Education  Master
Theses/ExamensarbetenFor a list
of courses given at Mathematical Physics, please follow this link.
If you
are interested in doing your Master Thesis at the
division of Mathematical Physics, some inspiration can
be found in the list below. For more information and
to discuss suggestions of topics, you are welcome to
contact Sven Åberg or
anyone that you would be interested in working
with.
Earlier Master Theses at Mathematical
Physics
Tunneling through nanostructures in the presence of Phonons
Student: Fikeraddis Damtie
Examiner: Carl Erik Magnusson
Supervisor: Andreas Wacker
Cosupervisor Olov Karlström
Year: 2011
In this thesis work electron transport through a double quantum dot in a
nanowire in the presence of phonon scattering was investigated. By using the
first order von Neumann approach, the equations of motion for the density
matrix were calculated including electron phonon scattering. By considering
deformation potential scattering mechanism, the matrix element for the
electron phonon coupling for the electrons and the first acoustic phonon
mode in the nanowire was calculated. An increase in transport in the presence of
phonon scattering was found as the phonons soften the resonance conditions.
Simulation of Acoustic Phonons in Nanowire and Nanowire Hetrostructure
Student: Hussein Ayedh
Examiner: Carl Erik Magnusson
Supervisor: Andreas Wacker
Year: 2011
This thesis presents a master project which involves simulations of acoustic
phonons in finite semiconductor nanostructures by using COMSOL Multiphysics
environments according to the elastic continuum model. In this work the
phonon dispersion relations have been explored and discussed in several
nanostructures under different conditions, and the phonon velocities in these
structures are calculated. We have proven that the dispersion relations of
phonon modes can be obtained in a ﬁnite nanostructure. The numerical
simulations of acoustic phonons have been done in two types of
nanostructures:
The first structure is nanowire made of pure IIIV semiconductors such as
GaAs, InAs and GaN. The second is Nanowireheterostructure made of two materials
like GaAs/AlAs, InAs/InP and GaN/AlN. The phonon modes with small wavevectors
in these two structures are compared to each other, where they manifest
similar behavior in both of these two structures. Strain energy and strain
components of phonon modes are discussed along line at the middle of
different nanostructures. They are compared to each other to prove the likeness of
acoustic phonons behavior in pure nanowire and nano heterostructure for
small wavevectors.
Thermal Conduction in Heterostructure Nanowires
Student: Martin Lindskog
Examiner: Carl Erik Magnusson
Supervisor: Andreas Wacker
Year: 2010
Populärvetenskaplig sammanfattning på svenska finns
här
Controlling the heat conduction of nanowires is important for operating
transistors and thermoelectric elements. The purpose of the
thesis is to investigate the effect on the thermal conduction by
heterostructures in the nanowire, and to what extent it could be
manipulated by the choice of materials and structure of the nanowire. To
this end, an estimation for the behavior of the heat conduction for a simple
nanowire was computed, and the dispersion relations for real and
imaginary wave vectors was determined. By the method of matching
modes, the calculation of the transmission and
reflection amplitudes
of the elastic continuum vibrational modes was attempted, but this
method failed in that the equations of the boundary conditions at
the interface could not be solved. It is suggested that the real and
imaginary modes split up into complex modes at the extrema of the
dispersion relations.
Hexadecapole deformation in nuclei
Student: Johan Silfverberg
Examiner: Sven Åberg
Supervisor: Ingemar Ragnarsson
Year: 2010
Populärvetenskaplig sammanfattning på svenska finns
här
In this thesis nuclei with high spin have been studied, or more specifically their
deformation at high spin. The total energy which is a renormalized sum of single
particle energies, is minimized in a set of multiple parameters. The most simple
deformation corresponds to elliptic shape described by two so called quadrupole
parameters epsilon2 and gamma. The aim of this thesis is to explore the next lowest order
in deformation, so called hexadecapole deformation. There are three hexadecapole
deformation parameters but they have generally been combined to one parameter.
In this thesis, however, the total energy is minimized in all three hexadecapole
parameters.
European Barrier Options: Analytical and Numerical Valuation
Student: Nils Rosendahl
Examiner: Ragnar Bengtsson
Supervisor: Sven Åberg
Year: 2010
European barrier options offer
investors opportunities to invest at a lower cost compared to
the corresponding ordinary European options. European barrier
options can either be of out type, meaning that the option
becomes worthless if the barrier is crossed, or of in type
meaning that a barrier has to be crossed, otherwise the payoff
is zero. This paper derives the well known closed form
solution for European barrier options, where the underlying is
assumed to follow a geometric Brownian motion. Two numerical
methods are applied to approximate the price of a barrier
option , the Monte Carlo method and the finite difference
method. The Monte Carlo method is first implemented for a
barrier option written on an asset that is assumed to follow
the so called Cox Ingersoll Ross dynamics as well as a Poisson
driven jump process. The finite difference method is used to
valuate a barrier option on an underlying asset that follows a
geometric Brownian motion. Two implementations of the explicit
finite difference method are made and compared, where the
second is an improvement of the first in the sense that it on
forehand can determine the stability of the
implementation.
