Akira Inomata

Path integrals with a periodic constraint: Entangled strings

Path integrals with a periodic constraint ∫θ ds =Θ+2πn (n=integer) are studied. In particular, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates. Applications are made for the entangled polymers with and without interactions, the Aharonov–Bohm effect, and the angular momentum projection of a spinning top.

Alternative exact-path-integral treatment of the hydrogen atom☆

Abstract An alternative exact-path-integral treatment of the hydrogen atom is proposed. The earlier treatment is based on the bijective transformation of Kustaanheimo and Stiefel. The proposed procedure reduces the radial path integral for the hydrogen atom into that for an oscillator in R 3 by one-to-one mapping.

Remarks on the Hamiltonian path integral in polar coordinates

Problems associated with the derivation of the Hamiltonian path integral in polar coordinates are examined. First the use of the ill‐defined asymptotic formula of the modified Bessel function is pointed out. A procedure is proposed to justify its practical use, in which the mass m is complexified and the limit Imm→0 is taken after path integrations. Hereby a restriction is imposed on the class of allowed potentials. The difference between the Hamiltonian path integral so obtained and the phase space path integral formally defined is also discussed.

Exact path-integration for the two-dimensional Coulomb problem

Abstract The lagrangian path integral for the Coulomb problem in two dimensions is explicitly calculated in the parabolic coordinates with the new “time” parameter of Duru and Kleinert.

Path integrals with a periodic constraint: The Aharonov–Bohm effect

The Aharonov–Bohm effect is formulated in terms of a constrained path integral. The path integral is explicitly evaluated in the covering space of the physical background to express the propagator as a sum of partial propagators corresponding to homotopically different paths. The interference terms are also calculated for an infinitely thin solenoid, which are found to contain the usual flux dependent shift as the dominant observable effect and an additional topological shift unnoticeable in the two slit interference experiment.

Transformation of the free propagator to the quadratic propagator

Abstract A space and time transformation is found, which changes the classical action for a quadratic lagrangian into that for a free particle. It is shown that the propagator for a time-dependent damped oscillator can be obtained from the free propagator.

Path-integral treatment of the morse oscillator

Abstract The path integral for the Green function of the Morse oscillator is evaluated by changing local variables and local time parameters. The exact energy spectrum for the Morse oscillator is obtained.

Topological shifts in the Aharonov-Bohm effect

Abstract The topological nature of the Aharonov-Bohm effect is examined. The interference terms are found to contain the usual flux dependent shift as the dominant observable effect and an additional topological shift unnoticeable in the two-slit interference experiment.

Path-integral formulation of the Langer modification and its applications to the hydrogen atom

Abstract The Larger transformation is performed in the path integral for the radial propagator. The semiclassical calculation of the transformed propagator results in the exact energy spectrum of the hydrogen atom and the semiclassical Coulomb phase shifts with the correct angular modification.

Manipulation of single electron spin in a GaAs quantum dot through the application of geometric phases: The Feynman disentangling technique

The spin of a single electron in an electrically defined quantum dot in a 2DEG can be manipulated by moving the quantum dot adiabatically in a closed loop in the 2D plane under the influence of applied gate potentials. In this paper we present analytical expressions and numerical simulations for the spin-flip probabilities during the adiabatic evolution in the presence of the Rashba and Dresselhaus linear spin-orbit interactions. We use the Feynman disentanglement technique to determine the non-Abelian Berry phase and we find exact analytical expressions for three special cases: (i) the pure Rashba spin-orbit coupling, (ii) the pure Dresselhause linear spin-orbit coupling, and (iii) the mixture of the Rashba and Dresselhaus spin-orbit couplings with equal strength. For a mixture of the Rashba and Dresselhaus spin-orbit couplings with unequal strengths, we obtain simulation results by solving numerically the Riccati equation originating from the disentangling procedure. We find that the spin-flip probability in the presence of the mixed spin-orbit couplings is generally larger than those for the pure Rashba case and for the pure Dresselhaus case, and that the complete spin-flip takes place only when the Rashba and Dresselhaus spin-orbit couplings are mixed symmetrically.