337 research outputs found
A QES Band-Structure Problem in One Dimension
I show that the potential V(x,m) = \big [\frac{b^2}{4}-m(1-m)a(a+1) \big
]\frac{\sn^2 (x,m)}{\dn^2 (x,m)} -b(a+{1/2}) \frac{\cn (x,m)}{\dn^2 (x,m)}
constitutes a QES band-structure problem in one dimension. In particular, I
show that for any positive integral or half-integral , band edge
eigenvalues and eigenfunctions can be obtained analytically. In the limit of m
going to 0 or 1, I recover the well known results for the QES double
sine-Gordon or double sinh-Gordon equations respectively. As a by product, I
also obtain the boundstate eigenvalues and eigenfunctions of the potential
V(x) = \big [\frac{\beta^2}{4}-a(a+1) \big ] \sech^2 x +\beta(a+{1/2})\sech
x\tanh x in case is any positive integer or half-integer.Comment: some corrections made, title slightly change
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
A General Approach of Quasi-Exactly Solvable Schroedinger Equations
We construct a general algorithm generating the analytic eigenfunctions as
well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians.
Both exact and quasi-exact Hamiltonians enter our formalism but we focus on
quasi-exact interactions for which no such general approach has been considered
before. In particular we concentrate on a generalized sextic oscillator but
also on the Lame and the screened Coulomb potentials.Comment: 23 pages, no figur
Quasi-Exactly Solvable Potentials with Two Known Eigenstates
A new supersymmetry method for the generation of the quasi-exactly solvable
(QES) potentials with two known eigenstates is proposed. Using this method we
obtained new QES potentials for which we found in explicit form the energy
levels and wave functions of the ground state and first excited state.Comment: 13 pages, Latex, replaced by revised versio
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
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
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
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
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