Statistical measures of simulated
financial correlation matrices
Student: Martin Ravn
Examiner: Ragnar Bengtsson
Supervisor: Sven Åberg
Year: 2009
Stock market time
series are noisy and unpredictable because the market
dynamics is very complex. Still there is interesting
information. Some of this information comes from
correlations between branches and from the
market. There are also for small time lags,
interesting time correlations. Because of ergodicity,
there will be noise in the correlation matrix
calculated from a portfolio with uncorrelated
stocks. The noise can be simulated with Random Matrix
Theory, or more precisely with Wishart matrices. By
simulating the time evolution of stock prices and add
financial correlations between the stocks, we can
generate financial correlation matrices. How will the
simulated financial correlation matrices be different
from the Wishart matrices? I will diagonalize the
correlation matrix and analyze how the eigenvalue
spectra for the correlation matrices will change when
I add financial correlations. The eigenvalues will be
tested using extreme value statistics. How will the
extreme value distributions depend on for example the
number of companies? Analyzing the eigenvalue time
dependence, several other measures can be done. For
example curvature distributions and autocorrelation
functions.
Spinorbit and L^{2} coupling
strengths in the Nilsson mean field model
Student: Jerker Tapper
Examiner: Ingemar Ragnarsson
Supervisor: Ragnar Bengtsson, Sven Åberg
Year: 2008
The Nilsson mean field model
in nuclear physics uses a spinorbit term and an
L^{2} term without having standardised coupling
strengths as function of the neutron and proton
numbers. Analytic expression were produced for these coupling
strengths so as to optimize the agreement between the Nilsson
model and the Folded Yukawa model. The implications of the
new isospindependent singleparticle coupling coefficients
are explored by comparing the root mean square deviances of
spectra produced by other existing varietes of spinorbit and
L^{2} coefficients. It is concluded that improvements
on the Nilsson model can be made in many regions.
Phenomenological realtions between
2^{+}energies and transition rates in nuclei
Student: Adam Tyszecki
Examiner: Carl Erik Magnusson, Ingemar Ragnarsson
Supervisor: Sven Åberg
Year: 2008
The 2^{+}state is the
first excited state of deformed eveneven nuclei, and the
0^{+} state is the groundstate of all eveneven
nuclei. This makes them ideal for studying relations
between the energy of an excited state and the transition
rate to or from that state. The relations of this kind
that work and are presently used are empirical fits to
data of formulas that are base on on inaccurate nuclear
structure assumptions, such as the irrational flow
model. Relations based on this model are called Grodzins
relations and they relate the energy of a state to the
transition rate of that state through the deformation parameter
\beta. The eperimental value of one observable gives an
estimate of the other.
The purpose of this thesis is
to investigate if a nonempirical nuclear model that
takes pairing effects into account can produce better
results tha the Grodzins relation and modifications fo
it. This model uses both the experimental mass and the
energy to produce an estimate of the transition rate.
CapacitanceVoltage characteristics, a way
to determine doping profiles in wrapgated nanowire transistors.
Student: Olov Karlström
Examiner: Ragnar Bengtsson
Supervisor: Andreas Wacker
Year: 2008
Populärvetenskaplig sammanfattning på svenska finns
här
A wrapgated doped nanowire
structure is studied by implementing a PoissonSchrödinger solver. Doping is
assumed to be only radially dependant. Special interest is taken to the
relation between doping profile and capacitancevoltage characteristics. Good
agreement with experimental data is achieved.
Quantum Information in Nanowires
Student: Katja Szybek
Examiner: Sven Åberg
Supervisors: Peter Samuelsson, Claudio Verdozzi
Year: 2007
This thesis deals with some key aspects of quantum
information and quantum computation. We have developed a theoretical model of the basic
element of the quantum computer  the quantum bit (qubit). The qubit was defined as the two
bottom levels of an electronically controlled double qantum dot system created in a
homogeneous nanowire and charged with a single electron. We discussed the system's ability to
work in a sequence of three operations: initialization, manipulation and measurement. We also
analyzed the decoherence in the double quantum dot due to electronphonon interaction under
conditions of free electron evolution and when an external field was applied.
