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Topic 1. Mathematical and cosmological aspects of the evolution of gravitational fields (Prof. Jerzy Kijowski)

This work deals with fundamental properties of gravitational fields, whose evolution is
described by Einstein's equations, a highly nonlinear system of partial differential equations.
The structure of the initial-value problem characteristic for hyperbolic equations is very
atypical here, as a unique solution is obtained only with the precision of arbitrary space-time
transformations. In the Hamiltonian formulation, the evolution of the field is generated by
what is known as quasi-local gravitational energy, many mathematical aspects of which
remain very mysterious. In particular, this value cannot be additive: the energy (mass)
contained in the sum of two regions A and B cannot be equal to the sum of the energies E_{A}
and E_{B} contained in the two regions, because it must be reduced by the energy of the
interaction (gravitational attraction) between the two energies (masses). This phenomenon,
which does not occur in other gauge field theories, requires the use of completely new,
original methods for describing field evolution, using among other things the notion of "rigid
spheres" which we recently introduced in one of our papers. Important results were also
recently obtained concerning the structure of Cauchy data for Einstein's equations, based on
what is called a (2+2)-distribution of space-time. These results offer hope for the construction
of a completely new formulation of the discrete version of Einstein's equations, which could
also lead to progress with what is known as "numerical gravity".

This research will lead to the development of new methods for describing the evolution of a
gravitational field, in both quasi-local and global aspects. In particular, we hope to explain the
links between the nonequivalent expressions of gravitational energy that have been
proposed by the leading researchers working on the basic structures in the theory of gravity,
such as R. Penrose, S. Hawking and S.T. Yau. We also plan to study possible quantum
implementations of the gravitational Hamiltonians so obtained. Another important aspect will
be to compare the quantum aspect of the gravitational wave description obtained using
"Ashtekar-Lewandowski variables" and using the variables resulting from our description.
This research will be carried out in broad international collaboration with the Max Planck
Institute for Gravitational Physics and the University of Leipzig in Germany, and the
University of Vienna in Austria.

Topic 2. Quantum mechanics of nonlinear and complex systems (Prof. Marek Kuś)

This line of research addresses theoretical foundations and fundamental aspects of quantum
systems with particular importance and applications in quantum engineering. The theory of
nonlinear systems and chaos finds application in various subfields of physics and also in
other fields, including chemistry and biology. In particular, there are interesting applications
of the theory to describe nonlinear problems in the micro-scale world. The objective will be to
apply the methods so developed to both model systems and to concrete physical systems
where nonlinear and quantum effects occur. One particular challenge is how to combine
probabilistic methods with those deriving from differential and algebraic geometry and the
theory of dynamical systems. One new direction will involve studying the probabilistic
foundations of quantum mechanics in order to understand its role among other probabilistic
theories and the related possibilities for its use in practice, in storing and transmitting
information.

We will continue work on developing new methods of quantum analysis of the properties of
complex systems, encompassing probabilistic methods like stochastic matrix theory,
statistical physics of classical nonlinear systems, and above all geometric and algebraic
methods in the study of the integrability of dynamical systems on the classical and quantum
level. The results obtained in previous years concerning methods of analyzing differential
equations on Lie groups will be used to study the dynamics of quantum systems important to
modern quantum engineering. Results concerning the geometric description of correlations in
complex quantum systems will be applied to studying the engineering of quantum systems
useful in quantum information theory and the control of such systems. One new issue
involves analyzing probabilistic foundations of quantum mechanics. Another, purely
theoretical objective of a fundamental nature involves gaining a better understanding the role
of quantum mechanics in contrast to other probabilistic theories and, from the standpoint of
potential applications, analyzing the possibility for the unconditional certification of random
number generators, which is of great importance in cryptology and for the numerical
simulation of physical systems. Some of the research will be carried out under the grants
NCN MAESTRO "Solvability, Chaos and Control in Quantum Systems", ERC QOLAPS
"Quantum resources: conceptuals and applications", and the John Templeton Foundation
Grant "Intrinsic Randomness in the Quantum World"

Topic 3. Physical foundations of information processing (Prof. Karol Życzkowski)

The study of quantum effects important in the description of information processing is gaining
in importance, given the ongoing miniaturization of the physical systems now in use. On the
other hand, the rapid advancement of experimental physics motivated by quantum
information theory is stimulating theoretical research which could give rise to new
technologies in the future (quantum cryptography, quantum communication and quantum
computing).

Research into quantum information theory is currently being done around the world,
especially in the European Union. Research at CTP looks at the theoretical foundations of
quantum information theory, with the aim of describing the basic resources that quantum
mechanics has to offer: non-classical correlations between individual subsystems of a
composed system. The studies on quantum entanglement and their mathematical properties
are of fundamental importance for understanding the theoretical foundations of quantum
informatics, especially those that are independent of the specific construction of the physical
systems necessary for processing and transmitting information. The innovative and original
aspects of the research done at CTP include transferring methods previously used in other
fields of mathematical physics - such as the theory of stochastic matrices, statistical
properties of quantum system spectra, and differential geometry - to the domain of quantum
information. Such methods will be used to characterize resources of quantum information
processing. In the near future, the research will be expanded to include the study of the
structure of multi-molecular entangled states and quantum error correction codes, applying
results obtained under research Topic 2 ("Quantum mechanics of nonlinear and complex
systems", concerning the integrability of quantum systems) to the issues of control and
optimization of quantum informatics devices. A large share of this research is done in
national and international collaboration with centers in Barcelona, Bochum, Duisburg-Essen,
Freiburg, Madrid, Naples, Padua and Stockholm.

