We have endorsed the European Charter for Researchers [link].
2. Task purpose:
Astrophysics is one of the most dynamically developing fields of physics in the world, as it allows testing the laws of physics under extreme conditions. Theoretical studies of space source processes, conducted both by analytical methods and using advanced computer techniques, are supported by space observatories. X-ray and gamma-ray satellites such as the Chandra X-ray Observatory, Swift and Fermi, operated by NASA, XMM Newton, NTEGRAL, and by the European Space Agency, continue to provide exciting new information. New observations are also expected soon, thanks to the new Athena mission. Ground-based observatories, such as the Large Synoptic Survey Telescope (LSST), are also in the pipeline and will give unprecedented insight into the dynamics of space source processes. They will make it possible to verify models of the structure and evolution of objects such as distant quasars, nearby active galaxies, the Centre of the Milky Way, ultra-bright X-ray sources, black holes in binary systems with stars, and gamma-ray flares. The scientific goal of our research is to model phenomena occurring in a strong gravitational field. This field is produced by compact stars, such as astrophysical black holes and neutron stars. Magnetized, ionized, often relativistic plasma takes part in them, emitting radiation in a wide range of the electromagnetic spectrum and absorbed by the central object in the process of accretion. This can be accompanied by constant or episodic ejection of matter streams in the directions of the rotation axis of the compact star. Modelling the environment of compact stars requires a description of the dynamics of matter and light propagation within the framework of the general theory of relativity, as well as the inclusion of nuclear processes (in the case of gamma flares, we observe the so-called Kilonova phenomenon). It is particularly difficult to take into account the effect of magnetic fields on the dynamics of matter. The research requires very advanced numerical methods and the use of supercomputers.
3. Planned scientific and practical effects:
The astrophysics topic pursued at the Center for Theoretical Physics is concerned with basic research, as it proposes original research work in the field of theoretical physics, undertaken primarily to gain new knowledge about the fundamentals of phenomena and observable facts. It is not oriented towards direct practical application or use. Our work is concerned with the nature of compact stars, including astrophysical black holes, which are sources of gravitational potential that allow the emission of enormous amounts of energy. Particular attention is paid to the aspects of the possible unification of the description of objects on very broad scales, from a few solar masses to several hundred million, on the basis of the common physics of the processes occurring in their environment.
This in-depth understanding of the nature of bright objects, observed from cosmological distances, in turn opens the possibility of using these objects as samplers of the dynamics of the Universe at these distances, i.e., testing cosmological models, in particular the rate of expansion of the Universe, and the possibility of showing deviations in the observed accelerated expansion from the description by the cosmological constant. This, in turn, is opening the way for the search for new physics based on direct observational tests on the scale of the Universe. We are just now achieving the first preliminary results on the latter topic. The activity of the astrophysics group at CTP PAS, led by Prof. Dr. Agnieszka Janiuk, is supported by grants from the National Science Centre: OPUS-funded "Origin of gamma-ray flares and their multiband characterization" (2019-2025) and MAESTRO-funded "Dynamics of processes around compact stars" (2024-2028). The activity of the astrophysics group led by Prof. Dr hab. Bożena Czerny is supported by the OPUS-LAT grant (2022-2025) and the ERC Synergy grant (2021-2027). The two groups collaborate with one another.
In addition, we use computational resources at the N. Copernicus Astronomical Center of the Polish Academy of Sciences, at Interdisciplinary Centre for Mathematical and Computational Modelling of the University of Warsaw, and at the PL-GRID network, as well as the resources of the Euro-HPC (supercomputer) LUMI in Finland. International cooperation is based on individual scientific contacts (including with the staff of the University of Rome, and the National Astronomical Observatory of Japan - A. Janiuk), as well as thanks to the funds won in a competition for bilateral exchange with the Czech Academy of Sciences.
