TY - UNPB

T1 - A nonlinear quantum dynamical system of spin 1/2 particles based on the classical Sine-Gordon Equation

AU - Zarmi, Yair

PY - 2012/10/1

Y1 - 2012/10/1

N2 - The Hirota transformation for the soliton solutions of the classical
Sine-Gordon equation is suggestive of an extremely simple way for the
construction of a nonlinear quantum-dynamical system of spin 1/2
particles that is equivalent to the classical system over the soliton
sector. The soliton solution of the classical equation is mapped onto an
operator, U, a nonlinear functional of the particle-number operators,
that solves the classical equation. Multi-particle states in the Fock
space are the eigenstates of U; the eigenvalues are the soliton
solutions of the Sine-Gordon equation. The fact that solitons can have
positive as well negative velocities is reflected by the
characterization of particles in the Fock space by two quantum numbers:
a wave number k, and a spin projection, {\sigma} (= +-1). Thanks to the
simplicity of the construction, incorporation of particle interactions,
which induce soliton effects that do not have a classical analog, is
simple.

AB - The Hirota transformation for the soliton solutions of the classical
Sine-Gordon equation is suggestive of an extremely simple way for the
construction of a nonlinear quantum-dynamical system of spin 1/2
particles that is equivalent to the classical system over the soliton
sector. The soliton solution of the classical equation is mapped onto an
operator, U, a nonlinear functional of the particle-number operators,
that solves the classical equation. Multi-particle states in the Fock
space are the eigenstates of U; the eigenvalues are the soliton
solutions of the Sine-Gordon equation. The fact that solitons can have
positive as well negative velocities is reflected by the
characterization of particles in the Fock space by two quantum numbers:
a wave number k, and a spin projection, {\sigma} (= +-1). Thanks to the
simplicity of the construction, incorporation of particle interactions,
which induce soliton effects that do not have a classical analog, is
simple.

KW - Nonlinear Sciences - Exactly Solvable and Integrable Systems

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BT - A nonlinear quantum dynamical system of spin 1/2 particles based on the classical Sine-Gordon Equation

ER -