Anthony Streklas

 Panahaidas Athinas   95 Patras,  dassilion Greece Τel:. +30 - 2610 - 270442  Personal Page http://www.math.upatras.gr/~streklas/ Assistant  Professor   Department of Mathematics University of Patras, e-mail:  streklas@math.upatras.gr Tel. +30 - 2610 - 997 395

Personal Information

Born 16 October 1951
1975 :         B.C. Degree in Mathematics, University of Patras, Greece.
1980 :         Ph. D. Degree.   University of Patras, Greece.
Title of thesis:  The ordering of the operators in Quantum Mechanics. Supervisor Asterios Jannussis.

Professional Employment

1975 - 80 :  Post Graduate Researcher, Department of Mathematics, University of Patras, Greece.
1982 - 88 :  Lecturer, Department of Mathematics, University of Patras, Greece.
1988 - 13 :  Assistant Professor, Department of Mathematics, University of Patras, Greece.

Research Interests

• Quantum Mechanics.
• Open Quantum Systems and Quantum Friction.
• Particle Physics on Noncommutative Space
• Functional Analysis and Operator Theory.

Books

1. Classical Mechanics. A.Streklas Publisher University of Patras  http://www.math.upatras.gr/~streklas/public_html/syxroni.pdf
2. Quantum Mechanics. A.Streklas Publisher University of Patras   http://www.math.upatras.gr/~streklas/public_html/quant.pdf

Selected Publications Τotal number 22

1. Non commutative Quantum Mechanics in time - dependent backgrounds.     Antony Streklas.     Published in:  Theoretical Conscepts of Quantum Mechanics. InTech. 2012.
Abstract: The idea of non commutative space - time was presented by Snyder in 1947, with respect to the need to regularize the divergence of the quantum field theory. The idea was suggested by Heisenberg in 1930. In the past few years there has been an increasing interest in the non commutative geometry. For a manifold parameterized by the space - time coordinates x_m, the commutation relations can be written as [x_m,x_n]=i l_mn. In this article we have found the exact propagator of a two dimensional harmonic oscillator in non commutative quantum mechanics, where the ordinary non commutative parameters l_m are time dependent. Non commutativity of the momenta means that there is a time dependent magnetic field present. The Hamiltonian of the system is a linear combination of two Caldirola - Kanai Hamiltonians with two distinct friction parameters. We find the exact propagator of the system.

2. Quantum damped harmonic oscillator on non - commuting plane.     Antony Streklas.     Published in: physica A 385 (2007) pp 124 - 136.

3. Harmonic Oscillator in non Commuting two Dimensional Space.     Antony Streklas.     Published in:   Int . J. of Mod. Phys. B, Vol.21, No.33 (2007) pp 5363 - 5380.
Abstract: In the present paper we study the two dimensional Harmonic Oscillator in a constant magnetic field in non commuting space. We first prove that the system is equivalent  with a two dimensional system where the new operators of the momentum and the coordinate of the second dimension satisfies a deformed commutation relation. Then we write the time evolution operator in a appropriate normal ordered form, so that we can calculate the exact propagator in a straightforward manner. We prove that the unknown functions can be found with the help of the solutions of the equivalent classical problem. The method can be applied easily in the case where the frequencies or the mass m are time dependent. We find as well the time evolution of the coordinates and momenta operators.

4. Deformed Harmonic Oscillator for Non-Hermitian Operator and the Behavior of pt and CPT Symmetries     A. Jannussis, K. Vlachos, V. Papatheou, A. Streklas.     Published in:     Int. J. of Mod. Phys. B, Vol. 20,16 (2006) pp2313-2322.

5. Bolttzmann Statistics of Quantum Friction.     M. Mijatovic, A.Jannussis and  A. Streklas.     Published in:  Physics Letters, V. 122, 1 (1987)  pp 31-35.

6. Foundation of the Lie Admissible Fock Space of the Hadronic Mechanics.     A.Jannussis, G. Brodimas, D. Sourlas,  A. Streclas, P. Siafaricas, L. Papaloucas and N. Tsangas.     Published in:  Hadronic Lournal 5,   (1982),  pp. 1923 -1947.
Abstract:  In the present paper we study the case of coupling systems in hadronic mechanics. The non-canonical commutation relations of position and momentum operators are reduced, by Fock representation, to the known relations of $Q-$ algebra.of a Lie-admissible algebra, where $Q$ is an operator, we can define new Fock creation and annihilation operators, which describe some particles only under certain conditions, which must be fulfilled by the operator $\hat Q$. When we have a simple hadronic harmonic oscillator, the $\hat Q$ is a scalar less than 1, and we have energy saturation in eigenvalues spectrum. In this case the generalized uncertainty principle of Heisenberg is valid according to Santilli's theory. Finally, the coherent states of annihilation operator $A$ are given and the Weyl displacement operator is generalized in $Q-$ algebra.

7. Propagator with Friction in Quantum Mechanics.     A.Jannussis, G. Brodimas and  A. Streclas     Published in:  Physics Letters Vol. 74A, N.1,2 (1979)   pp 6 - 10.
Abstract: In this paper we calculate the propagator for some quantum - mechanical systems with friction. The friction is a linear function of the velocity with friction constant $\gamma$ and the system looks like a system with time dependent mass. We can calculate the exact propagators of some systems with quadratic Hamiltonians. Expecially we study the forced and damped harmonic oscillator in a uniform electromagnetic field.

8. Relativistic Wigner Operator and its Distribution.     A.Jannussis, A. Streclas, D.Sourlas and K. Vlachos.      Published in:      Lettere al Nuovo Cimento Vol.18, 11 (1977), pp. 349 - 351.
Abstract:
It has been proved that the Wigner operator which results from the quantum - mechanical foundation of Bopp and Kubo in phase space, admits as eigenvalues the deference of the eigenvalues of two equivalent Shrodinger equations and as eigenfunction the well known Wigner distribution function. In this paper we apply this method to the relativistic case and we find that the eigenvalues are again the 'difference of the eigenvalues of two equivalent Dirac equations. The eigenfunction is a 4Χ4 matrix with elements Wigner type distribution functions, which are Fourier transforms of the four Dirac's spinors.