Abstract:
This paper focuses on the process of euroisation of the Albanian economy. Like any other process, even euroisation has its benefits and costs. The prevailing opinion is that the advantages of euroisation, at least for a short period, are profoundly evident especially in developing countries where aspirations for EU entry are great. The Albanian economy has experienced the financial euroisation since 1992. Considering the actual conditions, for Albania, an alternative to be considered would be the unilateral euroisation. Costs and benefits of unilateral euroisation are related to each-other, but in the case of Albania, they tend to benefit especially from a considerable expansion of trade. We all understand that the road towards European integration will pass through the euroisation of the economy. The question that arises is not if will be the Albanian economy euroised but when this will happen.

Abstract:
The purpose of the paper is to analyze the informal economy in Albania. The measurement of informal economy may be realized through direct and indirect methods. The collection of data about informal economic activities, the frequency and the volume of the underground activities present a challenge, because of the data limitations. Therefore, to measure it used more indirect methods. Albanian governments have always adopted a philosophy that aims to formalize the economy through legal and institutional improvements, reducing taxes, fighting corruption and tax evasion; improvement in revenue collection from customs and taxes in general, improving governance and increasing efficiency of public institutions. Albania is on the way of the integration in the EU. The integration perspective should be supported by concrete politics on the improvement of government functioning and decrease of the informal sector, so that the people think that their country is on the right way toward modernization and prosperity.

Abstract:
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the theory). This is possible provided we adopt Feynman's suggestion of dropping the assumption that the probability for an event must always be a positive number. This approach has the advantage of allowing a reformulation of quantum theory in phase space without introducing the unphysical concept of probability amplitudes, together with all the problems concerning their ambiguous properties.

Abstract:
Quantum rings connected to ballistic circuits couple strongly to external magnetic fields if the connection is not symmetric. By analytical theory and computer simulation I show that properly connected rings can be used to pump currents in the wires giving raise to a number of interesting new phenomena. One can pump spin polarized currents into the wires by using rotating magnetic fields or letting the ring rotate around the wire. This method works without any need for the spin-orbit interaction, and without stringent requirements about the conduction band filling. On the other hand, another method works at half filling using a time-dependent magnetic field in the plane of the (fixed) ring. This can be used to pump a pure spin current, excited by the the spin-orbit interaction in the ring. One can use magnetizable bodies as storage units to concentrate and save the magnetization in much the same way as capacitors store electric charge. The polarization obtained in this way can then be used on command to produce spin currents in a wire. These currents show interesting oscillations while the storage units exchange their polarizations and the intensity and amplitude of the oscillations can controlled by tuning the conductance of the wire used to connect the units.

Abstract:
The
current study reports the concentration of lead in top of the soil samples and
its penetration until the depth of approximately 120 cm. Representative soil samples
are collected around the former Factory Production of Batteries to Berat,
Albania at a distance 80 - 900 m from factory. We have chosen 12 sampling
points. We have collected a total of 55 samples where 31 were soil samples (12
top of soil and 19 were profile soil samples) and 24 were random vegetation
samples. All soil samples were analyzed using Atomic Absorption Spectrometry
for their lead content, at the Institute of Applied Nuclear Physics, University
of Tirana, Albania. From results obtained the fraction of lead in profile soil
samples was in range: 78 mg/kg - 52,982 mg/kg and average concentration of lead
was 2976 mg/kg, while in random vegetation samples was in range: 0.238 - 5.573
mg/kg. In general, trend of the content of lead in profile soil samples was
decreasing compared to the content of lead in the respective top soil samples.
The concentrations of lead which have been found in analyzed soil samples are
compared with the Maximum Contaminant Levels specified by the Directive
86/278/EEC. Also, we have calculated Hazardous Quoted for each sampling point
which is found very high. HQ in representative surface soil samples is 0.4 - 80.7
times higher than normal.

Abstract:
We show that a tight-binding model device consisting of a laterally connected ring at half filling in a tangent time-dependent magnetic field can in principle be designed to pump a purely spin current. The process exploits the spin-orbit interaction in the ring. This behavior is understood analytically and found to be robust with respect to temperature and small deviations from half filling.

Abstract:
In two-dimensional systems possessing a high degree of symmetry, the repulsive electron-electron interaction produces a pairing force; the mechanism would fail in the presence of strong distortions. We have studied this in the one-band and three-band Hubbard Model. From partially occupied orbitals one obtains pair eigenstates of the Hamiltonian with no on-site repulsion (the W=0 pairs). The concept of W=0 pairs allows to make qualitative and quantitative predictions about the behaviour of interacting many-body systems, a quite remarkable and unusual situation. Exact numerical solutions for clusters with ``magic'' hole numbers reveal attraction between the holes in W=0 pairs. The effect occurs in all fully symmetric clusters which are centered on a Cu site; then holes get paired in a wide, physically relevant parameter range and show superconducting quantization of the magnetic flux. A canonical transformation of the Hamiltonian, valid for clusters and for the full plane, leads to a Cooper-like equation for the W=0 pairs. We have evaluated the effective interaction and found that W=0 pairs are the bare quasiparticles which, once dressed, become two-hole bound states. We applied the above theory to the doped antiferromagnet, and found that the ground state at half filling is the singlet component of a determinantal state. We write down this determinant and the ground state wave function explicitly in terms of a many-body W=0 eigenstate. Our analytical results for the $4\times 4$ square lattice at half filling and with doped holes, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power.

Abstract:
As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph $\L={\cal A}\cup{\cal B}$ with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal B}$). In this paper we analytically find the {\it exact} ground state for $N_{A}=N_{B}=N$ at half filling for any $N$; the ground state expectation value of the repulsion term has a maximum at a critical $N$-dependent value of the on-site Hubbard $U$ and then drops like 1/U for large $U$. The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for $N \ra \inf$. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero $U$ even in the thermodynamic limit. This is the first explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.

Abstract:
We model a Superconducting Single-Electron Transistor operating by repulsive interactions. The device consists of a ring of Hubbard clusters, placed between electrodes and capacitively coupled to a gate potential. In each cluster, a pair of electrons at appropriate filling feels a weak effective interaction which leads to pairing in part of the parameter space. Thus, the system can host many bound pairs, with correlation induced binding. When the charging energy exceeds the pairing energy, single-electron tunneling prevails; in the opposite regime, we predict the Coulomb blockade pattern of two-electron tunneling. This suggests that in tunneling experiments repulsion-induced pairs may behave in a similar way as phonon-induced ones.

Abstract:
We investigate the interplay of phonons and correlations in superconducting pairing by introducing a model Hamiltonian with on-site repulsion and couplings to several vibration branches having the Cu-O plane of the cuprates as a paradigm. We express the electron-phonon coupling (EP) through two force constants for O-Cu and O-O bond stretchings. Without phonons, this reduces to the Hubbard Model, and allows purely electronic W=0 pairing. A W=0 pair is a two-body singlet eigenstate of the Hubbard Hamiltonian, with no double occupancy, which gets bound from interactions with background particles. Indeed, this mechanism produces a Kohn-Luttinger-like pairing from the Hubbard repulsion, provided that its symmetry is not severely distorted. From the many-body theory, a canonical transformation extracts the effective two-body problem, which lends itself to numerical analysis in case studies. As a test, we use as a prototype system the $\cu$ cluster. We show analytically that at weak EP coupling the additive contributions of the half-breathing modes reinforce the electronic pairing. At intermediate and strong EP coupling and $U \sim t$, the model behaves in a complex and intriguing way.