2. Task purpose:
We will study a manifold M of odd dimension (2n+1) with a smooth mapping D assigning to each point x a vector subspace D(x) of space T(x) to M in x. Such a mapping is called a distribution D on M. When the dimension of D(x) is equal to 2n at each point x and when the distribution D is maximally non-integrable (which means non-degeneracy of some bilinear form defined on D), the distribution D is called a contact distribution, and the manifold (M,D) is called a contact manifold. The local geometry of contact manifolds is very poor, and therefore one equips the contact manifolds with additional geometric objects G making the contact manifold (M,D) special and the contact manifold (M,D,G) already locally distinguishable. Of particular interest are special contact manifolds that allow a description by Cartan connections. For them, all local invariants are given by the curvature of such a connection, which allows full classification of locally non-equilibrium models of such manifolds. In particular, this also allows finding homogeneous models.
The purpose of this task is to distinguish interesting special contact manifolds, with particular emphasis put on those whose homogeneous models can be realised as nonholonomic mechanical systems occurring in the real world. A more ambitious goal is to link the following issues: control of nonholonomic kinematic systems and the theory of maximally non-integrable distributions and parabolic geometries. Its realisation involves: characterisation of contact distributions admitting a description in the language of parabolic geometry, construction of kinematic models for such distributions, interpretation of the rich structure of parabolic geometry in terms of a kinematic model.
3. Planned scientific and practical effects:
Research in this area has recently been very intensive, and has been conducted both in Europe (Austria, Belarus, France, Poland, Russia, Italy), on the American continent (Brazil, Mexico, USA), in Asia (Japan, Korea), and in Australia. We are developing them in collaboration with mathematicians at IM PAN in Warsaw, as well as with the groups of Mike Eastwood at Australian National University, Ian Anderson at Utah State University, Andreas Cap at Universität Wien, and Gil Bor at CIMAT in Mexico.
The research is fundamental in nature. It concerns the theoretical foundations and fundamental aspects of complex and nonlinear systems, both classical and quantum. The theory of complex, nonlinear systems, and chaos is used in various branches of physics, as well as in other disciplines, such as chemistry and biology. It is interesting to apply this theory to the description of nonlinear problems of the micro-world, when quantum effects are involved. On the other hand, with the help of complex and nonlinear systems it is possible to model phenomena on a completely different scale that constitute the research area of social sciences (sociology, epidemiology). The purpose of the planned research is to apply the methods developed in the course of the tasks carried out so far, both to model systems and to specific physical systems in which nonlinear effects occur.
3. Planned scientific and practical effects:The task investigates applications of the theory of nonlinear and complex systems in several areas of knowledge. At the microscopic level, the research deals with the theoretical foundations of quantum computing and aims to describe the basic resources offered by quantum mechanics to computer science: correlated quantum states and their geometries.
This research is fundamental to understanding the theoretical foundations of quantum computing, particularly those that are independent of the specific design of the physical systems needed to process and transmit information. The novel and original aspects of the ongoing research at CTP primarily involve applications of stochastic matrix theory and differential geometry to the field of quantum computing. Such mathematical methods will be used to describe and measure quantum computing resources such as non-classical correlations in complex systems and optimal ways of producing quantum states relevant to more efficient and faster information processing and transmission.
Classical complex and nonlinear systems will be used to model biological, social and human science phenomena (visual and auditory perception, the spread of epidemics). Novel mathematical methods will be used in modeling, primarily methods of algebraic geometry, geometry of dynamical systems and Lie group theory. The expected results will allow, firstly, quantitative characterization of the described phenomena (so far, usually described in statistical terms) and new insights into their sources and dynamics, and thus understanding of their essence.
2. Task purpose:
The research is fundamental in nature. The physical nature of the dark energy (DE) associated with the accelerated expansion of the Universe and the dark matter (DM) that forms the gravitational scaffolding for the large-scale structure of the Universe (LSSU) remains unrecognised. Our research aims to determine a better and more complete physical understanding of the influence of various phenomenological models of DE and DM on the formation and evolution of the large-scale structure of the Universe and galaxies themselves. Recognising this influence will allow us to relate the free parameter space of the DE and DM models to the physical properties of the observed LSSU and galaxies.
3. Planned scientific and practical results:
The outcome of our research will be the determination of accurate and reliable predictions on the effect that the physics of the DM and DE models has on the statistical and physical properties of the observed LSSU and galaxies, and the use of these predictions to determine and estimate new and improved observational constraints on the parameter space of the DE and DM models. Additional results will include datasets containing new or improved catalogs related to galaxy surveys (such as photometric redshift, galaxy velocity, and spectroscopic redshift datasets), and novel cosmological simulations on a range of models under investigation including, among others, the following: models of cold dark matter, the sterile-neutrino dark matter model, the model of self-interacting dark matter, models of extended gravity of the f(R) type,the universe of 5-dimensional brane gravity, generalised Hordenski models, the model of dynamical dark energy.
