Download Abstracts - Physics @ Bilkent

Fall 2016 PHYS 491 Senior Project I: Project Titles and
Abstracts
Advisors
Prof.Dr. Ekmel Özbay
Prof.Dr. Bilal Tanatar
Prof. Dr. Cemal Yalabık
Prof. Dr. Salim Çıracı
Prof. Dr. Oğuz Gülseren
Assoc. Prof. Dr. Ceyhun
Bulutay
Assoc. Prof. Dr. Özgür
Oktel
Asst. Prof. Dr. Şahin
Büyükdağlı
Asst. Prof. Dr. Balazs
Hetenyi
Dr. Agnese Calleqari
Assoc. Prof. Ömer İlday
Titles of their projects
1) Optical antennas with phase change materials 2) Off-Axis beaming
1) Variational and numerical calculations for Bose-Einstein
condensed gases in power law traps 2) Investigation of selfgravitating Bose-Einstein condensates for astrophysical applications
1) Simulation of classical and quantum random walkers through mazes
2) Simulation of a quatum heat engine
1) Study of Topological Insulators in 3D and 2D 2) Study of Weyl
Fermions in Condensed Systems
1) Tight binding electronic band structure of silicene: 2) Friction
forces from 1D Prandtl-Tomlinson model 3) Brownian motion 4) Traffic
Flow
1) Quantum spin dynamics and decoherence in nitrogen vacancy centers
1) Numerical Study Of the Aubry-Andre Model Proposal 2)
Diffraction from one- and two-dimensional quasicrystalline gratings
(experimental)
1) Trapping translocating polymers in dielectric membranes 2)
Adsorption of DNA molecules by like-charged nanopores
1) Localization in the Haldane model 2) One dimensional topological
models
1) Dynamics of dielectric microparticles in an optical field
2) Collective motion of active particles
1) Dynamic self-assembly of nanoparticles
Abstracts
Prof. Dr. Ekmel Özbay
1) Title: Optical antennas with phase change materials
The antennas operating in optical and visible wavelength range has fascinating potential
applications, for example, in single molecule spectroscopy by fluorescence and directionality
enhancement of molecules.
In this project, we will study optical antennas with phase change materials, such as VO2. We
will investigate the change in the resonances of infrared plasmonic antennas which can be
tuned or switched on/off by taking advantage of the thermally driven insulator-to-metal phase
transition. Moreover, we will explore the steering of the beam using these antennas.
2) Title: Off-Axis beaming
Metallic with gratings structures support surface plasmons and enhance the transmission.
Moreover, these nanostructures act as the periodic array of antennas which focus and beam
light. In this project, subwavelength plasmonic apertures will be used to enhance and beam the
emission. The periodic grooves will be designed as 2D periodic asymmetric structures to
investigate the control in beaming in 2 axes.
Prof. Dr. Bilal Tanatar
1) Variational and numerical calculations for Bose-Einstein condensed gases in power law traps
Recently Bose-Einstein condensation (BEC) of an atomic gas in a quasi-uniform potential of
optical box has been experimentally observed. [1] In particular, for a trapping potential of
the form V (r) ∝ r n with n = 13±2 has been observed. Motivated by this result, in this
project, we shall consider the solution of the non-linear Schrodinger equation (NSE) with a
power law potential using analytical and numerical techniques. We shall introduce the
generalization of the q-Gaussian trial functions [2] to develop a variational approach. We
shall also use the full numerical solution of the NSE to assess the quality of the variational
results.
Quantum Mechanics, Statistical Physics and Numerical Methods courses are needed to undertake
this project.
[1] A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Phys. Rev.
Lett. 110, 200406 (2013).
[2] K. S. Fa, R. S. Mendes, P. R. B. Pedreira, and E. K. Lenzi, Physica A 295, 242 (2001).
2) Investigation of self-gravitating Bose-Einstein condensates for astrophysical applications
We investigate the ground state of a self-gravitating Bose-Einstein condensate (BEC). The
bosons are assumed to be interacting via a short-range contact interaction as well as the
Newton’s law of gravitation because of their mass. The Gross-Pitaevski equation describing the
BEC and the Poisson equation for the gravitational potential are solved self-consistently.
These equations model astrophysical objects such as boson stars, dark matter, and galactic
halos.
Quantum Mechanics, Statistical Physics and Numerical Methods courses are needed to undertake
this project.
Asst. Prof. Dr. Şahin Büyükdağlı
1)
Trapping translocating polymers in dielectric membranes
Polymer translocation is a promising DNA sequencing method whose precision depends on our
ability to reduce the translocation velocity of the DNA molecule. This requires in turn an
accurate understanding of the electrostatic interactions between the polymer and the membrane.
The project will consists in calculating the free energy of a translocating polymer and
identifying the dielectric conditions where the membrane traps the polymer [1]. If time
permits, the theory will be extended to the non-linear regime of electrostatic many-body
effects [2].
