarrow$-H$downarrow$ clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two or three D$downarrow$ atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T$downarrow$ trimer.
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