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Peter Borrmann

Publications and source records attributed to Peter Borrmann.

14 recordsLinked to original sources
arXiv2001

Deceptive signals of phase transitions in small magnetic clusters

We present an analysis of the thermodynamic properties of small transition metal clusters and show how the commonly used indicators of phase transitions like peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.

cond-mat.stat-mech↗
arXiv2001

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.

cond-mat.stat-mech↗
arXiv2001

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. Due to the small number of particles the transition extends over a broad temperature range and is clearly identifiable from the electron pair correlation functions.

cond-mat.str-el↗
arXiv2001

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 $Ω(E)\sim E^{d-1}$ 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.

cond-mat.stat-mech↗
arXiv2001

Paradoxical Magnetic Cooling in a Structural Transition Model

In contrast to the experimentally widely used isentropic demagnetization process for cooling to ultra-low temperatures we examine a particular classical model system that does not cool, but rather heats up with isentropic demagnetization. This system consists of several magnetite particles in a colloidal suspension, and shows the uncommon behavior of disordering structurally while ordering magnetically in an increasing magnetic field. For a six-particle system, we report an uncommon structural transition from a ring to a chain as a function of magnetic field and temperature.

cond-mat.stat-mech↗
arXiv2000

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 linear 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 numbers of particles enclosed in containers of different shapes.

cond-mat.stat-mech↗
arXiv2000

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.

cond-mat.stat-mech↗
arXiv2000

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 transitions in a finite system and to small Ar clusters.

cond-mat.stat-mech↗
arXiv1996

Thermodynamics of finite magnetic two-level systems

We use Monte Carlo simulations to investigate the thermodynamical behaviour of aggregates consisting of few superparamagnetic particles in a colloidal suspension. The potential energy surface of this classical two-level 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 intriguing system and analyze thermodynamically the nature of the transition between the ring and the chain `phase'.

cond-mat↗
arXiv1994

Magnetism of small transition metal clusters and the effects of isomerisation

We investigate the magnetic properties of small transition metal clusters using a simple statistical model, which requires some input data from ab initio spin-density functional calculations. In our study we consider a thermodynamically equilibrated ensemble of clusters with different structures, spin multiplicities, and ground state energies. We calculate the physical properties of this system by weighting the individual configurations according to the Boltzmann statistics. We find that presence of isomers with very similar ground state energies, yet very different magnetic properties, gives rise to a rich magnetic behaviour of the system which differs significantly from what would be expected for single configurations. We apply the present model to to determine the magnetic susceptibility of a cluster ensemble of Langevin paramagnets. Our results show that some of the anomalies in the magnetic behaviour of transition metal clusters might be understood in the framework of our model which is, of course, limited by the extremely high computational effort needed to obtain the input data.

cond-mat↗
arXiv1994

Specific heat in the thermodynamics of clusters

The thermodynamic properties such as the specific heat are uniquely determined by the second moments of the energy distribution for a given ensemble averaging. However for small particle numbers the results depend on the ensemble chosen. We calculated the higher moments of the distributions of some observables for both the canonical and the microcanonical ensemble of the same van der Waals clusters. The differences of the resulting thermodynamic observables for the two ensembles are calculated in terms of the higher moments. We demonstrate how for increasing particle number these terms decrease to vanish for bulk material. For the calculation of the specific heat within the microcanonical ensemble we give a new method based on an analysis of histograms.

chem-ph↗
arXiv1994

Path Integral Density Functional Theory

A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly calculating individual wave functions. These densities can directly be used as an input to energy density functionals. Thus our method makes full use of the theorem of Hohenberg, Kohn and Sham which shows, that the energy of a many electron system only depends on the particle density. At glance we present a recursion formula for the calculation of many fermion and boson particle densities from one-particle densities at a set of different temperatures. For both statistics the numerical effort of our method increases only with the square of the particle number.

cond-mat↗
arXiv1994

New enhancements to Feynmans Path Integral for fermions

We show that the computational effort for the numerical solution of fermionic quantum systems, occurring e.g., in quantum chemistry, solid state physics, field theory in principle grows with less than the square of the particle number for problems stated in one space dimension and with less than the cube of the particle number for problems stated in three space dimensions. This is proven by representation of effective algorithms for fermion systems in the framework of the Feynman Path Integral.

cond-mat↗