Good skills in analytical and numerical computation, and a solid background in electrostatics,
classical statistical physics, and applied mathematics are required.
[1] S. Buyukdagli and T. Ala-Nissila,
J. Chem. Phys.
145, 014902
(2016).
[2] S. Buyukdagli and R. Blossey, Arxiv : 1607.00194
2)
Adsorption of DNA molecules by like-charged nanopores
Polymer-nanopore interactions play a crucial role in the design of lab-on-a-chip devices. In
this project, the student will scrutinize the effect of polyvalent counterions on the
interaction between a negatively charged polymer and a similarly charged nanopore. Beyond a
characteristic charge density, these counterions are expected to turn the DNA-pore interaction
from repulsive to attractive [1,2]. This is a nice example of similar-charge attraction that
contradicts our mean-field level intuition. The causal relationship between this effect and
DNA charge inversion will be also investigated.
Good skills in analytical and numerical computation, and a solid background in electrostatics,
classical statistical physics, and applied mathematics are required.
[1] S. Buyukdagli, C.V. Achim,
and T. Ala-Nissila,
J. Chem. Phys.
137, 104902
(2012).
[2] S. Buyukdagli and R. Blossey, Arxiv : 1607.00194
Prof. Dr. Cemal Yalabık
1) Simulation of classical and quantum random walkers through mazes
Motion of a classical random walker within a variety of boundary conditions and potentials is
a well studied problem. Recently, quantum random walkers under various effects have also
attracted interest. (See for example, this reference.) The problem has relevance to transport
through disordered media.
The project will involve:


Construction of a random maze through which the particle will move.

Simulation of the random quantum walker through the maze and obtaining the final
probability distribution of its position.
Simulation of the random classical walker through the maze and obtaining the final
probability distribution of its position.
The student is expected to have a reasonable amount of computational skill. (Improvement of
computational skills should also be seen as a part of the aims of this project.) It is best
that the student discuss the project with me before applying for assignment.
2) Simulation of a quatum heat engine
Second law of thermodynamics does not allow the transfer of energy from a heat source at a
lower temperature to another at a higher temperature (refrigeration) without doing work.
Equivalently, a machine should not produce work while it has contact with a single heat bath.
"Maxwell's demon" is a hypothetical being which seems to go around these restrictions of the
second law, if one ignores the information contained in the decisions of the demon.
Indeed, it is important to understand the interrelation of entropy and information to
understand why the second law cannot be circumvented by the demon.
Mandal, Quan and Jarzynski have proposed a classical refrigerator (Phys. Rev. Lett. 111,
030602 (2013)), which pumps heat from a lower to higher temperature, without any work input but in the process modifies a series of (low entropy) binary bits of information so that they
are more random (and hence have greater entropy).
Quantum heat engines have also attracted interest. It has similarly been demostrated that such
machines can generate work even when connected to a single heat source. (See for example, this
reference.)
Second law is again not violated, as the loss of coherence of the quantum system corresponds
to an increase in entropy.
The project will involve the design and simulation of a quantum heat engine.
The student is expected to have a reasonable amount of computational skill. (Improvement of
computational skills should also be seen as a part of the aims of this project.) It is best
that the student discuss the project with me before applying for assignment.
Assoc. prof. Dr. Özgür Oktel
1) Numerical Study Of the Aubry-Andre Model
This senior project involves the study of a one dimensional quantum mechanical model with a
quasiperiodic potential. The simplest tight binding model with quasiperiodic properties is
the Aubry-Andre model (S. Aubry and G. Andre, Ann. Isr. Phys. Soc. ´ 3, 133 (1980)). The
student will be expected to numerically reproduce the analytical results for this model and
then work on extensions of the model to long range hopping ( Similar to: PHYSICAL REVIEW B
83, 075105 (2011) ) and spatially inhomogeneous models.
Familiarity with MATLAB and/or Python, and
required.
a strong foundation in Quantum Mechanics is
2) Diffraction from one- and two-dimensional quasicrystalline gratings (experimental)
This senior project involves the design and construction of quasicrystalline diffraction
gratings. The student will be expected to produce a high quality diffraction grating using a
laser printer and characterize it from its diffraction pattern. The minimum requirement for
success is the reproduction of results in American Journal of Physics 72, 1241 (2004).
The project will require the student to use a computer program to design the grating, and the
basic understanding of diffraction in optics for characterization.
