2,625 research outputs found
An exactly solvable many-body problem in one dimension
For N impenetrable particles in one dimension where only the nearest and
next-to-nearest neighbours interact, we obtain the complete spectrum both on a
line and on a circle. Further, we establish a mapping between these N-body
problems and the short-range Dyson model introduced recently to model
intermediate spectral statistics in some systems using which we compute the
two-point correlation function and prove the absence of long-range order in the
corresponding many-body theory. Further, we also show the absence of
off-diagonal long-range order in these systems.Comment: LaTeX, 4 pages, 1 figur
Off-diagonal long-range order in one-dimensional many-body problem
We prove that there is off-diagonal long-range order in the symmetrised
version of the one-dimensional many-body problem presented by Jain and Khare
(Phys. Lett. A262 (1999)35). This model is related to the short-range Dyson
model employed to study intermediate statistics in systems like the Anderson
model in three dimensions at the metal-insulator transition point and
pseudointegrable billiards. To the best of our knowledge, this is the only
example showing quantum phases and possibility of Bose-Einstein condensation in
one-dimensional statistical mechanics.Comment: LaTeX2e, submitted to Phys. Lett.
Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\"odinger Equation with Saturable Nonlinearity
We show that the two-dimensional, nonlinear Schr\"odinger lattice with a
saturable nonlinearity admits periodic and pulse-like exact solutions. We
establish the general formalism for the stability considerations of these
solutions and give examples of stability diagrams. Finally, we show that the
effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero
Affine Toda-Sutherland Systems
A cross between two well-known integrable multi-particle dynamics, an affine
Toda molecule and a Sutherland system, is introduced for any affine root
system. Though it is not completely integrable but partially integrable, or
quasi exactly solvable, it inherits many remarkable properties from the
parents. The equilibrium position is algebraic, i.e. proportional to the Weyl
vector. The frequencies of small oscillations near equilibrium are proportional
to the affine Toda masses, which are essential ingredients of the exact
factorisable S-matrices of affine Toda field theories. Some lower lying
frequencies are integer times a coupling constant for which the corresponding
exact quantum eigenvalues and eigenfunctions are obtained. An affine
Toda-Calogero system, with a corresponding rational potential, is also
discussed.Comment: LaTeX2e 22 pages with amsfonts and graphicx, 5 eps figure
A class of N-body problems with nearest- and next-to-nearest neighbour interactions
We obtain the exact ground state and a part of the excitation spectrum in one
dimension on a line and the exact ground state on a circle in a case where N
particles are interacting via nearest- and next-to-nearest neighbour
interactions. Further, using the exact ground-state, we establish a mapping
between these N-body problems and the short-range Dyson models introduced
recently to model intermediate spectral statistics. Using this mapping we
compute the one- and two-point functions of a related many-body theory and show
that there is no long-range order in the thermodynamic limit. However, quite
remarkably, we prove the existence of an off-diagonal long-range order in the
symmetrised version of the related many-body theory. Generalisation of the
models to other root systems is also considered. Besides, we also generalize
the model on the full line to higher dimensions. Finally, we consider a model
in two dimensions in which all the states exhibit novel correlations.Comment: LaTeX2e, 40 pages, 2 figures, submitted to Nucl. Phys. B [FS
New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
Quantum mechanical potentials satisfying the property of shape invariance are
well known to be algebraically solvable. Using a scaling ansatz for the change
of parameters, we obtain a large class of new shape invariant potentials which
are reflectionless and possess an infinite number of bound states. They can be
viewed as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for energy eigenvalues,
eigenfunctions and transmission coefficients are given. Included in our
potentials as a special case is the self-similar potential recently discussed
by Shabat and Spiridonov.Comment: 8pages, Te
Spin-independent v-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation
Electrons in one-dimension display the unusual property of separating their
spin and charge into two independent entities: The first, which derive from
uncharged spin-1/2 electrons, can travel at different velocities when compared
with the second, built from charged spinless electrons. Predicted theoretically
in the early sixties, the spin-charge separation has attracted renewed
attention since the first evidences of experimental observation, with usual
mentions as a possible explanation for high-temperature superconductivity. In
one-dimensional (1D) model systems, the spin-charge separation leads the
frequencies of Friedel oscillations to suffer a 2k_F -- 4k_F crossover, mainly
when dealing with strong correlations, where they are referred to as Wigner
crystal oscillations. In non-magnetized systems, the current density
functionals which are applied to the 1D Hubbard model are not seen to reproduce
this crossover, referring to a more fundamental question: Are the Wigner
crystal oscillations in 1D systems non-interacting v-representable? Or, is
there a spin-independent Kohn-Sham potential which is able to yield spin-charge
separation? Finding an appropriate answer to both questions is our main task
here. By means of exact and DMRG solutions, as well as, a new approach of
exchange-correlation potential, we show the answer to be positive.
Specifically, the v-representable 4k_F oscillations emerge from attractive
interactions mediated by positively charged spinless holes -- the holons -- as
an additional contribution to the repulsive on-site Hubbard interaction
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