7 research outputs found
Complex collective states in a one-dimensional two-atom system
We consider a pair of identical two-level atoms interacting with a scalar
field in one dimension, separated by a distance . We restrict our
attention to states where one atom is excited and the other is in the ground
state, in symmetric or anti-symmetric combinations. We obtain exact collective
decaying states, belonging to a complex spectral representation of the
Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and
the real parts give the average energy of the collective states. In one
dimension there is strong interference between the fields emitted by the atoms,
leading to long-range cooperative effects. The decay rates and the energy
oscillate with the distance . Depending on , the decay rates
will either decrease, vanish or increase as compared with the one-atom decay
rate. We have sub- and super-radiance at periodic intervals. Our model may be
used to study two-cavity electron wave-guides. The vanishing of the collective
decay rates then suggests the possibility of obtaining stable configurations,
where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.
On the Thermal Symmetry of the Markovian Master Equation
The quantum Markovian master equation of the reduced dynamics of a harmonic
oscillator coupled to a thermal reservoir is shown to possess thermal symmetry.
This symmetry is revealed by a Bogoliubov transformation that can be
represented by a hyperbolic rotation acting on the Liouville space of the
reduced dynamics. The Liouville space is obtained as an extension of the
Hilbert space through the introduction of tilde variables used in the
thermofield dynamics formalism. The angle of rotation depends on the
temperature of the reservoir, as well as the value of Planck's constant. This
symmetry relates the thermal states of the system at any two temperatures. This
includes absolute zero, at which purely quantum effects are revealed. The
Caldeira-Leggett equation and the classical Fokker-Planck equation also possess
thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov
transformation in related fields and discuss the effects of the symmetry on the
shape of a Gaussian wave packet.Comment: Eqs.(64a), (65a)-(68) are correcte