Topic 4. Thermodynamics and dynamics of mesoscopic quantum systems (Prof. Kazimierz Rzążewski)

This work seeks greater insight into the properties of quantum gasses. It will lead to a better
understanding of the quantum properties of materials and, perhaps, to new technological
applications, especially the development of quantum informatics. We will continue to study
the influence of nonzero temperature on the course of such phenomena, utilizing the
classical field methods we developed. We will devote particular attention to studying the role
of long-range interactions, linking this research to cooperation with Prof. Tilman Pfau's
experimental group at the University of Stuttgart. In particular, we are studying the role of
long-range interactions for the statistical properties of condensate under quasi single-
dimensional states. We are looking to find solitons in such gas, studying the dynamics of
condensate in which a single atom in a Rydberg state has been generated, and using the
innovative method of "photographing" the electron orbital of a Rydberg state. We are
studying system behavior using the method of direct Hamiltonian diagonalization. The results
of this research will be of fundamental importance for both current and planned experimental
research.

Topic 5. High-energy astrophysics (Prof. Agnieszka Janiuk)

High-energy astrophysics is one of the world's most dynamically developing fields of
astrophysics. Theoretical research on high-energy processes taking place within cosmic
sources, carried out both by means of analytical methods and using increasingly advanced
computer techniques, is now being further supported by cosmic observatories. X-ray and
gamma satellites such as the Chandra X-ray Observatory, Swift and Fermi operated by
NASA and the XMM Newton and INTEGRAL operated by the European Space Agency, as
well as ground-based Cherenkov telescopes gathering data in the teraelectonvolt energy
range, such as the HESS, MAGIC and Veritas, continue to supply new exciting information.
This is making it possible to verify models of the structure and evolution of such objects as
distant quasars, nearby active galaxies, the Galactic Center of the Milky Way, ultrabright X-
ray sources, pulsars, black holes and neutron stars in binary systems with stars,
microquasars, and also gamma ray bursts.
The scientific objective of this line of research carried out at the CTP is the analysis and
numerical modeling of phenomena occurring in the strong gravitational field of compact stars,
mainly astrophysical black holes. Black holes and neutron stars are the most extreme objects
in the Universe and the phenomena occurring around them involve magnetized and ionized
relativistic plasma, emitting radiation across a broad range of the electromagnetic spectrum
while being absorbed by the central object in a process of accretion. This may be
accompanied by an permanent or episodic stream of matter in the directions of the black
hole's rotational axis, perpendicular to the disc plane.

In our work, we will be trying to create the fullest possible physical model of flowing plasma,
taking account of conditions important from the standpoint of real cosmic objects and the
testability of the calculations. Generally this is not possible using analytical methods, and
modeling has to be based on advanced numerical techniques. Our research will be subject to
verification in observational terms, thanks to more and more new discoveries continually
being made based on both data from the instruments newly coming online and new searches
of existing archival data.
The high-energy astrophysics work carried out at the CTP pertains to fundamental research
issues, as it proposes original research projects in the field of theoretical physics aimed
primarily at yielding new knowledge about basic phenomena and observed facts. It is not
geared towards direct practical applications or uses.
We strive to answer fundamental questions concerning the nature of astrophysical black
holes as sources of gravitational potential, facilitating the emission of vast quantities of
energy. Particular attention is directed at aspects of the possible unification of the description
of objects on a very broad scale, ranging from several solar masses up to several hundred
million solar masses, based on the common physics of the processes occurring in their
vicinity. Important contributions to this line of research will come from the work of the new
astrophysics group at the CTP PAS, led by Asst. Prof. Agnieszka Janiuk, as well as from our
cooperation with domestic and foreign research centers, such as the PAS Astronomical
Center in Warsaw, the University of Warsaw, Nicolas Copernicus University in Toruń,
Charles University in Prague, and the Institute of Astronomy of the Czech Academy of
Sciences, the Centre for Astronomy and Astrophysics in Pune in India, the Institute of
Astrophysics INAF in Rome, and Nevada State University in the United States.
The research will be supported thanks to funding from the Polish Ministry of Science and
Higher Education under a SONATA BIS grant, awarded for the 2013-2018 timeframe. We
also utilize computing clusters, made accessible thanks to the current and planned new
computing grants that can be obtained from the Interdisciplinary Modelling Centre at the
University of Warsaw, the PL-GRID network, and others. Continually striving to further
advance the research methods, to bolster the communication and collaboration within the
group, to train young researchers and to maintain an active presence among the research
community will bear fruit in a considerable number of achievements suitable for publication in
world-class journals, especially in terms of better explaining some of the riddles and
mysteries of the Universe.