Asst. Prof. Dr. Balazs Hetenyi
1) One dimensional topological models
Materials which exhibit nontrivial topological behavior have been of central interest in the
last decades [1]. In higher dimensions topologically nontrivial phenomena include the quantum
Hall effect, or topological insulation. There are also one-dimensional models which exhibit
non-trivial topological behavior. Two common examples are the Rice-Mele model [2], which
exhibits polarization reversal as the system is carried around the topologically nontrivial
point in the parameter space, or the Su-Schrieffer-Heeger model [3] proposed to account for
solitons in polyacetylenes. In this project the conduction and localization properties of
these models will be studied. The wavefunction of the two Hamiltonians will be obtained and
the polarization, conductivity, as well as the Drude weight will be calculated. The
polarization and its moments can be calculated via the tools of the modern theory of
polarization [4]. The conductivity is to be obtained by use of the Kubo formula [5]. The Drude
weight, the peak of the conductivity at zero frequency can be obtained by calculating the
response of the ground state energy to an AharonovBohm flux[6]. Of particular interest will be
the interplay of these quantities with the topologically non-trivial behavior.
References:
[1] D. Xiao, M. C. Chang, and Q. Niu Rev. Mod. Phys. 82 1959 (2010).
[2] M. J. Rice and E. J. Mele, Phys. Rev. Lett. 49 1455 (1982).
[3] W. P. Su, J. R. Schrieffer, A. J. Heeger, Phys. Rev. Lett. 42 1698 (1979).
[4] R. Resta, Rev. Mod. Phys. 66 899 (1994). [5] G. D. Mahan, Many-particle physics
(Springer, 2000)
[6] W. Kohn, Phys. Rev. 133 A171 (1964).
2) Localization in the Haldane model
The Haldane model [1] can be viewed as a precursor to topological insulation. It was the first
model to exhibit quantized Hall conductance in the absence of an external magnetic field. The
celebrated Kane-Mele model[2], which does exhibit topological insulation, consists of two
Haldane models, one for each spin channel, connected by spin-orbit coupling. In this project,
the nature of localization in the Haldane model will be studied. The tools for this study will
be based on the modern theory of polarization[3], since the appropriate way to calculate the
position of charge carriers and the associated moments was developed therein. The approach
will be to diagonalize the Hamiltonian of the model, and calculate the spread in the total
position of charge carriers. If time permits one can also apply the recent developments[4,5]
in calculating the orbital magnetic moment of the system.
References:
[1] F. D. M. Haldane, Phys. Rev. Lett. 61 2015 (1988).
[2] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95 226801 (2005).
[3] R. Resta, Rev. Mod. Phys. 66 899 (1994).
[4] R. Bianco and R. Resta, Phys. Rev. B 93 174417 (2016).
[5] A. Marrazzo and R. Resta, Phys. Rev. Lett. 116 13
Assoc. Prof. Dr. Ceyhun Bulutay
A nitrogen vacancy (NV) center is formed inside a diamond crystal when a nitrogen atom
substitutes one of the carbon atoms where a vacancy occurs next to
it. They occur either naturally, or can be formed by techniques such as ion implantation.
Currently its target market appears to be in the field of quantum
metrology, particularly for measuring weak magnetic fields below the nano Tesla level. From
the fundamental physics point of view,
they enable doing AMO (atomic, molecular and optical) physics in a solid-state setting. In
this project, the decoherence of spins in NV centers will
be computationally modeled. Therefore, very strong knowledge of quantum mechanics (in the
level of Phys 326 QM-II course) and high-level programming
skills (preferably Python) are essential.
Prof. Dr. Salim Çıracı
1) This project will comprise following stages. In the first stage, the definition of the
topological insulators in 3D and 2D will be presented by clarifying their types. The relation
between the Quantum Spin Hall Effect and Quantum Anomalous Hall Effect will be clarified. In
the second stage, a comprehensive study of the theory and available experiments on diverse
topological insulators will be carried out. In the third stage, methods/criteria will be
presented to identify topological insulator and its types. In the final stage, original
research will be performed to reveal whether strictly 1D systems can show a topological
behavior.
2) Fermions are classified as Dirac, Majorana and Weyl Fermions, which are observed in
graphene, topological superconductors and semimetals. This project focuses on the theory of
Weyl fermions in condensed systems. In the first stage, original definition of Weyl Fermions
having Lorentz invariance will be presented and Weyl fermions in condensed systems will be
reviewed by clarifying their differences from Dirac fermions. In the second stage, the theory
and experiments on Weyl semimetals with their Type-I and Type-II characters will be reviewed.
Condensed systems showing Type-I and Type-II behavior will be presented. In the final stage,
novel materials comprising Weyl fermions will be predicted.
Prof. Dr. Oğuz Gülseren
1) Tight binding electronic band structure of silicene:
In recent years, motivated from extra-ordinary properties of graphene, several new 2
dimensional (2D) materials are proposed known as van der Waals 2D materials. 2D structures
based on Group IV elements are one of the widely studied systems.
These materials form layered structures similar to the graphene with hexagonal lattice, but
every other Si atom is buckled , so it is a quasi-2D structure formed.
