Phase-space approach to Berry's phases

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are related with the averaging procedure: Hannay's angle with averaging over the classical torus and Berry's phase with averaging over the entire classical phase space with respect to the corresponding Wigner function. Generalizations to the non-abelian Wilczek--Zee case and mixed states are also included.Comment: 5 page

Wigner function for damped systems

Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It turns out that one may construct out of a pair of resonant states an analog of the stationary Wigner function.Comment: 18 page

New tools for investigating positive maps in matrix algebras

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as reduction map, generalized reduction, Robertson map, and many others). Furthermore, we use it to construct a new family of linear maps and prove that they are positive, indecomposable and (nd)optimal.Comment: 10 page

Non-Markovian quantum dynamics: local versus non-local

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.Comment: 4.5 pages; new examples are adde

Generation of a dipole moment by external field in Born-Infeld non-linear electrodynamics

The mechanism for the generation of a dipole moment due to an external field is presented for the Born-Infeld charged particle. The 'polarizability coefficient' is calculated: it is proportional to the third power of the characteristic length in the Born-Infeld theory. Some physical implications are briefly discussed.Comment: 8 pages, LATE

The Study of Interdependence between Capital and Currency Markets Using Multivariate GARCH Models

In the article an attempt was made to investigate the interaction among the various stock exchanges as well as various exchange rates and then to determine the direction of information flow between capital and currency markets. Tools used in this study are Multivariate GARCH models. Presented results developed an earlier study of World Stock Exchange classification. These stock exchanges will be further analysed according to their interaction.Multivariate GARCH Model, independence analysis, stock exchange, exchange rate.

On the structure of entanglement witnesses and new class of positive indecomposable maps

We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.Comment: 18 page