The role of
artificial viscosity in Smoothed Particle Hydrodynamics (SPH)
Student: Joakim Darelid
Examiner: Ragnar Bengtsson
Supervisors: Enrique GarciaBerro, Domingo GarciaSenz (Universitat Politecnica de Catalunya,
Barcelona)
Year: 2007
Populärvetenskaplig sammanfattning på svenska finns här
The simulation of extremely violent events, such as novae and
supernovae explosions or the rapid merging of two compact objects (like double white dwarfs,
double neutron stars and black holes) is an exciting subject in modern astrophysics.
With the advent of massive parallel computational facilities and the associated increase of
the computational power available today, many of the above mentioned problems can be handled
and simulated in a quite realistic way. One such numerical schemes is a widely spread
numerical technique called Smoothed Particle Hydrodynamics (SPH), which allows to
approximately simulate astrophysical phenomena like those previously mentioned. Here, an SPH
code is tested and its performance is evaluated. In particular, several recipes for the
artificial viscosity are adapted and checked. The tests are done using as benchmark a problem
which has an analytic solution, the Sedov problem, which consists in studying the propagation
of a shock wave in a polytropic gas of constant initial density. The tests indicate that,
given an appropriate choice of the artificial viscosity, the SPH code under study yields
satisfactory results that are in very good agreement with the analytical solution.
Creating an
agentbased artificial market
Student: Per Berseus
Examiner: Gunnar Ohlén
Supervisors: Thomas Guhr, Rudi Schäfer
Year: 2007
Full version is available
This thesis is a study within econophysics, a research field
where financial problems are investigated using methods from statistical physics. An
artificial stock market was implemented in Java and used to assess some assertions made in
empirical studies by J.P. Bouchaud and collegues. The model was able to reproduce several
characteristics of highfequency data from financial markets, e.g. a leptocurtic return
distribution and a nearly constant return function. Much of the emphasis of this report is
made on the methodology itself, since many modelling issues remain to be solved in the
agentbased computational economics field. However, the market was also used to simlulate
trading scenarios, where the impact of different trading strategies was analysed. More
specifically, it was shown in simulation that an overall diffusive price development can
result from a competition between two populations of traders: one of liquidity providers, who
create persistence in the prices, and another of liquidity takers, who create
antipersistence. It was also shown that a slowly decaying trade sign autocorrelation
function could result from similar trading criteria, but not in any obvious way from
liquidity provider's division of large market orders into several smaller ones.
Loschmidt echo for
one and manybody systems
Student: Anders Nilsson
Examiner: Thomas Guhr
Supervisor: Sven Åberg
Year: 2007
In this thesis, the Loschmidt echo for one and manybody
systems are studied. Random matrix theory is used to simulate Hamiltonian systems with
different statistical properties depending on if the systems are quantum regular or quantum
chaotic. The systems are then subjected to a time independent perturbation. The Loschmidt
echoes are then studied for these systems. The results are studied for different time regimes
and for different strengths of the perturbation. Comparison is made to find out if the
Loschmidt echo has different features depending on if the unperturbed Hamiltonian system is
quantum chaotic or quantum regular.
Nuclear radii for
excited states
Student: Emanuel Ydrefors
Examiner: Ingemar Ragnarsson
Supervisor: Sven Åberg
Year: 2006
In this thesis the charge radius and the neutron radius for
the ground state and the wellknown 16^{+} isometric state of ^{178}Hf are
investigated. In an experiment published 12 years ago the charge radius of this isometric
state was measured to be slightly smaller than for the ground state. Different effects which
influence the radii are investigated in this thesis. The nilsson model is used to calculate
singleparticle energies and radii. The BCStheory is then used to treat the pairing
interactions in the ground state. The deformation of the nucleus in the two states is also
discussed. Another effect on the radius comes from the collective motion of the nucleus
around its equilibrium deformation according to Heisenberg's uncertainty principle is
discussed. The charge radius for the excited state is found to have a slightly smaller charge
radius than the ground. Compared to the experimental value the result has the correct sign
but the absolute value is smaller.
Optical Response of Quantum Dots embedded in a Quantum wire
Student: Greta Lindwall
Examiner: Ragnar Bengtsson
Supervisor: Andreas Wacker
Year: 2006
Populärvetenskaplig sammanfattning på svenska finns här
Linear and nonlinear properties of semiconductor quantum dots embedded
in a quantum wire are studied. The pure dephasing of the optical polarization
due to the interaction of the exciton to acoustic phonons is calculated.
