Theoretical and mathematical physics students – master studies

The aim of the work is to study the properties and evolution of shell sources within the general theory of relativity in relation to the cosmic censorship hypothesis.

Goal of the thesis is to study the interation of a current flowing throug a molecular junction with the vibrations of the molecule using the methods of many-body physics. The starting point will be the self-consistent Born approximation within the nonequilibrium Green\'s function formulation of the transport, which has already been used for similar problems recently and is well described in literature.

Černoděrové prostoročasy spojují v sobě téměř ploché oblasti v nichž platí obvyklá fyzika s obecně relativistickými gravitačními singularitami a horizonty. V mnoha situacích je potřeba zkoumat najednou vzdálené pole i oblast pod horizontem, například jedním z faktorů vedoucím k nedávnému průlomu v numerické relativitě bylo nalezení vhodného dynamického pokrývání vyvíjeného prostoročasu souřadnicemi, přičemž některé z jeho vlastností zůstávají i nadále nejasné.

Study of numerical methods for solving the time-dependent Schrödinger equation and their application to the twodimensional model of electron-molecule collisions.

Kompaktní hvězdné objekty (bílí trpaslíci, neutronové hvězdy, černé díry) umožňují pozorovat projevy velmi silných gravitačních polí. K porovnání teoretických předpovědí s výsledky pozorování je však třeba detailně rozpracovat klasické i relativistické modely dynamiky a záření hmoty v blízkosti těchto objektů.

In extremely strong gravitational fields in the vicinity of black holes, interesting deviations from Newtonian dynamics may arise. These include, for instance, reversal in dependence of the orbital acceleration on angular velocity. This general relativistic effect occurs below the free photon orbit and so far it has been mainly studied on circular trajectories in stationary axisymmetric spacetimes. It would be interesting to learn how the effect manifests itself on polar orbits and whether somet...

Kerr metric is one of the most famous and explored solutions of Einstein equations. It should roughly describe the black holes which probably exist in galactic nuclei and in some X-ray binaries. The properties of Kerr space-time are usually discussed on coordinate pictures, but the very basic question of its 'shape' is not easy to answer in a 'proper', geometric way. This diploma thesis should examine some possibilities of such an answer, in particular those following the geophysical methods used in determining the Earth's gravitational field, and also the possibilities based on finding the isosurfaces of important geometrical quantities.

Passage of light through the gravitational field of two bodies is generally studied in two regimes. The more common one is the thin lens regime, when both bodies are considered to lie at the same distance from the observer and affect passing light precisely at the same time. The other regime is the one of two independent lenses, in which the light first passes through the gravitational field of one body and the deflected ray later passes through the field of the other body. The objective of the ...

Student by se měl seznámit s různými popisy interakce gravitačních vln s látkou. Mezi ně patří jak "mikroskopický" popis, tak perturbační analýza svázaného systému Einsteinových rovnic a odpovídajících polních rovnic hmoty. Soustředit by se měl na druhý jmenovaný přístup a pokusit se provést konzistentní zjednodušení, aby bylo možno alespoň kvalitativně odhadnout důsledky interakce pro případné tlumení gravitačních vln. Případně je možno analýzu zjednodušit předpokladem fixního pozadí.

V nedávné době byly některé klasické matematické metody obecné relativity (Petrovova klasifikace, Newmanův-Penroseův formalismus a Gerochův-Heldův-Penroseův formalismus) zobecněny na případ libovolné dimenze. Ukazuje se, že téměř všechna známá přesná řešení Einsteinových rovnic ve vyšších dimenzích jsou algebraicky speciální a studium algebraicky speciálních prostoročasů je tedy relevantní. Několik aspektů algebraicky speciálních prostoročasů ve vyšších dimenzích byly těmito metodami již studováno, ale stále zůstává dlouhá řada neřešených otázek.

Macroscopic gravity is based on the mathematically precise formulation of the averaging problem in Einstein equations which is very essential, because they are nonlinear. So far the main applications are in cosmology and galactic dynamics. It might offer an alternative explanation for the flat galactic rotation curves without the need for dark matter or modification of the Theory of Relativity.

An extrasolar analog of the Sun - Jupiter - Saturn system has been found recently by detecting its gravitational influence on the passage of light from a more distant star (Gaudi et al. 2008). At the same time, gravitational microlensing by a system of three bodies (star + 2 planets, star + planet + moon, 3 stars) has not yet been satisfactorily analyzed theoretically. What has been fairly well explored is gravitational microlensing by two bodies (2 stars, star + planet), and analogous techniques can be used even for astrophysically relevant systems of three or four bodies. The objective of this work is to explore the character of microlensing by different systems of three (or even four) bodies.

In present time accuracy of spectroscopic measurements achieved fantastic accuracy 1 part in 10 to the 14-th power. If these measures are followed by theoretical calculations of similar accuracy we can test quantum electrodynamics by comparing theory and experiment and set some of the basic physical constants like Rydberg constant, mass and radius of nucleus, constant of fine structure and it´s variation in time etc. For achieving this kind of accuracy of calculations one must take into account ...

This thesis is concerned with particle plasma simulations and focuses on the electrostatic part of the problem. The primary intended application is probe diagnostics in high-temperature plasma. Two two-dimensional plasma models with different methods of computing the electrostatic interaction are designed. These model are able to represent internal electrodes of arbitrary shapes in the two-dimensional geometry and include the influence of external magnetic field. The particle-in-cell method is a...

In this work we study the asymptotic directional structure of specific exact solutions belonging to the large family of black hole spacetimes of type D found by Plebanski and Demianski. We discuss the radiation in the case of spacelike and timelike conformal infinity. With the aim of further interpretation, we have found the relation between the structure of the sources (the mass, the charge, the NUT parameter, the rotational parameter, the acceleration) and the properties of radiation generated by them.

The Kerr metric is an exact stationary axially symmetric solution of the Einstein equations, which describes gravitational field around a rotating body. There is no simple answer to the question of shape of this field looks like as it is not clear what are field lines and equipotentials. In the Newtonian case and in the Schwarzschild spacetime of a non-rotating source field lines are integral curves of the gravitational acceleration of static observers and equipotentials are surfaces of constant...

A basic feature of open thermodynamic systems is the existence of 'path-observables' like work and heat, which are functionals on trajectories of the system. A prominent role is played by the entropy production since it 'measures' the irreversibility of a thermodynamic process, i.e., how much it breaks the time-reversal symmetry. A consequence of this relation is that the fluctuations obey certain symmmetries. However, these classical ideas need a revision in quantum domain where the microscopic or mesoscopic trajectories are not well defined and where the fluctuations of path-observables hence become ambiguous. The present thesis will analyze some of the proposed concepts and it will demonstrate them on examples.

The objective of the diploma thesis is a theoretical study of magnetic properties of strongly correlated electrons within the single-impurity Anderson model. The means for the study will be field-theoretic and diagrammatic methods, many-body Green functiuons, and a renormalized parturbation expansion. One needs to employ nonperturbative methods in the limit of strong electron correlations. A simplifed parquet schneme developed in the diploma thesis of P. Augustinský will be used to achieve nontr...

Detailed understanding of quantum physics of black holes seems to be the most logical first step towards reaching the 'holy grail of theoretical physics', namely the unification or 'reconciliation' of general relativity and quantum mechanics. String theory allows us to compute the black hole entropy from a microscopic perspective for a variety of mostly supersymmetric or extremal blackholes in spacetimes of various dimensionalities. The basic idea is that certain objects in string theory (such a...