On qpqp-Deformations in Statistical Mechanics of Bosons in D Dimensions

The Bose distribution for a gas of nonrelativistic free bosons is derived in the framework of $qp$-deformed second quantization. Some thermodynamical functions for such a system in D dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters q and p as well as a parameter $\nu_0'$ which characterizes the representation space of the oscillator algebra.Comment: 15 pages, Latex File, to be published in Symmetry and Structural Properties of Condensed Matter, Eds. T. Lulek, B. Lulek and W. Florek (World Scientific, Singapore, 1997

Unified scheme for correlations using linear relative entropy

A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which we determine the total, classical and quantum correlations. We also give the explicit expressions of its closest product state, closest classical state and the corresponding closest product state. A closed additive relation, involving the various correlations quantified by linear relative entropy, is derived.Comment: 20 page

On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on a decomposition in which a Q-uon gives rise to an ordinary boson and a k-fermion (a k-fermion being an object interpolating between boson and fermion). The second one starts from a generalized Weyl-Heisenberg algebra. Finally, the third one relies on the quantum algebra Uq(sl(2)) where q is a root of unity.Comment: 14 pages, LaTex file. Paper written from a lecture presented (by M.R.K.) at the Sixth International School on Theoretical Physics ``Symmetry and Structural Properties of Condensed Matter'', a school devoted to the memory of Louis Michel, Myczkowce (Poland), 31 August - 6 September 2000. To be published in ``Symmetry and Structural Properties of Condensed Matter'', eds. T. Lulek, B. Lulek and A. Wal (World Scientific, Singapore, 2001

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.Comment: 26 page