192 research outputs found
Some properties of the resonant state in quantum mechanics and its computation
The resonant state of the open quantum system is studied from the viewpoint
of the outgoing momentum flux. We show that the number of particles is
conserved for a resonant state, if we use an expanding volume of integration in
order to take account of the outgoing momentum flux; the number of particles
would decay exponentially in a fixed volume of integration. Moreover, we
introduce new numerical methods of treating the resonant state with the use of
the effective potential. We first give a numerical method of finding a
resonance pole in the complex energy plane. The method seeks an energy
eigenvalue iteratively. We found that our method leads to a super-convergence,
the convergence exponential with respect to the iteration step. The present
method is completely independent of commonly used complex scaling. We also give
a numerical trick for computing the time evolution of the resonant state in a
limited spatial area. Since the wave function of the resonant state is
diverging away from the scattering potential, it has been previously difficult
to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde
Exact Markovian kinetic equation for a quantum Brownian oscillator
We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte
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.
Electron Trapping in a One-Dimensional Semiconductor Quantum Wire with Multiple Impurities
We demonstrate the trapping of a conduction electron between two identical adatom impurities in a one-dimensional semiconductor quantum-dot array system (quantum wire). Bound steady states arise even when the energy of the adatom impurity is located in the continuous one-dimensional energy miniband. The steady state is a realization of the bound state in continuum (BIC) phenomenon first proposed by von Neuman and Wigner [Phys. Z. 30, 465 (1929)]. We analytically solve the dispersion equation for this localized state, which enables us to reveal the mechanism of the BIC. The appearance of the BIC state is attributed to the quantum interference between the impurities. The Van Hove singularity causes another type of bound state to form above and below the band edges, which may coexist with the BIC
Microscopic nonequilibrium structure in quantum fields and H-functions
AbstractExact dynamical models for entropy production and entropy flow are introduced by means of the complex spectral representation and illustrated by using a simple conservative Hamiltonian system for multileveled atoms coupled to an external time-dependent field. The dynamical form of the H-function is introduced corresponding to the Friedrichs model coupled with the external periodic force. The external force destroys the monotonicity of the H-function evolution and leads to a model for the “entropy flow”. As the result of competition between the dissipation inside the system and the regeneration of the excited states due to the external field, there appears a steady structure of the emitted field around the unstable particle, which corresponds to the “dissipative structure” and is intrinsic to the system as it does not depend on its initial preparation. The behavior of the H-function is investigated for the “velocity inversion experiment”
Causality, delocalization and positivity of energy
In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.Comment: 14 pages, 5 figure
Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity
We provide detailed analysis of the complex energy eigenvalue spectrum for a
two-channel quantum wire with an attached adatom impurity. The study is based
on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we
presented the quasi-bound states in continuum (or QBIC states). These are
resonant states with very long lifetimes that form as a result of two
overlapping continuous energy bands one of which, at least, has a divergent van
Hove singularity at the band edge. We provide analysis of the full energy
spectrum for all solutions, including the QBIC states, and obtain an expansion
for the complex eigenvalue of the QBIC state. We show that it has a small decay
rate of the order , where is the coupling constant. As a result of
this expansion, we find that this state is a non-analytic effect resulting from
the van Hove singularity; it cannot be predicted from the ordinary perturbation
analysis that relies on Fermi's golden rule. We will also numerically
demonstrate the time evolution of the QBIC state using the effective potential
method in order to show the stability of the QBIC wave function in comparison
with that of the other eigenstates.Comment: Around 20 pages, 50 total figure
Quantum Zeno subspaces
The quantum Zeno effect is recast in terms of an adiabatic theorem when the
measurement is described as the dynamical coupling to another quantum system
that plays the role of apparatus. A few significant examples are proposed and
their practical relevance discussed. We also focus on decoherence-free
subspaces.Comment: 5 pages, 1 figure, to be published in Phys. Rev. Let
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