194 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
Functional integral for non-Lagrangian systems
A novel functional integral formulation of quantum mechanics for
non-Lagrangian systems is presented. The new approach, which we call "stringy
quantization," is based solely on classical equations of motion and is free of
any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the
theory. The functionality of the proposed method is demonstrated on several
examples. Special attention is paid to the stringy quantization of systems with
a general A-power friction force . Results for are
compared with those obtained in the approaches by Caldirola-Kanai, Bateman and
Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon
approach are discussed as well.Comment: 14 pages, 7 figures, corrected typo
Perturbative Calculation of the Adiabatic Geometric Phase and Particle in a Well with Moving Walls
We use the Rayleigh-Schr\"odinger perturbation theory to calculate the
corrections to the adiabatic geometric phase due to a perturbation of the
Hamiltonian. We show that these corrections are at least of second order in the
perturbation parameter. As an application of our general results we address the
problem of the adiabatic geometric phase for a one-dimensional particle which
is confined to an infinite square well with moving walls.Comment: Plain Latex, accepted for publication in J. Phys. A: Math. Ge
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
Wave packet evolution in non-Hermitian quantum systems
The quantum evolution of the Wigner function for Gaussian wave packets
generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical
limit this yields the non-Hermitian analog of the Ehrenfest
theorem for the dynamics of observable expectation values. The lack of
Hermiticity reveals the importance of the complex structure on the classical
phase space: The resulting equations of motion are coupled to an equation of
motion for the phase space metric---a phenomenon having no analog in Hermitian
theories.Comment: Example added, references updated, 4 pages, 2 figure
WKB approximation for multi-channel barrier penetrability
Using a method of local transmission matrix, we generalize the well-known WKB
formula for a barrier penetrability to multi-channel systems. We compare the
WKB penetrability with a solution of the coupled-channels equations, and show
that the WKB formula works well at energies well below the lowest adiabatic
barrier. We also discuss the eigen-channel approach to a multi-channel
tunneling, which may improve the performance of the WKB formula near and above
the barrier.Comment: 15 pages, 4 eps figure
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
Exact Thermodynamics of the Double sinh-Gordon Theory in 1+1-Dimensions
We study the classical thermodynamics of a 1+1-dimensional double-well
sinh-Gordon theory. Remarkably, the Schrodinger-like equation resulting from
the transfer integral method is quasi-exactly solvable at several temperatures.
This allows exact calculation of the partition function and some correlation
functions above and below the short-range order (``kink'') transition, in
striking agreement with high resolution Langevin simulations. Interesting
connections with the Landau-Ginzburg and double sine-Gordon models are also
established.Comment: 4 pages, 3 figures (embedded using epsf), uses RevTeX plus macro
(included). Minor revision to match journal version, Phys. Rev. Lett. (in
press
Resonant tunneling in a schematic model
Tunneling of an harmonically bound two-body system through an external
Gaussian barrier is studied in a schematic model which allows for a better
understanding of intricate quantum phenomena. The role of finite size and
internal structure is investigated in a consistent treatment. The excitation of
internal degrees of freedom gives rise to a peaked structure in the penetration
factor. The model results indicate that for soft systems the adiabatic limit is
not necessarily reached although often assumed in fusion of nuclei and in
electron screening effects at astrophysical energies.Comment: 7 pages, 7 figure
Quantum tunneling on graphs
We explore the tunneling behavior of a quantum particle on a finite graph, in
the presence of an asymptotically large potential. Surprisingly the behavior is
governed by the local symmetry of the graph around the wells.Comment: 18 page
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