983 research outputs found
Ground state and low excitations of an integrable chain with alternating spins
An anisotropic integrable spin chain, consisting of spins and
, is investigated \cite{devega}. It is characterized by two real
parameters and , the coupling constants of the spin
interactions. For the case and the ground state
configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore
the low excitations are calculated. It turns out, that apart from free magnon
states being the holes in the ground state rapidity distribution, there exist
bound states given by special string solutions of Bethe ansatz equations (BAE)
in analogy to \cite{babelon}. The dispersion law of these excitations is
calculated numerically.Comment: 16 pages, LaTeX, uses ioplppt.sty and PicTeX macro
Effects related to spacetime foam in particle physics
It is found that the existence of spacetime foam leads to a situation in
which the number of fundamental quantum bosonic fields is a variable quantity.
The general aspects of an exact theory that allows for a variable number of
fields are discussed, and the simplest observable effects generated by the foam
are estimated. It is shown that in the absence of processes related to
variations in the topology of space, the concept of an effective field can be
reintroduced and standard field theory can be restored. However, in the
complete theory the ground state is characterized by a nonvanishing particle
number density. From the effective-field standpoint, such particles are "dark".
It is assumed that they comprise dark matter of the universe. The properties of
this dark matter are discussed, and so is the possibility of measuring the
quantum fluctuation in the field potentials.Comment: 18 pages, minor corrections added to the published varian
Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
We report on the experimental study of an exceptional point (EP) in a
dissipative microwave billiard with induced time-reversal invariance (T)
violation. The associated two-state Hamiltonian is non-Hermitian and
non-symmetric. It is determined experimentally on a narrow grid in a parameter
plane around the EP. At the EP the size of T violation is given by the relative
phase of the eigenvector components. The eigenvectors are adiabatically
transported around the EP, whereupon they gather geometric phases and in
addition geometric amplitudes different from unity
Rotating saddle trap as Foucault's pendulum
One of the many surprising results found in the mechanics of rotating systems
is the stabilization of a particle in a rapidly rotating planar saddle
potential. Besides the counterintuitive stabilization, an unexpected
precessional motion is observed. In this note we show that this precession is
due to a Coriolis-like force caused by the rotation of the potential. To our
knowledge this is the first example where such force arises in an inertial
reference frame. We also propose an idea of a simple mechanical demonstration
of this effect.Comment: 13 pages, 9 figure
Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field
We show that in multidimensional gravity vector fields completely determine
the structure and properties of singularity. It turns out that in the presence
of a vector field the oscillatory regime exists in all spatial dimensions and
for all homogeneous models. By analyzing the Hamiltonian equations we derive
the Poincar\'e return map associated to the Kasner indexes and fix the rules
according to which the Kasner vectors rotate. In correspondence to a
4-dimensional space time, the oscillatory regime here constructed overlap the
usual Belinski-Khalatnikov-Liftshitz one.Comment: 9 pages, published on Classical and Quantum Gravit
Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]
Tensor operators in graded representations of Z_{2}-graded Hopf algebras are
defined and their elementary properties are derived. Wigner-Eckart theorem for
irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of
tensor operators in the irreducible representation space of Hopf algebra
U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the
irreducible tensor operators are calculated. A construction of some elements of
the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late
Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition
We consider the classical response of a strongly chaotic Hamiltonian system.
The spectrum of such a system consists of discrete complex Ruelle-Pollicott
(RP) resonances which manifest themselves in the behavior of the correlation
and response functions. We interpret the RP resonances as the eigenstates and
eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal
noise term to the first-order Liouville operator. We demonstrate how the
deterministic expression for the linear response is reproduced in the limit of
vanishing noise. For the second-order response we establish an equivalence of
the spectral decomposition with infinitesimal noise and the long-time
asymptotic expansion for the deterministic case.Comment: 16 pages, 1 figur
Integrability of a t-J model with impurities
A t-J model for correlated electrons with impurities is proposed. The
impurities are introduced in such a way that integrability of the model in one
dimension is not violated. The algebraic Bethe ansatz solution of the model is
also given and it is shown that the Bethe states are highest weight states with
respect to the supersymmetry algebra gl(2/1)Comment: 14 page
The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
We prove that the extended Poincare group in (1+1) dimensions is
non-nilpotent solvable exponential, and therefore that it belongs to type I. We
determine its first and second cohomology groups in order to work out a
classification of the two-dimensional relativistic elementary systems.
Moreover, all irreducible unitary representations of the extended Poincare
group are constructed by the orbit method. The most physically interesting
class of irreducible representations corresponds to the anomaly-free
relativistic particle in (1+1) dimensions, which cannot be fully quantized.
However, we show that the corresponding coadjoint orbit of the extended
Poincare group determines a covariant maximal polynomial quantization by
unbounded operators, which is enough to ensure that the associated quantum
dynamical problem can be consistently solved, thus providing a physical
interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published
in J. Math. Phys. 45, 1156 (2004
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