6,796 research outputs found
On the existence of a gap in the energy spectrum of quantum systems
A theorem on the existence of a gap in the energy spectrum of quantum systems, the exact ground state of which is known explicitly, is proved. The theorem is applied to a three-dimensional Heisenberg spin-1/2 ferromagnet, with anisotropic nearest-neighbour interactions, and to an alternating Heisenberg antiferromagnet, with nearest- and next-nearest-neighbour interactions
Exact ground states for a class of linear quantum spin systems
The singlet pair state (S.P.S.) is shown to be the exact ground state for a class of linear quantum spin systems with anisotropic interactions
Competitive forms of symmetry breaking in linear antiferromagnetic systems
Two different forms of symmetry breaking are considered for linear antiferromagnetic systems (S = 1/2 ). Their relative stability is examined by considering small fluctuations in the harmonic oscillator approximation. Imaginary frequencies correspond with an unstable phase, and the ground state represents an absolute minimum of the total energy, including contributions from the zero-point fluctuations
Some exact excited states in a linear antiferromagnetic spin system
Exact expressions are derived for some excited states in a linear quantum spin system for which the exact ground state has been studied in the last decade
An analogue of the Magnus problem for associative algebras
We prove an analogue of the Magnus theorem for associative algebras without
unity over arbitrary fields. Namely, if an algebra is given by n+k generators
and k relations and has an n-element system of generators, then this algebra is
a free algebra of rank n
The Majumdar-Ghosh chain. Twofold ground state and elementary excitations
Recently it was proved that the Majumdar-Ghosh chain with the Hamiltonian H=4 Sigma j=12NSj.Sj+1+2 Sigma j=12N Sj.Sj+2, Si+2N identical to Si, Si=1/2, has at least two ground states, in which the spins are arranged in nearest-neighbour singlet pairs. In this work it is shown that these two states are the only ground states. Besides, a rapidly converging variational method is given to determine the elementary excitation
Numerical Calculation of Bessel Functions
A new computational procedure is offered to provide simple, accurate and
flexible methods for using modern computers to give numerical evaluations of
the various Bessel functions. The Trapezoidal Rule, applied to suitable
integral representations, may become the method of choice for evaluation of the
many Special Functions of mathematical physics.Comment: 10 page
Calculation of Superdiffusion for the Chirikov-Taylor Model
It is widely known that the paradigmatic Chirikov-Taylor model presents
enhanced diffusion for specific intervals of its stochasticity parameter due to
islands of stability, which are elliptic orbits surrounding accelerator mode
fixed points. In contrast with normal diffusion, its effect has never been
analytically calculated. Here, we introduce a differential form for the
Perron-Frobenius evolution operator in which normal diffusion and
superdiffusion are treated separately through phases formed by angular wave
numbers. The superdiffusion coefficient is then calculated analytically
resulting in a Schloemilch series with an exponent for the
divergences. Numerical simulations support our results.Comment: 4 pages, 2 figures (revised version
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
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