Signatures of the lowest phonon modes in the absorption spectrum is
observed and, in contrast to bulk phonons, a broadened zerophonon
line. Furthermore, the dephasing of Rabi oscillations is discussed.
Twocomponent Bose gas under rotation
Student: Jonas Christensson
Examiner: Sven Åberg
Supervisor: Stephanie Reimann
Year: 2006
A rotating twocomponent BoseEinstein condensate has been
investigated theoretically, using exact diagonalization. Equal repulsive interactions were
assumed between all particles. With different number of particles in the two components, they
were found to separate in space with one component orbiting the other. With equal numbers, no
such separation was found.
A study of five highz
Type Ia supernovae
Student: Jakob Nordin
Examiner: Ragnar Bengtsson
Supervisor: Ariel Goobar
Year: 2006
Observations of type Ia supernovae (SNE), as a type of
standard candle, give constraints on the behaviour of the scale factor of the universe. These
observations now seem to indicate an accelerated expansion, caused by some still unknown Dark
Energy. In this work a study of Hubble Space Tele scope images of five distant SNE is
presented, together with a description of some of the theories, techniques and uncertainties
involved.
ThreeDimensional
Spiral Waves in Cardiac Tissue
Student: Johathan Johnsson
Supervisor: Gunnar Ohlén
Year: 2006
The properties of some simple types of 3D spiral waves,
scroll waves, in a model of cardiac tissue are investigated, using the simplified
WohlfartArlock model to describe the excitability of the cells, and their interconnections.
Algorithms are developed to find and follow the tip of twodimensional spirals, which leads
to the discovery of the flower like quasiperiodical trajectory of the spiral tip. The tissue
size needed for a spiral to survive for a long time is determined to be slightly larger than
the area that the trajectory of a single spiral tip covers, when a spiral propagate in a
large piece of tissue. When comparing the propagation of the 2D double spiral and the 3D
scroll ring, the extra curvature dependency added when going from two to three dimensions is
found to be negligible.
Regular and chaotic
contributions to the shell structure of a finite Fermi system
Student: Marc Puig von Friesen
Supervisor: Sven Åberg
Year: 2006
The purpose of this paper is to study the shell effects in a
dilute interacting fermionic gas trapped in a 3dimensional harmonic oscillator. The
expressions of the variance of the oscillating part of the energy will be studied within the
\tau_{min} approximation, a semiclassical model based upon periodic orbit theory, where one
separates the total expression into a regular and a chaotic contribution. These results will
be compared with the outcome from the HartreeFock procedure and the explicit expressions for
two periodic orbits.
Exact Diagonalization of
a Rotating BoseEinstein Condensate Confined in an Anharmonic Potential
Student: Sara Bargi
Supervisors: Stephanie Reimann & Georgios Kavoulakis
Year: 2005
The purpose of this Master Thesis is to perform an exact
diagonalization for a system of cold bosons confined in an anharmonic potential subject to
rotation. We examine the lowest state of the system as a function of the rotational frequency
and the interaction strength for both repulsive and attractive interactions, and find the
resulting phases of vortex structures and centerofmass rotation to be consistent with
previous meanfield calculations.
Investigation of the
'magnetic bands' in the Pbregion in a 'tilted' cranked NilssonStrutinsky
formalism
Student: ClaesGöran Zander
Supervisor: Ingemar Ragnarsson
Year: 2005
In this thesis the Cranking NilssonStrutinsky (CNS) model is
extended by adding the spin component, perpendicular to the rotation axis, for specific
orbitals. This is done by first transforming the total angular momentum operator into the
stretched representation, which leads to supplementary operators $f_i$ in addition to the
stretched angular momentum operators $(j_i)_t$. Single and double commutators are used to
describe the first and second order terms of the $f_i$operators and the functions inside the
commutators are represented with spherical harmonics. Matrix elements of the spherical
harmonics, the stretched representation of the orbital operators and the spin operators are
calculated in the N,l,j,omega>basis. The expectation values of the joperator along the
perpendicular axis are then calculated and added to the total spin in a semiclassical
approach using Pythagoras' theorem. The modified CNS model is used for different fixed
configurations in 199Pb and the results are compared with previous calculations, using
standard CNS, and with experimental results. From this comparison the expected result is
obtained, that is the added component is mainly contributing to the total spin for low and
intermediate spin values. This results in a lower total energy in this spin region compared
with the standard CNS model. In addition, a better correspondence to the experimental values
for the transition energies between different spinstates is achieved.
