299 research outputs found
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
Canonical description of incompressible fluid -- Dirac brackets approach
We present a novel canonical description of the incompressible fluid
dynamics. This description uses the dynamical constraints, in our case
reflecting "incompressibility" assumption, and leads to replacement of usual
hydrodynamical Poisson brackets for density and velocity fields with Dirac
brackets. The resulting equations are then known nonlinear, and non-local in
space, equations for incompressible fluid velocity.Comment: 7 pages, late
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
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