Energy spectrum of strongly correlated particles in quantum dots

The ground state and the excitation spectrum of strongly correlated electrons in quantum dots are investigated. An analytical solution is constructed by exact diagonalization of the Hamiltonian in terms of the $N$-particle eigenmodes.Comment: 10 pages, 10 figures, to appear in Journal of Physics: Conf. Serie

Phase Transition in Strongly Degenerate Hydrogen Plasma

Direct fermionic path-integral Monte-Carlo simulations of strongly coupled hydrogen are presented. Our results show evidence for the hypothetical plasma phase transition. Its most remarkable manifestation is the appearance of metallic droplets which are predicted to be crucial for the electrical conductivity allowing to explain the rapid increase observed in recent shock compression measurments.Comment: 1 LaTeX file using jetpl.cls (included), 5 ps figures. Manuscript submitted to JETP Letter

Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering as an application a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.Comment: 10 pages and 8 figures, to appear in PRB April 1

Effective interaction potential and superfluid-solid transition of spatially indirect excitons

Using an adiabatic approximation we derive an effective interaction potentially for spatially indirect excitons. Using this potential and path integral Monte Carlo simulations we study exciton crystllization and the quantum melting phase transition in a macroscopic system of 2D excitons. Furthermore, the superfluid fraction is calculated as a function of density and shown to vanish upon crystallization. We show that the commonly used dipole model fails to correctly describe indirect excitons in quantum well structures

Hole crystallization in semiconductors

When electrons in a solid are excited to a higher energy band they leave behind a vacancy (hole) in the original band which behaves like a positively charged particle. Here we predict that holes can spontaneously order into a regular lattice in semiconductors with sufficiently flat valence bands. The critical hole to electron effective mass ratio required for this phase transition is found to be of the order of 80.Comment: accepted for publication in J. Phys. A: Math. Ge

Wigner function quantum molecular dynamics

Classical molecular dynamics (MD) is a well established and powerful tool in various fields of science, e.g. chemistry, plasma physics, cluster physics and condensed matter physics. Objects of investigation are few-body systems and many-body systems as well. The broadness and level of sophistication of this technique is documented in many monographs and reviews, see for example \cite{Allan,Frenkel,mdhere}. Here we discuss the extension of MD to quantum systems (QMD). There have been many attempts in this direction which differ from one another, depending on the type of system under consideration. One direction of QMD has been developed for condensed matter systems and will not discussed here, e.g. \cite{fermid}. In this chapter we are dealing with unbound electrons as they occur in gases, fluids or plasmas. Here, one strategy is to replace classical point particles by wave packets, e.g. \cite{fermid,KTR94,zwicknagel06} which is quite successful. At the same time, this method struggles with problems related to the dispersion of such a packet and difficulties to properly describe strong electron-ion interaction and bound state formation. We, therefore, avoid such restrictions and consider a completely general alternative approach. We start discussion of quantum dynamics from a general consideration of quantum distribution functions.Comment: 18 pages, based on lecture at Hareaus school on computational phyics, Greifswald, September 200

Influence of the nature of confinement on the melting of Wigner molecules in quantum dots

We analyze the quantum melting of two-dimensional Wigner molecules (WM) in confined geometries with distinct symmetries and compare it with corresponding thermal melting. Our findings unfold complementary mechanisms that drive the quantum and thermal crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale $n_X$. This is because the zero-point motion screens the boundary effects within short distances. The phase diagram as a function of thermal and quantum fluctuations determined from independent criteria is unique, and shows "melting" from the WM to both the classical and quantum "liquids." An intriguing signature of weakening liquidity with increasing temperature, $T$, is found in the extreme quantum regime. The crossover is associated with production of defects. However, these defects appear to play distinct roles in driving the quantum and thermal "melting." Our study will help comprehending melting in a variety of experimental traps - from quantum dots to complex plasma.Comment: 14 pages, 9 figure