2. Task purpose:
The research is fundamental in nature. Its goal is to go beyond the treatment of the environment only as a source of noise, standard in open systems theory, and to understand its role as a potential carrier of information about the quantum system. In addition to studying what type of information can accumulate in the environment during evolution and how it can accumulate, the goal is to look for ways to utilise it. In particular, emphasis will be put on the search for non-standard methods of mitigating the effects of decoherence, for example in popular quantum teleportation-type algorithms.
3.Planned scientific and practical results:The quantum-classical transition is still not fully understood and remains one of the big challenges of modern physics. The main planned scientific results are to bring fresh and new pieces to the understanding of this complex problem, as well as to the attempts to utilise it in a non-standard way. In particular, it is planned to understand through the use of modern quantum information theory how quantum systems acquire objective characteristics (e.g., position, track, etc.) during their interaction with the environment.
In parallel with the research on the quantum-to-classical transition, studies are being conducted on the influence of the environment on quantum algorithms. This is important for the development of applications of quantum mechanics. In particular, various versions of quantum teleportation protocols and error correction algorithms are being investigated.
This aspect of the quantum-classical transition has been recognized within the idea of the so-called ‘quantum Darwinism’. The effect of the application of quantum information methods will be a deeper understanding of the decoherence processes themselves, which have recently been the subject of active research in the world, among other things, from a practical point of view due to the rapid development of quantum technologies, such as quantum control or communication. The knowledge gained will then be used to develop new methods to combat decoherence and, as a result, create new defence protocols. Research results will be published in leading journals and presented at conferences.
2. Task purpose:
The research is fundamental in nature. Its goal is to develop general, noise-proof and experimental imperfections-proof methods to certify quantum systems based on observed non-classical correlations, such as Bell nonlocality, quantum controllability, and quantum contextuality. Particular emphasis will be placed on multiparticle systems. Designing methods of this type is an important task in the context of the buoyant development of quantum technologies that has been taking place in recent years. This is because methods are needed to determine whether a given quantum device uses quantum effects in its operation and whether it produces the correct result. A second goal will be to study the quantum correlations that underlie the certification methods.
3. Planned scientific and practical effects:
Bell's nonlocality, quantum controllability or quantum contextuality are among the most distinctive features of quantum theory, distinguishing it from classical physics. At the same time, they are important resources for certain applications not achievable within the framework of classical physics such as device-independent quantum information processing cryptographic key distribution. In recent years, resources have also been used to create methods that allow certification of quantum systems and even protocols or devices that exploit quantum effects. For example, Bell's nonlocality is used in self-testing, which allows verification that a quantum device uses a given entangled quantum state based on observed correlations.
The planned outcome of this task is new methods to certify entangled quantum states and quantum measurements, as well as certain quantum properties like true quantum randomness. Mainly scenarios based on Bell's nonlocality and quantum controllability will be considered. In addition, the goal will be to create methods that can be easily implemented in an experiment, i.e. methods that are based on minimal knowledge of the system under study and use a minimal number of quantum measurements. An additional but equally important result of our research will be new methods and tools for studying Bell's nonlocality, or quantum controllability, and also entanglement, in complex quantum systems. Although this research is purely theoretical, the results obtained may contribute to the development of future quantum technologies based on quantum correlations.
2. Task purpose:
The aim is to better understand fundamental properties of quantum gases. This basic research will be persuaded in the context of quantum technologies.
3. Planned scientific and practical results:
At ultra-low temperatures (on the order of hundreds of nanokelvins), the wave-nature of matter and quantum properties of gases are revealed. At such temperatures a phase transition can be observed: the gas goes into the state of a Bose-Einstein condensate (bosons), or becomes a so-called degenerate fermion gas. We are engaged in the theoretical description of such systems and their practical applications.