Write down the unit cell of the 2D silicene, and then derive the tight-binding band structure
based on s and p orbitals of the Si atom.
Then, write a program to fit the tight-binding energy parameters, and fit these by comparing
the first principles energy band diagram.
2) Friction forces from 1D Prandtl-Tomlinson model:
Tribology, the study of friction, is both an old theoretical problem in physics and an area of
great practical importance. The invention of experimental instruments such as Atomic Force
Microscope (AFM) has lead to the emergence of the field of nanotribology, the exploration of
friction phenomenon at the nanoscale. While more complete descriptions of friction make use of
density functional theory (DFT) and molecular dynamics (MD) simulations, many essential
features of frictional phenomena are accurately modeled by so called "reduced order models"
such as the Prandtl-Tomlinson (PT) Model.
Illustrate the PT model in both one-dimensional and two-dimensional forms via application to
various crystal lattice surfaces (cubic, planar hexagonal) and reproduce important results
from the literature by solving the resulting Langevin equation within the PT model.Discuss the
parameter dependence in this model via relevant simulations.
3) Brownian motion:
A Brownian particle in a optical trapped simulation that is the best way to observe nanoscopic
forces and sensitive probe of molecular forces. By using finite difference method which is a
numerical method to solve ordinary differential equations to solve Langevin Equations to
simulate the brownian motion of a particle in various trapping potential.
4) Traffic Flow:
From fluid mechanics, we know that the mass flux equals the mass density times the fluid
velocity, v, so the equation of motions reduces to
 ( x, t )

    ( x, t )v( x, t )
t
x
which is the equation of continuity. One of the simplest nontrivial flow involves the velocity
of only function of density. For traffic flow, we should have the velocity of the fluid (flow)
decreases linearly with increasing density as

 
v(  )  vm 1 

 m 
where vm > 0 is the maximum velocity (speed limit) and
 m  0 is
the maximum density. If the
density is near zero (few cars on the road), then the traffic moves at the speed limit. The
maximum density
 m  0 is
achieved when the traffic is bumper-to-bumper.
Suppose that we have a uniform density of traffic with a small congested area.
initial condition be
Hence, let the
 ( x, t  0)  0 1   exp   x 2 / 2 2 
where ,  and ρ0 are constants.
A) Show that for light traffic (for example ρ0= ρm/4) the
perturbation moves forward. What is its speed? B) Show that for heavy traffic (for example ρ0=
3ρm/4) the perturbation moves backward. What does this mean physically? C) Show that for ρ0=
ρm/2 the perturbation is almost stationary, it drifts and distorts slightly.
Dr. Agnese Calleqari
1) Dynamics of dielectric microparticles in an optical field
Optical tweezers is an established technique to manipulate microscopic objects like dielectric
particles and cells: thanks to the difference in the relative refractive index, a focused
laser beam is able to trap microscopic objects that, otherwise, would be prone to move
erratically because of the thermal noise (Brownian motion).
In this project we will learn how to describe the dynamics such microscopic particles
(Brownian particles) and then how to compute the effect of an optical field on dielectric
microscopic particles. We will start from the simplest case (homogeneous spherical particles)
and proceed to more complex situations (elongated shapes; inhomogeneity in the refracting
index). We will then use the acquired knowledge to reproduce the behaviour a prototype system
of physical interest.
Depending on the preferences and inclination of the student, the project may be focused on
simulation only or may include also some lab practice.
2) Collective motion of active particles
In nature large groups of living organisms (like flocks of birds, schools of fish, herds of
cattle, bacteria swarms, …) exhibit a collective behaviour, i.e., the spontaneous emerging of
an ordered and coordinated movement of each single individual constituting the group. This
collective behaviour may have the most disparate purposes: maximise the chances to escape from
a predator, optimise the distribution/exploitation of the resources, etc. Nowadays,
understanding the universality behind this phenomenon is one of the hot topics in active
matter.
In this project, we will start by learning one of the first models accounting for swarm
behaviour (Vicsek model). Though simple, this model is very rich and depending on the
conditions (density of the individuals, intensity of the noise, ...) it may show the behaviour
of a disordered gas phase or of an ordered liquid.
We will then use the acquired knowledge to describe the behaviour a prototype system of
physical interest.
Assoc. Prof. Ömer İlday
1) Dynamic self-assembly of nanoparticles
This topic focuses on numerical analysis of fluid dynamics that arise as a result of nonlinear
absorption of ultrafast laser pulses in a fluid environment, which, in turn, can be used to
drive self-assembly of nanoparticles under far-from-equilibrium conditions. This effort
involves, solution of Navier-Stokes equations in the low Reynolds number limit, as well
incorporation of a model for nonlinear heat injection into the system. This is part of an
ongoing effort in collaboration with Prof. Gülseren.