HighSpeed
Astrophysics: Chasing NeutronStar Oscillations
Student: Ricky Nilsson
Examiner: Ragnar Bengtsson
Supervisor: Dainis Dravins
Year: 2005
The purpose of this thesis is to investigate the potential of
high timeresolution optical observations to explore highspeed astrophysicsl phenomena,
focusing on neutron star oscillations, and also which methods and instruments that should be
required for detection of such. In addition, the thesis contains an account of the initial
testing of a high timeresolution photoncorrelator, intended to be part of a future mobile
observation instrument, QVANTOS (QuantumOptical Spectrometer) Mark II, and the programming
of its control and data acquisitionprogram. We had the opportunity to test the correlator
both in actual astronomical observations at Skinakas Observatory in Crete together with the
OPTIMA group from Max Planck Institute for Extraterrestrial Physics (MPE) in Garching near
Munich and their OPTIMAdetector instrument, and prior to that in the optics laboratory at
lund Observatory. Subsequent preliminary analyses of data from the observations at Mt.
Sinakas are also presented.
To comprehend the implications on neutron star oscillation detection on the research of
neutron star structure and nuclear physics, some introductory theory on these subjects will
be given, concentrating on pmodes in the oscillation part. My hope is that this thesis will
serveas a presentation of one possible application offered by the promisisng future of high
timeresolution astrophysics.
Spontaneous
magnetisation in quantum dots
Student: Keith Edmonds
Supervisor: Stephanie Reimann
Year: 2004
This thesis analuses magnetism in quantum dots for both
isolated dots and lattices of dots. The formalism used is spin Density Functional Theory in
local denstiy approximation with the correlation functional from the paper by Attaccalite et
al. (2002). A six electron parabolic quantum dot is found to have a transition between the
zero spin ground state and the spin one ground state relative to coupling , $r_s$, and
ellpsoidal deformation $\delta$. A lattice of similar dots display antiferromagnetic
behaviour for all lattice constants, a, investigated. 7 electron isotropic dots are modelled
collectively in a lattice. A transition between metallic, ferromagnetic and antiferomagnetic
is found relative to the lattice constant, 2, and coupling $r_s$. A crude estimate of hte
magnetic moment and field for basic lattices is given.
Modeling of Static and
Dynamic properties for 1D Bosegases at T=0
Student: Magnus Ögren
Supervisor: Sven Åberg
Year: 2004
Starting from Lieb's and Liniger's work on Bose gases with a
homogeneous particle density, we derive three different examples of nonlinear
Schrödingerlike equations for modeling static and dynamical properties of (effectively)
one dimensional Bose gases at zero temperature (1DBEC) with different
atomatominteractions.
The equations are studied numerically using an imaginary time
method for obtaining the manyparticle ground state density, after an excitaion of the lowest
breathing mode (to a harmonic oscillator potential). The oscillator frequency ($\omega_B$) is
easured by averaging over a few periods in the real time development. The breathing mode
ratio ($\omega^2_B/\omega^2$) is studied in the intermediate regime, i.e. in the transition
from the GrossPitaevski i regime to the TonkGirardeau regime where the bosons obey a
fermionic behaviour.
The major result is that we can achieve confidence breathing
mode ratios for the entire intermediate regime with only a simple correction term to the
1DGrossPitaevskii equation. This gives us confidence that also other properties can be
modeled this way.
From one of the equations we also develop a parameter
dependent generalization from of the ThomasFermi approximation useful as a 'first
estimation' of properties in the intermediate regime when the number of particles is
large.
Anharmonicallytrapped BoseEinstein condensates under rotation
Student: Johan Bergelin
Supervisor: Georgios Kavoulakis
Year: 2004
We investigate the lowest state of a trapped BoseEinstein
condensate under rotatio, for various forms of confinement, namely a harmonic, a weakly
anharmonic, and a purely quartic trapping potential. In the harmonic confinement there are
only two singlyquantized vortex states. In the other two cases there are phases involving
both singly as well as multiplyquantised vortices depending on the rotational frequencuof
the trap andof the coupling constant. We derive the corresponding phase diagram
variationally.
The Nilsson model
for TwoDimensional Quantum Dots
Student: Johnny Kvistholm
Supervisor: Ingemar Ragnarsson and Stephanie Reimann
Year: 2004
Full version is available
An anisotropic twodimensional model for a quantum dot is
constructed. An analogous treatment as for the construction of the Nilsson model is done in
two dimensions, with an $l_z^2$ term and a Rashba spinorbit term. The spectrum of the
twodimensional Nilsson model is investigated for modulations of the Rashba spin orbit
coupling, the Nilsson interpolation variable and the elongation parameter. A previously
unknown distinct shell pattern for the Rashba spinorbit coupling is discovered. A study of
the magic numbers shows a characteristic level drop between the shells and the 'bent' shape
of the pattern account for a beating mode. An investigation of the hard wall limit, energy
spectra, addition energies, energy shifts and fluctuations, shell corrections, total ground
state energies and magic numbers is performed. A method of determining the interpolation
variable for the twodimensional Nilsson model is presented. The twodimensional Nilsson
model is compared with spindensity functional theory with encouraging results.
