arXiv subjects

T. Hakioglu

Publications and source records attributed to T. Hakioglu.

22 records · Page 2Linked to original sources

arXiv1999

Linear canonical transformations and quantum phase:a unified canonical and algebraic approach

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action-angle phase space formalism is established and it is shown that the conceptual foundation of the quantum phase problem lies within the algebraic properties of the quantum canonical transformations in the quantum phase space. The representations of the Wigner function in the generalized action-angle unitary operator pair for certain Hamiltonian systems with the dynamical symmetry are examined. This generalized canonical formalism is applied to the quantum harmonic oscillator to examine the properties of the unitary quantum phase operator as well as the action-angle Wigner function.

quant-ph↗

arXiv1999

Operational approach in the weak-field measurement of polarization fluctuations

The operational approach to the measurement of phase studied by Noh, Fougeres and Mandel is applied to the measurement of the state of polarization of fully polarized light. Operational counterparts of the quantum Stokes parameters are introduced and their fluctuations are examined. It is shown that if the polarized field is weak, the measured fluctuations are influenced not only by the quantum properties of the source field but also that of the measurement. This character is reflected on the measured probability distributions of the parameters of polarization, which are also investigated independently for the fully polarized coherent states and the Fock states as the initial field strength is varied. Finally, connection between the operational approach to the measurement of polarization and the su(2) interferometry is examined.

physics.optics↗

arXiv1998

Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase

Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice ${\ee Z}_{D} \times {\ee Z}_{D}$ with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the algebraic formulation of the quantum phase problem. Certain equivalence classes in the space of labels are identified within each subalgebra, and connections with area-preserving canonical transformations are examined. The generalized representations of the Wigner function are examined in the finite-dimensional cyclic Schwinger basis. These representations are shown to conform to all fundamental conditions of the generalized phase space Wigner distribution. As a specific application of the Schwinger basis, the number-phase unitary operator pair in ${\ee Z}_{D} \times {\ee Z}_{D}$ is studied and, based on the admissibility of the underlying q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum phase operator is established. This being the focus of this work, connections with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well as standard action-angle Wigner function formalisms are examined in the infinite-period limit. The concept of continuously shifted Fock basis is introduced to facilitate the Fock space representations of the Wigner function.

quant-ph↗

arXiv1998

Dynamical properties of the two-dimensional Holstein-Hubbard model in the normal state at zero temperature: A fluctuation-based effective cumulant approach

The two-dimensional many-body Holstein-Hubbard model in the T=0 normal state is examined within the framework of the self-consistent coupling of charge fluctuation correlations to the vibrational ones. The parameters of our model are the adiabaticity, the electron concentration, as well as the electron-phonon and the Coulomb interaction strengths. A fluctuation-based effective cumulant approach is introduced to examine the T=0 normal-state fluctuations and an analytic approximation to the true dynamical entangled ground state is suggested. Our results for the effective charge-transfer amplitude, the ground state energy, the fluctuations in the phonon population, the phonon softening as well as the coupling constant renormalizations suggest that, the recent numerical calculations of de Mello and Ranninger (Ref.5), Berger, Valasek and von der Linden (Ref.2) and Marsiglio (Ref. 4 and 8) on systems with finite degrees of freedom can be qualitatively extended to the systems with large degrees of freedom.

cond-mat.str-el↗