We are currently studying the statistical properties of ultracold interacting atoms. This is a classical problem, undertaken by many researchers in the recent decades. Recently, we were able to derive and implement a new algorithm, based on the Monte-Carlo method, which builds on other phase space methods developed in the group over the past two decades (using classical fields). We intend to calculate the effect of interactions on the fluctuation of the number of condensed atoms in the canonical and microcanonical ensemble.
The second direction of research is the study of phenomena in ultra-cold gases, trapping in narrow dipole traps. In 2025, we intend to complete an ongoing project with the University of Barcelona and the Polytechnic University of Barcelona on the formation of correlated states in so-called topological pumping. Together with groups from the University of Warsaw and the Warsaw University of Technology, we are studying scattering processes in this geometry and looking for a many-body Ansatz,based on Jastrow's Ansatz, a quantum dot.
The research will result in publications and conference reports. Research under this task will be supported by three projects: “Real-world statistics of ultracold gases and their consequences” (NCN, OPUS 2024-2029), EUCENTRAL (European Commission, ERA Chair, 2025-2030) and “NUANCE: Novel qUAntum phases iN Cold gasEs” (NCN, SONATA BIS, 2020-2025).
In quantum computers, information is encoded in quantum states, and transformations between different states are realised by quantum evolution.The basic task of a quantum computer is to evolve an initial quantum state to a target state. A priori the target state can be any (it depends on the problem we want to solve with our quantum computer). A quantum computer that allows us to reach any final state is called universal. In typical quantum architectures, evolution is implemented by a quantum circuit made of quantum gates. Quantum gates can operate on a single qubit or on several qubits. For a fixed unitary operation U, which realises evolution, and for a selected universal set of gates S, there are many quantum circuits with different layout and number of quantum gates, realizing U. Moreover, the length of the circuit may also depend on the choice of the universal set S, i.e., some universal sets of gates (we call them efficient or effective) may yield much shorter circuits than others. Practical realisations of quantum computers are limited by the noise and decoherence that affect many-body quantum circuits. Given these destructive effects, it is crucial to find circuits with the smallest number of gates, i.e., circuits with the smallest depth.The main idea of this task is to combine the latest advanced techniques from representation theory and the theory of random walks on compact groups with specific problems concerning the efficiency of quantum gates and shallow quantum circuits. In particular, we would like to learn as much as possible about the performance/efficiency of a universal set of gates S by studying the properties of the averaging operator that corresponds to the random walk generated by S.
3. Planned scientific and practical effects:
The research will result in publications and conference reports. The topic is supported by the Opus grant 2020/37/B/ST2/02478.
The effect of this research topic will be to create a research group (within the Team Net grant) and to solve specific problems of contemporary quantum mechanics.
The emergence in the first half of the 21st century of serious problems of a global nature - such as the energy crisis, the climate crisis, mass migration, the crisis in education or the challenges of artificial intelligence development - as predicted and warned of by scientists, not only confirms the effectiveness of scientific analysis of reality, but also underscores the need to develop solutions based on sound scientific findings rather than on wishful thinking.
Strengthening public awareness of the importance and role of science is becoming a key challenge. The Center for Theoretical Physics PAS, since its inception, has been actively working towards this goal through initiatives such as the Science Picnic, the Science Festival, the Khan Academy in Polish, and the growing popularity of the YouTube channel, which allows wide distribution of the results of the latest scientific research. The Center's staff also pursues an educational mission, teaching physics and mathematics in elementary schools.
3. Planned scientific and practical effects:Analysis of the state of natural sciences education in Polish schools, taking into account local needs and comparing it to global trends in the field.
Cooperation with institutions responsible for shaping educational policy in Poland.
Developing thematic pathways, lesson plans and experiments in the fields of mathematics and physics that can be implemented in schools.
Using the Center's teaching experience in research on cognitive processes and teaching methodology.
Participation in national and international seminars and scientific conferences on cognitive science, education, and science popularisation in order to present research results and exchange experiences with other professionals.
Thanks to the extensive structure of cooperation with schools, the Center for Theoretical Physics PAS can directly test and implement its research achievements in educational practice.
The research focuses on developing a quantum description of photon-exciton interactions in the strong coupling regime, which plays a key role in modern quantum technologies such as polariton optics and quantum optoelectronics. The goal is to understand in detail the mechanisms governing the formation and evolution of polariton states and their dynamics under various physical conditions, including in the presence of decoherence and interactions.