Correcting the
Dipole Cascade with Matrix Elements in Hadron Collisions
Student: Nils Lavesson
Examiner: Ragnar Bengtsson
Supervisor: Leif Lönnblad, theoretical high energy
physics
Year: 2004
There are two main ways of describing multi particle
production: fixed order matrix elements and parton showers. They provide a good description
in complementary regions of phase space. There is an algorithm available for correcting the
dipole cascade model with fixed order matrix elements in e+e collisions. This algorithm is
modified to be used for hadronhadron collision in general and W+ production in proton
antiproton collisions at the Tevatron in particular.
Determinations of
Oscillator Strengths in Zr II using Fourier Transform Spectrometry
Student: Gunilla Ljung
Examiner: Ragnar Bengtsson
Supervisors: Sveneric Johansson & Hampus Nilsson, Atomic
Astrophysics, Lund Observatory
Year: 2004
Using the Fourier Transform Spectrometer at Lund Observatory,
spectra from zirconium have been recorded and analyzed. From these spectra measured relative
intensities have been used to derive branching fractions for singly ionized zirconium, Zr II.
Oscillator strengths for 263 spectral lines in Zr II have been derived by combining the
branching fractions with previously measured radiative lifetimes.
Stabilization and
synchronization behavior of a large lattice of coupled limit cycle oscillators
Student: Jan Eric Sträng
Supervisor: Per Östborn and Gunnar Ohlén
Year: 2003
The stabilization and synchronization of a large lattice of
coupled oscillators is studied. This is done by numerical integration of a system resembling
the sino atrial node of the heart. Under the integration process, iterated for different
inter oscillator couplings, composite values of the state of the system are measured. From
quantities describing phases and periods of oscillators, a stabilization pattern is
recognized. A stabilization time can therefore be introduced. This stabilization time seems
to diverge at two interoscillator couplings consistent with prior investigations where only
stabilized periods and period distributions were taken into account. The possibly of a third
new critical interoscillator coupling is suggested. At this critical coupling, the phase
landscapes changes drastically.
An unexpected
connection in Random Matrix Theory
Student: Johan Grönqvist
Supervisor: Thomas Guhr
Year: 2003
Random Matrix Theory was proposed for the study of
excitations in nuclei, and is now used to study systems in many different areas, including
e.g. quantum chaos, mesoscopic physics and signal transmission. In order to compare theory
and data, one often wants to compare correlations between eigenvalue distributions. To this
end, kPoint correlation functions are introduced. A method of calculation of these is
by introducing so called generating functions, and making use of supersymmetry. Here, a
previously unknown connection is proven, which makes it possible to obtain the kpoint
correlations from the simplest cases of the generating functions.
Quantum Chaos in
Nuclear Masses
Student: Henrik Olofsson
Supervisor: Sven Åberg
Year: 2003
Full version is available
A random matrix model is set up to incorporate possible
chaotic motion in the nucleus in the shell correction energy. This gives a contribution to
the nucleus total energy i.e. its mass. The discrepancy between calculated and measured
masses can be reproduced in a statistical sense.
Rotational band
structures in 86Nb, 87Nb and 86Zr
Student: Gillis Carlsson
Supervisor: Ingemar Ragnarsson
Year: 2003
Full version is available.
The rotational band structures in 86Nb, 87Nb and 86Zr were
analysed and most of the bands could be explained using the cranked NilssonStrutinsky model.
Investiations were also made to improve the $\kappa$ and $\mu$ values in the A=90 region. The
investigation revealed difficulties in producing a consistent set of $\kappa$ and $\mu$
values valid in all three nuclei.
Credit risk
modeling  A structural approach
Students: Andreas Sundin & Michal Wolanski
Supervisor: Thomas Guhr
Year: 2003
Accurate and reliable credit risk models are of great
importance for creditors like banks and other financial institutions. In the credit risk
management business there is a wide range of vendor credit risk models at hand, both reduced
form models and structural models. A structural model is based on an underlying microeconomic
process to which it is possible to apply the mathematical tools of statistical physics. This
thesis presents a structural credit risk model based on a jumpdiffusion process. The most
important input parameters of the model are asset volatility, asset drift, asset
correlations, jump intensity, leverage and portfolio size. The primary model outputs are the
default probability and the distribution of credit losses. The model is analyzed by means of
both analytical and numerical calculations. The analytical analysis shows that it is not
possible to get a closed form solution of the loss distribution unless a number of crucial
simplifications are done. The numerical analysis of the model is more extensive and includes
a comprehensive investigation of the parameter space of the model. The most important
conclusion of the thesis is that a structural credit risk model is a powerful instrument to
acquire valuable knowledge of how different economical parameters affect the default
probability and the distribution of credit losses.
