Peter Borrmann

Classification of Phase Transitions in Small Systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transition in a finite system and to small Ar clusters.

The structure of small clusters : multiple normal-modes model

A simple model for the structural fluctuations, isomerizations, and phase transitions of small rare‐gas clusters is defined (multinormal‐model) which studies the statistical equilibrium of several isomers making use of the normal mode expansion of the free energy. It is evaluated classically and quantum mechanically and its results are compared to those of extensive (path integral) simulation calculations.

Recursion formulas for quantum statistical partition functions

Recursion formulas are derived for Fermi–Dirac and Bose–Einstein statistical partition functions for systems where the energy can be written as a sum of one particle energies. Thus, their exact partition functions can be calculated for any N.

Calculation of thermodynamic properties of finite Bose-Einstein systems

We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in some approximation, e.g., like Bose-Einstein condensates in magnetic traps. The numerical effort of our computation scheme grows only linearly with the number of particles. As an example, we calculate the relative ground-state fluctuations and specific heats for ideal Bose gases with a finite number of particles enclosed in containers of different shapes.

The interplay between shell effects and electron correlations in quantum dots

We use the path integral Monte Carlo method to investigate the interplay between shell effects and electron correlations in single quantum dots with up to 12 electrons. By use of an energy estimator based on the hypervirial theorem of Hirschfelder we study the energy contributions of different interaction terms in detail. We discuss under which conditions the total spin of the electrons is given by Hund’s rule, and the temperature dependence of the crystallization effects.

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose systems in power-law traps within a semi-analytic approach with a continuous one-particle density of states O(E)~Ed-1 for different values of d and to a three-dimensional harmonically confined ideal Bose gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.

Order-disorder transition in nanoscopic semiconductor quantum rings

Using the path integral Monte Carlo technique we show that semiconductor quantum rings with up to six electrons exhibit a temperature, ring diameter, and particle number dependent transition between spin ordered and disordered Wigner crystals. Because of the small number of particles the transition extends over a broad temperature range and is clearly identifiable from the electron pair correlation functions.

Classification of the nuclear multifragmentation phase transition

Using a recently proposed classification scheme for phase transitions in finite systems [Phys. Rev. Lett. 84, 3511 (2000)] we show that within the statistical standard model of nuclear multifragmentation the predicted phase transition is of first order.

How should thermodynamics for small systems be done

Abstract We show that the question of which simulation method is the right one to describe the thermal behaviour of clusters is not a philosophical one. Moreover we point out that getting better results might be accompanied by a loss of information. Different points of view yield different results. The number of iterations, let us call it simulation time, plays a central role here. Making use of the simulation data at higher temperatures the phase transitions and the effects of isomerisation are easy to understand.

Thermodynamics of finite magnetic two-isomer systems

We use Monte Carlo simulations to investigate the thermodynamical behavior of aggregates consisting of few superparamagnetic particles in a colloidal suspension. The potential energy surface of this classical two-isomer system with a stable and a metastable “ring” and “chain” configuration is tunable by an external magnetic field and temperature. We determine the complex “phase diagram” of this system and analyze thermodynamically the nature of the transition between the ring and the chain “phase.”