In addition, the task includes the search for new regimes of polariton dynamics, such as nonlinear effects, Bose-Einstein condensation in strongly coupled systems. An important aspect will also be the study of the influence of optical cavity geometry and material properties (e.g., two-dimensional semiconductors) on quantum phenomena.
3. Planned scientific and practical results:The regime of strong coupling of light and matter is a fundamental area of modern physics, where the boundaries between optical systems and condensed matter are blurred. The main planned scientific outcomes include the development of theory and computational tools to describe these phenomena, especially in the context of applications in quantum optics and information technology.
Expected practical results include the development of new methods for controlling quantum states in polariton systems, which could find applications in fields such as quantum photonic processors, ultrasensitive sensors based on quantum effects, and new high-performance light sources.
The research results will provide new data on the dynamics of polaritons, including their role in nonlinear optical processes, and enable the development of new materials and structures for applications in quantum technology. The results will be published in recognised scientific journals and presented at international conferences.
2. Task purpose:
The task concerns the mathematical and applied general theory of relativity. Research topics include problems of gravitational field energy definition and geometrical optics in curved space-time with applications in cosmology and astrophysics.
Attempts to describe the energy carried by the gravitational field date back to the time of the General Theory of Relativity. Beginning with the unsuccessful theory of the so-called. "pseudo-tensors" of energy-momentum, through the great success of the definition of the "ADM mass" for an isolated gravitating system in the fifties by Arnowitt, Deser and Missner, and the equally great success of the description of the energy carried by gravitational waves proposed by Andrzej Trautman, we have now come to the contemporary attempts to describe the so-called "quasi-local" field energy (the term comes from R. Penrose). Existing definitions of such a quantity do not meet the fundamental postulate, which should be the identification of the energy of the field with the Hamiltonian of its evolution. Starting from the results obtained by us, we conduct a study of the relationship of non-equilibrium definitions of ,,quasi-local" with non-equilibrium boundary conditions imposed on the evolution of the field. The criterion of "adiabatic isolation" of the considered system should be positivity and convexity of the corresponding Hamiltonian, guaranteeing the stability of the evolution. An important element of this research is the description of the evolution of the field at light-like infinity (Scri), and the application of the results obtained to the linearised theory of gravity.
The second direction of research is geometric and wave optics in the general theory of relativity as applied to astrophysics. We are concerned with electromagnetic and gravitational waves. In particular, we want to investigate what information can be obtained by studying the effects of position drift and redshift drift of distant objects. The drifts, i.e. changes on time scales of about 10 years, are small, but can and in some situations have already been measured. We are particularly interested in the possibility of studying so-called bulk flows and deviations from the isotropic expansion of the Universe.
A related issue is the effects of mutual motion of the lens, source and observer in gravitational lensing. In the case of strong lensing, we can expect very rapid changes of position in the sky and redshift of all images of the source. We will investigate to what extent this phenomenon is observable with microlensing on the scale of our Galaxy and for extragalactic sources.
The third issue, finally, is the application of geometric optics during numerical simulations of large-scale structure in the Universe.
3. Planned scientific and practical effects:
The result of this research will be the development of new methods for describing the evolution of the gravitational field, both in quasi-local and global aspects. In particular, we hope to clarify the relationships between the non-equilibrium expressions for gravitational energy proposed so far by the most prominent researchers working on the basic structures of gravitational theory, such as R. Penrose, S. Hawking and S.T. Yau. We also plan to investigate possible quantum implementations of the gravitational Hamiltonians thus obtained. This research will be conducted in extensive international cooperation with the Max Planck Institute for Gravitational Physics in Golm near Berlin, Leipzig University (Germany), and the University of Vienna (Austria).
As for the topics related to optics and light propagation, the results of our investigation will be papers describing what we can learn from drifts and evaluating the possibility of observing them assuming adequate measurement precision. We will also determine what additional information about microlensing and lensing can be obtained from the wave effects. The research will be conducted in collaboration with the group of Asta Heinesen from the Niels Bohr Institute in Copenhagen and Marius Oancea of the University of Vienna.