Complex Cardiac
Excitation in Inhomogeneous Tissue
Student: Liselotte Rydqvist
Supervisor: Gunnar Ohlén and Per Östborn
Year: 2002
This study deals with the propagation of electric waves in
cardiac tissue. The object of this project was to investigate whether chaos is possible for
the simplified WohlfartArlock model if the tissue is inhomogeneous. Specific questions
investigated in this project were:
 Can a region of idle cells cause chaos?
 Can inhomogeneous coupling between adjacent cells give
rise to an aperiodic behaviour
 If there is one single spiral wave rotating in the tissue,
can this spiral wave split into several spiral waves? If that is the case, what is the
underlying reason?
The investigation showed that changed coupling between adjacent cells was the only
possibility to cause chaos. For idel cells there was no such behaviour found.
For a single spiral wave rotating in the tissue, we found that the wave could multiply if a
region, containing idel cells or containing cells with changed coupling, was placed in a
special way.
Synchronisation
of pulsecoupled nonlinear oscillators
Student: Martin Folkesson
Supervisor: Gunnar Ohlén and Per Östborn
Year: 2001
In this thesis a system similar to the sinoatrial
node, or sinus node, is studied. The sinus node is the natural pacemaker of the
heart. Experiments show that sinus nodal cells fire an action potential periodically
in time. Such firings, pulses, affect the firings of neighbouring cells. The effect of
these pulses is dependent on the state of the cell subject to the pulse. This is an important
feature of the system. In this study a large system of such pulsecoupled, nonlinear
oscillators was simulated. The model of the network was applied on a twodimensional
lattice. Each oscillator was connected to it four nearest neighbours.
Synchronisation is in our model studied outgoing from the oscillators' mean periods of
firing. Nodes that become stable with the same mean period, ideally measured over an infinite
amout of time, are said to be synchronised. Interacting synchronised nodes are
assigned to one and the same cluster.
Defining clusters as above, a sinusnodal system seems to have two phase
transitions. The first takes places as the largest cluster of a network grows dramatically in
size. The simulations performed show that this growth follows a power law with respect to the
coupling strength. The cluster sizes are at this point critically distributed, thus the
behaviour seems analogous to a second order phase transition. The second assumed phase
transition takes place when the system becomes entirely synchronised, which is seen for a
finite coupling strength. This is in contrast to perfect spin alignment in the Ising
model, which appear only for infinite coupling strength or at absolute zero temperature.
Spin ~ 60 hbar i
156Dy
Rotationsband och partikelhål excitationer vid höga spinn
Student: Fikret Saric
Supervisor: Ingemar Ragnarsson
Year: 2000
En beräkningsmetod för kärnans
högspinntillstånd med cranking NilssonStrutinsky modellen har studerats. Med
denna metod har flera olika egenskaper studerats. Bland annat: kärnans formändring,
band korsningar och band terminering. 156Dy kärnan har studerats i ett område av
deformation från epsilon = 0 till epsilon = 0.30 och vissa ändringar har gjorts i
de numeriska beräkningarna som möjliggör att man kan särskilja
rotationsband med en partikel i (d 3/2,s 1/2) från rotationsband utan någon
sådan partikel. En jämförelse har gjorts med experimentella data och med de
tidigare teoretiska värdena för protonneutron konfigurationer för 156Dy
kärnan.
Modelling of
Cardiac Excitation
Student: Åsa Bergkvist
Supervisor: Gunnar Ohlén and Per Östborn
Year: 2000
Two existing models for describing the cardiac action
potential, the Wohlfart Arlock model and the FitzHughNagumo equations, are investigated and
compared. A new simplified version of the WohlfartArlock model is derived and compared to
the ordinary one. Spiral waves are initiated and the effect of reentry is studied.
