K. Vlachos

Ordering of the Exponential of Quadratic Forms in Boson Operators and Some Applications

In the present paper we order operators of the general form exp [αa2 + βa+2 + γ(a+a + aa+) + δa + a+], using parametric differentiation. Using this ordered form we derive the density matrices and the canonical Wigner distribution function of the harmonic oscillator and of the electromagnetic field in a simple straightforward manner.

Some Properties of Commutators and the Equations of Motion

In this paper we calculate the commutators of operator functions for non-commuting operators on a Heisenberg ring. The commutator of two operators can be expressed with the help of the fundamental operators and their differentials. Using the theorem of the derivative of a function of operators with respect to any parameter, we can find tne equation of motion of a system, in canonical and non-canonical quantum mechanics.

Wigner representation of Bloch electrons in uniform fields

In this paper we calculate the Wigner distribution function and the partition function of Bloch electrons in uniform electric and magnetic fields with the help of the effective hamiltonian. We also calculate the magnetic and the electric susceptibilities. Using standard techniques of operator ordering, the above quantities are calculated in a manner which shows the exact contribution of the electric field.

Statistical mechanics and the quantum friction

Abstract In this paper we calculate the density matrix for quantum-mechanical systems where the hamiltonian is similar to that of Caldirola-Kanai. For the case where the friction is a linear function of the velocity with a friction constant γ, we can calculate exactly the density matrix and the partition function of the harmonic oscillator and the oscillator in a uniform magnetic field.

Perturbation expansion for the partition function of a generalized anharmonic oscillator

Abstract In this paper another form of the Schwinger perturbation expansion for the partition function of a generalized anharmonic oscillator is found. This form makes a numerical evaluation of higher order terms of the expansion possible. The expansion is applied to the 2 k -anharmonic oscillator and the two coupled anharmonic oscillators, for which some numerical results have been also drawn.

The partition function of the three-dimensional anharmonic oscillator

Abstract The thermodynamic perturbation theory is applied to the three-dimensional anharmonic oscillator. Numerical results are obtained for the partition function of the quartic anharmonic oscillator.

Quantum friction in a periodic potential

In this paper we study the quantum friction problem using the Hamiltonian of Caldirola-Kanai for a periodic Mathieus type potential. In the sequel we study the lattice electron with friction we introduce a new effective Hamiltonian of the Caldirola-Kanai form for a Blochs band. Finally we study the cases of closed solutions of Schrodingers equation.

Fermi-Dirac statistics for free electrons in uniform electric and magnetic fields

In this paper we study the De Haas-Van Alphen effect when an electric field is present. We prove that for sufficiently weak electric fields, where the conditions are favorable for energy quantization, the free energy is a quasi-periodical function with respect to the fields. As a consequence we find, for the magnetic susceptibility, periodical expressions which are easily reduced to the ones known for the De Haas-Van Alphen effect when the electric field vanishes.

DEFORMED HARMONIC OSCILLATOR FOR NON-HERMITIAN OPERATOR AND THE BEHAVIOR OF PT AND CPT SYMMETRIES

In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator where λ,θ are real positive parameters, since the parameters α,β,m are for the general case complex. For the case α=1,β=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex α=1,β=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case α,β,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters α,β the spectrum is real discrete and positive and the CPT symmetry is preserved. The general problem of deformed oscillator for non hermitian operators can be applied to the Solid State Physics.

Statistical mechanics of a confinement electron gas in a uniform electromagnetic field

In this paper we study an ideal electron gas in the presence of a uniform electromagnetic field and confinement by a three-dimensional harmonic potential. We find the partition function of this system and in the sequel we examine the Boltzmann statistics and Fermi-Dirac statistics applying the grand canonical ensemble method.