5,837 research outputs found
Transition Amplitudes within the Stochastic Quantization Scheme
Quantum mechanical transition amplitudes are calculated within the stochastic
quantization scheme for the free nonrelativistic particle, the harmonic
oscillator and the nonrelativistic particle in a constant magnetic field; we
close with free Grassmann quantum mechanics.Comment: 14 pages, LaTeX, UWThPh-1993-23 and DPUR 6
Completeness of scattering states of the Dirac Hamiltonian with a step potential
The completeness, together with the orthonormality, of the eigenfunctions of
the Dirac Hamiltonian with a step potential is shown explicitly. These
eigenfunctions describe the scattering process of a relativistic fermion off
the step potential and the resolution of the identity in terms of them
(completeness) is shown by explicitly summing them up, where appropriate
treatments of the momentum integrations are crucial. The result would bring
about a basis on which a field theoretical treatment for such a system can be
developed.Comment: 16 pages, 1 figure
A Simple Scheme to Entangle Distant Qubits from a Mixed State via an Entanglement Mediator
A simple scheme to prepare an entanglement between two separated qubits from
a given mixed state is proposed. A single qubit (entanglement mediator) is
repeatedly made to interact locally and consecutively with the two qubits
through rotating-wave couplings and is then measured. It is shown that we need
to repeat this kind of process only three times to establish a maximally
entangled state directly from an arbitrary initial mixed state, with no need to
prepare the state of the qubits in advance or to rearrange the setup step by
step. Furthermore, the maximum yield realizable with this scheme is compatible
with the maximum entanglement, provided that the coupling constants are
properly tuned.Comment: 9 pages, 3 figures; the version accepted for publication (with the
new title
Time development of a wave packet and the time delay
A one-dimensional scattering problem off a -shaped potential is
solved analytically and the time development of a wave packet is derived from
the time-dependent Schr\"odinger equation. The exact and explicit expression of
the scattered wave packet supplies us with interesting information about the
"time delay" by potential scattering in the asymptotic region. It is
demonstrated that a wave packet scattered by a spin-flipping potential can give
us quite a different value for the delay times from that obtained without
spin-degrees of freedom.Comment: 13 pages, plain TeX, 2 eps figures, tar+gzip+uuencode
Stochastic Quantization of Bottomless Systems: Stationary quantities in a diffusive process
By making use of the Langevin equation with a kernel, it was shown that the
Feynman measure exp(-S) can be realized in a restricted sense in a diffusive
stochastic process, which diverges and has no equilibrium, for bottomless
systems. In this paper, the dependence on the initial conditions and the
temporal behavior are analyzed for 0-dim bottomless systems. Furthermore, it is
shown that it is possible to find stationary quantities.Comment: LaTeX2e, 10 pages with 4 eps figures, to be published in Prog. Theor.
Phys. 102; revised page layou
Resonant Scattering Can Enhance the Degree of Entanglement
Generation of entanglement between two qubits by scattering an entanglement
mediator is discussed. The mediator bounces between the two qubits and exhibits
a resonant scattering. It is clarified how the degree of the entanglement is
enhanced by the constructive interference of such bouncing processes. Maximally
entangled states are available via adjusting the incident momentum of the
mediator or the distance between the two qubits, but their fine tunings are not
necessarily required to gain highly entangled states and a robust generation of
entanglement is possible.Comment: 7 pages, 13 figure
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