Equilibrium and
stability of Riemann ellipsoids
Student: Peter Olivius
Supervisor: Ragnar Bengtsson
Year: 1998
The Riemann ellipsoid is a homogeneous, incompressible
ellipsoidal fluid, without viscosity or temperature gradients. The equation of motion and
constants of the motion are determined. Equilibria are found when the rotational axis is
along a principal axis, and when the rotational axis lies in a principal plane. In the
principal plane case, the equilibria are always shape potential unstable, but in the
principal axis case, there are both stable and unstable equilibria. The regions of stable and
unstable equilibria in both principal axis and principal plane cases are graphically
illustrated. It is proved that when the rotational axis is not lying in a principal plane and
not along a principal axis, there cannot be equilibrium. A paper of Bernard Riemann
concerning these ellipsoids was studied in detail, and some minor mistakes were
found.
Simulation of sinus
nodal behaviour
Student: Per Östborn
Supervisor: Gunnar Ohlén, Björn Wohlfart
Year: 1998
We compare mathematical models of sinus nodal (SN) cell
activity. An elaborate model is found to be more sensitive to external pertubations than
simpler models. We conclude that phase response plots and circle mapls can be successfully
used to predict dynamical behaviour of a coupled pair of SN cells. We find that small, weakly
coupled cells in the SN interior and a high resistance in the immediately surrouding tissue
help meet the atial current load. The interwined SN cell arrangement make possible an
effective protection against spread of disturbances and helps reducing phase difference
between cells at different locations in the SN. Simulations suggest that a heavy atrial
current drain and/or internal SN conduction problems can give rise to slow rhythms, sometimes
with pauses which are multiples of normal interbeat intervals, quasiperiodic rhythms, chaotic
rhythms and frequency locked states. Frequency ratios of the latter form devil's staircases
in bifurcation trees. Quasiperiodic motion appears when intercellular coupling is very weak.
We suggest how time series of interbeat intervals can be used to identify two and
threeperiodic rhythms. Some information about the base frequencies ca be gained.
Twoperiodic rhythms may arise when there are two weakly interacting areas of reasonably
wellcoupled SN cells. A ring of model SN cells carry a reentrant of reasonably wellcoupled
SN cells. A ring of model SN cells can carry a reentrant rhythm with up to twice the normal
beating frequency. In contrast to the case of ordinary cardiac cells, no beating
irregularities can be obtained in the high frequency limit.
A Microscopic Model
of Friction in a Complex Quantum Mechanical System
Student: Daniel Almehed
Supervisor: Sven Åberg
Year: 1997
A time dependent random matrix model is used to study chaos
in complex quantum mechanical systems. An energy level density from a deformed nuclear model
is simulated. The heating effect given by the gradient of the level density can give a
microscopic explanation to a friction term in a macroscopic model of a chaotic quantum
mechanical system. An expression of how the frictionenergy depends on system parameters is
presented.
Chaos assisted
tunnelling
A simple model to describe the deexcitation of a superdeformed nucleus
Student: Jan Johansson
Supervisor: Sven Åberg
Year: 1997
A simple model, based on random matrices, is proposed to
model the deexcitation of a superdeformed nucleus. The class of random matrices which is used
is the Gaussian Orthogonal Ensembles. The system can be transferred from an ordered to a
chaotic system. The transformation depends implicit on the excitation energy.
Student: Magnus Oskarsson
Supervisor: Gunnar Ohlén, Björn Wohlfart
Year: 1997
The behavior of spiralwaves in a model of myocardial tissue
is studied numerically. Questions as how spirals are initiated, how they interact, how they
move, and how they can be destroyed are discussed.
Neutrino
Oscillations and The Solar Neutrino Problem
Student: Kristin Einarssdotter
Supervisor: Cecilia Jarlskog
Year: 1996
(No Abstract)
Aspects
of Spiral Wave Dynamics in Myocardial Tissue
Student: Mattias Christensson
Supervisor: Gunnar Ohlén, Björn Wohlfart
Year: 1996
(No Abstract)
Controling Chaos and Hyperchaos in Dynamical Systems
Student: Mattias Christensson
Supervisor: Gunnar Ohlén
Year: 1996
In this study we shall deal with dynamical systems which show
chaotic behaviour. These systems are inherently unpredictable in their long term evolution
and therefore it may be desirable to develop mehtods that can be used to control them. One
such method (originally developed by Ott and coworkers for time discrete systems, see Ott et
al. 1990 and Romeires et al. 1992) which uses the sensitive dynamics of a chaotic system in
order to control it is described here and we will subsequently develop a way to apply this
method to both autonomous an nonautonomous time continuous systems. We will also control a
system displaying hyperchaotic dynamics, which has not been done before.
A Critical Analysis
of Modifications of Gravity as an Alternative to Dark Matter
Student: Erik Lindahl
Supervisor: Ingemar Bengtsson, Cecilia Jarlskog
Year: 1995
(No Abstract)
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