114 research outputs found
Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect
An exactly-solvable model for the decay of a metastable state coupled to a
semi-infinite tight-binding lattice, showing large deviations from exponential
decay in the strong coupling regime, is presented. An optical realization of
the lattice model, based on discrete diffraction in a semi-infinite array of
tunneling-coupled optical waveguides, is proposed to test non-exponential decay
and for the observation of an optical analog of the quantum Zeno effect
Quantum simulator for the Ising model with electrons floating on a helium film
We propose a physical setup that can be used to simulate the quantum dynamics
of the Ising model with present-day technology. Our scheme consists of
electrons floating on superfluid helium which interact via Coulomb forces. In
the limit of low temperatures, the system will stay near the ground state where
its Hamiltonian is equivalent to the Ising model and thus shows phenomena such
as quantum criticality. Furthermore, the proposed design could be generalized
in order to study interacting field theories (e.g., ) and
adiabatic quantum computers.Comment: 4 page
Full transmission within a wide energy range and super-criticality in relativistic barrier scattering
For potential barriers with scalar and vector coupling, we show that a Dirac
particle could experience nearly full transmission within a wide sub-barrier
energy band. Moreover, for certain potential configurations, including
pseudo-spin symmetry where the scalar potential is the negative of the vector,
full transmission occurs for arbitrarily small momentum.Comment: 10 pages, 4 figures, 1 table, 1 video animatio
Quantum particle displacement by a moving localized potential trap
We describe the dynamics of a bound state of an attractive -well
under displacement of the potential. Exact analytical results are presented for
the suddenly moved potential. Since this is a quantum system, only a fraction
of the initially confined wavefunction remains confined to the moving
potential. However, it is shown that besides the probability to remain confined
to the moving barrier and the probability to remain in the initial position,
there is also a certain probability for the particle to move at double speed. A
quasi-classical interpretation for this effect is suggested. The temporal and
spectral dynamics of each one of the scenarios is investigated.Comment: 5 pages, 6 figure
Pulse Propagation in Resonant Tunneling
We consider the analytically solvable model of a Gaussian pulse tunneling
through a transmission resonance with a Breit-Wigner characteristic. The
solution allows for the identification of two opposite pulse propagation
regimes: if the resonance is broad compared to the energetic width of the
incident Gaussian pulse a weakly deformed and slightly delayed transmitted
Gaussian pulse is found. In the opposite limit of a narrow resonance the dying
out of the transmitted pulse is dominated by the slow exponential decay
characteristic of a quasi-bound state with a long life time (decaying state).
We discuss the limitation of the achievable pulse transfer rate resulting from
the slow decay. Finally, it is demonstrated that for narrow resonances a small
second component is superimposed to the exponential decay which leads to
characteristic interference oscillations.Comment: 6 pages, 4 figure
Enhancement and suppression of tunneling by controlling symmetries of a potential barrier
We present a class of 2D systems which shows a counterintuitive property that
contradicts a semi classical intuition: A 2D quantum particle "prefers"
tunneling through a barrier rather than traveling above it. Viewing the one
particle 2D system as the system of two 1D particles, it is demonstrated that
this effect occurs due to a specific symmetry of the barrier that forces
excitations of the interparticle degree of freedom that, in turn, leads to the
appearance of an effective potential barrier even though there is no "real"
barrier. This phenomenon cannot exist in 1D.Comment: 10 pages and 7 figure
Accurate numerical verification of the instanton method for macroscopic quantum tunneling: dynamics of phase slips
Instanton methods, in which imaginary-time evolution gives the tunneling
rate, have been widely used for studying quantum tunneling in various contexts.
Nevertheless, how accurate instanton methods are for the problems of
macroscopic quantum tunneling (MQT) still remains unclear because of lack of
their direct comparison with exact time evolution of the many-body Schroedinger
equation. Here, we verify instanton methods applied to coherent MQT.
Specifically applying the quasi-exact numerical method of time-evolving block
decimation to the system of bosons in a ring lattice, we directly simulate the
real-time quantum dynamics of supercurrents, where a coherent oscillation
between two macroscopically distinct current states occurs due to MQT. The
tunneling rate extracted from the coherent oscillation is compared with that
given by the instanton method. We show that the error is within 10% when the
effective Planck's constant is sufficiently small. We also discuss phase slip
dynamics associated with the coherent oscillations.Comment: 19 pages, 14 figures, 1 tabl
Periodic Quasi - Exactly Solvable Models
Various quasi-exact solvability conditions, involving the parameters of the
periodic associated Lam{\'e} potential, are shown to emerge naturally in the
quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity
of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible
for the surprisingly large number of allowed solvability conditions in the
associated Lam{\'e} case. We also study the singularity structure of the
quantum momentum function, which yields the band edge eigenvalues and
eigenfunctions.Comment: 11 pages, 5 table
Deformation Quantization of a Certain Type of Open Systems
We give an approach to open quantum systems based on formal deformation
quantization. It is shown that classical open systems of a certain type can be
systematically quantized into quantum open systems preserving the complete
positivity of the open time evolution. The usual example of linearly coupled
harmonic oscillators is discussed.Comment: Major update. Improved main statements. 21 page
Quantum probability distribution of arrival times and probability current density
This paper compares the proposal made in previous papers for a quantum
probability distribution of the time of arrival at a certain point with the
corresponding proposal based on the probability current density. Quantitative
differences between the two formulations are examined analytically and
numerically with the aim of establishing conditions under which the proposals
might be tested by experiment. It is found that quantum regime conditions
produce the biggest differences between the formulations which are otherwise
near indistinguishable. These results indicate that in order to discriminate
conclusively among the different alternatives, the corresponding experimental
test should be performed in the quantum regime and with sufficiently high
resolution so as to resolve small quantum efects.Comment: 21 pages, 7 figures, LaTeX; Revised version to appear in Phys. Rev. A
(many small changes
- …