CV Anđelo Samsarov
Nationality: Croatian
Present professional position: Research Associate in the area of Mathematical Physics
Academic/professional record:
08-03-2013 now: Research Associate – Ruđer Bošković Institute, Zagreb, Croatia
01-01-2010 – 07-03-2013: Senior Research Assistant – Ruđer Bošković Institute, Zagreb, Croatia
01-09-2003 – 24-11-2009: Research Assistant, PhD student – Ruđer Bošković Institute, Zagreb, Croatia/University of Zagreb
28-09-2002 – 31-08-2003: PhD student – University of Zagreb, Croatia
Academic profile:
Research area(s): Mathematical Physics
Date when PhD degree was awarded (if applicable): 24/11/2009
University where PhD was obtained (if applicable): University of Zagreb, Zagreb, Croatia
Main contributions/summary of research interests: The subjects of my research so far can generally be divided into three different areas, the first being related with the integrable models, the second being related with the description of the low energy excitations within the nanostructures such as graphene and the third being related to the noncommutative physics, particularly to the quantum group description of the symmetry deformation resulting from the modified spacetime geometry.
The first of the above mentioned topics, namely the integrable models, with the particular emphasis on the generalizations of the Calogero models, was actually a subject of my PhD thesis, which was worked out at the Theoretical Physics Department of the Rudjer Boskovic Institute in Zagreb. In my PhD thesis, two types of generalizations of the Calogero model were considered. These generalizations were carried out along two different routes. The first one has included multispecies, multidimensional and supersymmetrical extensions of the Calogero model.
The second one investigates the generalizations of the rational Calogero model which consists of adding the additional interactions, e.g. of Marchioro-Wolves or Coulomb type, to the basic inverse-square interaction. By algebraic methods, creation and annihilation operators are constructed for Hamiltonians describing one-dimensional and multidimensional multispecies Calogero model with two-particle and three-particle interactions. With the help of creation and annihilation operators, all polynomial eigen-solutions for investigated models are found. The spectrum corresponding to these states was shown to be linear in quantum numbers and also exhibits degeneracy for higher level excitations. The symmetry which is responsible for this degeneracy is SU(2) symmetry. It has been shown that all systems realizing conformal SU(1,1) symmetry can be algebraicaly mapped to a set of decoupled oscillators. This result enabled a development of a general method for constructing a complete set of eigenstates in the Bargmann representation, for all systems with underlying conformal symmetry. By using von Neumann”s theory of self-adjoint extensions, it has been shown that the rational Calogero models of the types A_N-1 and B_N, with or without harmonic coupling, allow a new class of bound states, as well as new states in the scattering sector. By the same method, nonequivalent quantizations of the N-particle rational Calogero model with an additional Coulomb-type interaction are investigated. As a result of this analysis, exact eigenstates and spectrum are obtained in the bound state sector as well as in the scattering sector. Another area of my research was focused on the investigation and description of the low energy excitations in graphene. It is known that the low energy dynamics of gapless graphene is described by a two-dimensional massless Dirac equation. These excitations are negatively charged and behave like the electrons with Fermi velocity playing the role of the velocity of light. In graphene, even a small charge impurity can produce a strong nonperturbative effects, since the effective Coulomb interaction strength is of the order or close to unity. The effect of charge impurities in gapless graphene is known to lead to a formation of bound states when the Coulomb charge (coupling) exceeds a certain critical value. When the charge impurities are not present, the bound states do not form in a gapless graphene due to the QED phenomenon known as the Klein paradox. The generalization of this model where a Dirac mass term is included in the Hamiltonian is known to describe gapped graphene. The effect of charge impurities in gapped graphene, contrary to the gapless case, is known to produce bound states for an arbitrarily small value of the Coulomb charge. Beside providing the long range Coulomb interaction, charge impurities may induce other short range interactions which might be very hard to insert directly in the Hamiltonian, especially when knowing that QED (Dirac)-like description is valid only in the long wavelength limit. However, one possible way to model their combined effect is through an appropriate choice of the boundary conditions. This can be done by following the principle of self-adjointness through the use of von Neumann’s theory. My collaborators and myself have analysed the effects of the Coulomb long range and of short range interactions on the scattering sector of the gapless as well as the gapped graphene in a presence of charge impurity. Particularly, I have investigated the phase shifts and the scattering S matrix and obtained the bound states from the poles of the S matrix. These quantities can be further used to calculate physical properties of the system, such as the local density of states (LDOS) and resistivity. Described formalism gives rise to the physical observables that depend on the self-adjoint extension parameter, which encodes boundary conditions and can be subsequently acquired by comparing the obtained results with experiment.
Third area of my research is related to various aspects of noncommutative physics and to Quantum Group description of symmetries underlying the Quantum Field Theory (QFT) on noncommutative spaces. Although my investigations include other types of noncommuttivity such as those of the Snyder type, they were primirily focused on Lie-algebraic noncommutativity, with κ-Minkowski spacetime being the main example.
In my research κ-deformed Minkowski spacetime with undeformed Lorentz symmetry and vector-like Dirac derivative is investigated. It is a Lie algebra type of noncommutative space which is found to allow an infinite number of realizations in terms of the nondeformed Heisenberg-Weyl algebra, i.e. commutative coordinates and their conjugated momenta. It is found that to each of this realizations there corresponds a particular coalgebra structure and the star product, as well as the ordering prescription. By using this cognition and the notion of the particular type of realization, namely classical Dirac operator representation, a scalar field theory on κ-deformed Minkowski spacetime is constructed and shown to be equivalent to a scalar, relativistically invariant and nonlocal field theory on the commutative Minkowski space. By further exploring the properties of the classical Dirac operator representation, it is found that its variant that is hermitian leads to a star product which has the property that under an integration sign it can be replaced by the standard pointwise multiplication, the property that was since known to hold for Moyal, but not for the κ-Minkowski spacetime. The consequence is that upon the transition to a Minkowski space, the corresponding noncommutative free scalar field theory does not reduce to a nonlocal theory anymore, but is equivalent to a standard, local free scalar theory on ordinary Minkowski space.
Additional qualifications:
I was involved in training young researchers and scientists. I have also led three students toward completing their diploma (master) theses, one with the title: “Supersymmetric quantum mechanics”, the second one with the title: “Minimal length and aspects of deformation of Special relativity theory” and the third one with the title „Dirac oscillator and Quantum Hall effect.“ Currently I am supervising the diploma (master) thesis under the title: „Representations of the Poincare group and the Landau-Yang theorem“.