Topic 6. Science and society (Prof. Łukasz Turski)

The CTP is the only research unit of the Polish Academy of Sciences that has been involved
for 17 years in a range of practical efforts to foster greater science awareness among the
broadest possible groups of society, in particular among school and university students. The
outcomes of such efforts have included the creation of an interdisciplinary "School of
Science" (subsequently incorporated into the Cardinal Stefan Wyszynski University in
Warsaw) and the organization by CTP staff members of Poland's largest science-education
initiatives: the Science Picnic, the Copernicus Science Centre, and most recently developing
a Polish version of the Khan Academy.

The massive changes that have occurred in the IT field in recent years demand a thorough
rethinking and recalibration of educational methods, if education is meant to be the main
driving force behind the development of a knowledge-based society in Poland. This explains
the need for a "Science and Society" line of research (which unfortunately gains insufficient
attention in Poland) at the CTP. The first study, slated for 2014, involved analyzing existing
practices and working out guidelines as to the necessary changes in how the natural
sciences are taught, starting from regular primary schools up, based on a critical analysis of
the current curriculum and an indication of the consequences of these changes in further
stages of education.

The outcome of this work will involve preparing an evaluation of the situation in Polish
schools in light of the changes taking place in the world in this respect. In recent years, the
CTP has done much work in the "Science and Society" field, though it was fragmented and
not systematized as a single research task. All educational results achieved in the "Science
and Society" field have a direct practical impact. The CTP is the only research unit in Poland
that has the ability to directly confront its research in this field against the actual practices of
education, through its existing strong cooperative ties with schools.

Topic 7. Optoelectronics and automation in studying the control and regulation of behavior using the methods of neuroengineering (Prof. Lech Mankiewicz)

This line of research is pursued under the framework of a grant entitled "Control and
regulation of behavior using the methods of neuroengineering" which won funding from
Poland's National Science Centre under the SYMFONIA 1 competition for interdisciplinary
research projects, carried out by distinguished scientists whose work is characterized by the
highest quality, boldly crossing the borders between different fields of science, contributing to
the creation of new values and opening up new perspectives in science. The project is being
pursued by a consortium consisting of the Nencki Institute of Experimental Biology (the
coordinator), AGH University of Science and Technology in Kraków (the Faculty of Physics
and Applied Mathematics), the University of Warsaw (the Faculty of Physics), and the Center
for Theoretical Physics, Polish Academy of Sciences. The CTP's task is to design, build, and
test automated, autonomous devices for studying the functionality of selected areas of the
brain by means of optogenetic methods. The project integrates knowledge, experience, and
the techincal capabilities attained at the CTP in pursing research topic no. 7 "Studying
cosmic phenomena at various timescales".

The outcome of this work will be the development of new technologies for powering,
controlling, and harnessing miniaturized sources of light for the purposes of polarizing
individual neurons or systems, making it possible to study the current condition and
orientation of caged laboratory animals. The technologies so developed will further the
advancement of brain research using optogenetic methods in Poland, based on domestic
engineering and technological potential. The methods devised will be utilized in products of a
similar character, pursued under international cooperation.

Topic 9. Observational constraints on the properties of dark energy (Prof. Bożena Czerny)

Dark energy is the greatest problem in modern cosmology. According to our current
knowledge, the kind of luminous matter that we are familiar with makes up just a few percent
of everything in the Universe, with more than 20 percent consisting of the mysterious dark
matter that physicists are intensively looking for in their laboratories, and more than 70
percent consisting of dark energy with exotic properties we do not understand. However, this
energy can be traced based on the effect it has on the movement of distant objects
composed of ordinary luminous matter.

Our project will use quasars to probe the properties of dark energy. More specifically, we
plan to use quasars to measure dark energy in a way analogous to how supernova stars are
used. To do so, we first need to pin down the absolute brightness of a quasar (the most
difficult, crucial part of the project), then its observed brightness and redshift. This will enable
us to identify the speed of the quasar and its distance, and therefore also the local pace of
the expansion of the Universe. Absolute brightness will be estimated in our project based on
the theory of Broad Line Emission Region formation put forward by Czerny & Hryniewicz
(2011). Observationally, this requires an evaluation of the delay of the emission lines relative
to the continuum, which means making a series of observations of the selected object.
This line of research carried out at the CTP addresses a range of fundamental issues. The
effect will be to develop a new method for studying dark energy. The topic is very important,
with the current and forthcoming extensive observational capabilities playing a key role. At
present, observations of a few quasars will be conducted using one of the world's largest
optical telescopes (SALT, the Southern African Large Telescope), and massive results will
be made possible through the planned sky surveys. Preparations for this stage requires
earlier theoretical work on developing appropriately precise and efficient methods, including
numerical methods. Some of the work will be carried out under the framework of involvement
in COST Action TD1403 - Big Data Era in Sky & Earth Observations.

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