14,084 research outputs found
Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs
We study the impact of the diagonal frustrating couplings on the quantum
phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2
rungs. As the coupling strength is increased the system successively exhibits
two gapped paramagnetic phases (a rung-singlet and a Haldane-like
non-degenerate states) and two ferrimagnetic phases with different
ferromagnetic moments per rung. The first two states are similar to the phases
studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear
as a result of the mixed-spin structure of the model. A detailed
characterization of these phases is presented using density-matrix
renormalization-group calculations, exact diagonalizations of periodic
clusters, and an effective Hamiltonian approach inspired by the analysis of
numerical data. The present theoretical study was motivated by the recent
synthesis of the quasi-one-dimensional ferrimagnetic material
FeFe (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar
ladder structure.Comment: 10 pages, 8 figure
A Poincar\'e section for the general heavy rigid body
A general recipe is developed for the study of rigid body dynamics in terms
of Poincar\'e surfaces of section. A section condition is chosen which captures
every trajectory on a given energy surface. The possible topological types of
the corresponding surfaces of section are determined, and their 1:1 projection
to a conveniently defined torus is proposed for graphical rendering.Comment: 25 pages, 10 figure
Ehrenfest-time dependence of counting statistics for chaotic ballistic systems
Transport properties of open chaotic ballistic systems and their statistics
can be expressed in terms of the scattering matrix connecting incoming and
outgoing wavefunctions. Here we calculate the dependence of correlation
functions of arbitrarily many pairs of scattering matrices at different
energies on the Ehrenfest time using trajectory based semiclassical methods.
This enables us to verify the prediction from effective random matrix theory
that one part of the correlation function obtains an exponential damping
depending on the Ehrenfest time, while also allowing us to obtain the
additional contribution which arises from bands of always correlated
trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for
secondary gaps in the density of states of Andreev billiards, can also be seen
to have strong effects on other transport quantities like the distribution of
delay times.Comment: Refereed version. 15 pages, 14 figure
Improved bounds for the crossing numbers of K_m,n and K_n
It has been long--conjectured that the crossing number cr(K_m,n) of the
complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):=
floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing
conjecture states that the crossing number cr(K_n) of the complete graph K_n
equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In
this paper we show the following improved bounds on the asymptotic ratios of
these crossing numbers and their conjectured values:
(i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1);
(ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and
(iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83.
The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8,
respectively. These improved bounds are obtained as a consequence of the new
bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for
cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to
set up a quadratic program on 6! variables whose minimum p satisfies
cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic
optimization techniques combined with a bit of invariant theory of permutation
groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure
Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice
We study the ground state of a spin-half Heisenberg antiferromagnet on the
stacked kagome lattice by using a spin-rotation-invariant Green's-function
method. Since the pure two-dimensional kagome antiferromagnet is most likely a
magnetically disordered quantum spin liquid, we investigate the question
whether the coupling of kagome layers in a stacked three-dimensional system may
lead to a magnetically ordered ground state. We present spin-spin correlation
functions and correlation lengths. For comparison we apply also linear spin
wave theory. Our results provide strong evidence that the system remains
short-range ordered independent of the sign and the strength of the interlayer
coupling
Phase--coherence Effects in Antidot Lattices: A Semiclassical Approach to Bulk Conductivity
We derive semiclassical expressions for the Kubo conductivity tensor. Within
our approach the oscillatory parts of the diagonal and Hall conductivity are
given as sums over contributions from classical periodic orbits in close
relation to Gutzwiller's trace formula for the density of states. Taking into
account the effects of weak disorder and temperature we reproduce recently
observed anomalous phase coherence oscillations in the conductivity of large
antidot arrays.Comment: 11 pages, 2 figures available under request, RevTe
From clean to diffusive mesoscopic systems: A semiclassical approach to the magnetic susceptibility
We study disorder-induced spectral correlations and their effect on the
magnetic susceptibility of mesoscopic quantum systems in the non-diffusive
regime. By combining a diagrammatic perturbative approach with semiclassical
techniques we perform impurity averaging for non-translational invariant
systems. This allows us to study the crossover from clean to diffusive systems.
As an application we consider the susceptibility of non-interacting electrons
in a ballistic microstructure in the presence of weak disorder. We present
numerical results for a square billiard and approximate analytic results for
generic chaotic geometries. We show that for the elastic mean free path
larger than the system size, there are two distinct regimes of behaviour
depending on the relative magnitudes of and an inelastic scattering
length.Comment: 7 pages, Latex-type, EuroMacr, 4 Postscript figures, to appear in
Europhys. Lett. 199
Investigation of the Spin-Peierls transition in CuGeO_3 by Raman scattering
Raman experiments on the spin-Peierls compound CuGeO and the substituted
(Cu,Zn)GeO and Cu(Ge,Ga)O compounds were
performed in order to investigate the response of specific magnetic excitations
of the one-dimensional spin-1/2 chain to spin anisotropies and
substitution-induced disorder. In pure CuGeO, in addition to normal phonon
scattering which is not affected at all by the spin-Peierls transition, four
types of magnetic scattering features were observed. Below T=14 K a
singlet-triplet excitation at 30 cm, two-magnon scattering from 30 to
227 cm and folded phonon modes at 369 and 819 cm were identified.
They were assigned by their temperature dependence and lineshape. For
temperatures between the spin-Peierls transition T and approximately 100
K a broad intensity maximum centered at 300 cm is observed.Comment: 7 pages, LaTex2e, including 3 figures (eps) to be published in
Physica B (1996
Quantum Corrections to Fidelity Decay in Chaotic Systems
By considering correlations between classical orbits we derive semiclassical
expressions for the decay of the quantum fidelity amplitude for classically
chaotic quantum systems, as well as for its squared modulus, the fidelity or
Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with
random matrix theory (RMT) and supersymmetry predictions in the universal Fermi
golden rule regime. The calculated quantum corrections can be viewed as arising
from a static random perturbation acting on nearly self-retracing interfering
paths, and hence will be suppressed for time-varying perturbations. Moreover,
using trajectory-based methods we show a relation, recently obtained in RMT,
between the fidelity amplitude and the cross-form factor for parametric level
correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity
amplitude. Furthermore our semiclassical approach allows for a unified
treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes,
demonstrating that quantum corrections are suppressed in the latter.Comment: 14 pages, 4 figure
Observation of a Chiral State in a Microwave Cavity
A microwave experiment has been realized to measure the phase difference of
the oscillating electric field at two points inside the cavity. The technique
has been applied to a dissipative resonator which exhibits a singularity --
called exceptional point -- in its eigenvalue and eigenvector spectrum. At the
singularity, two modes coalesce with a phase difference of We
conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure
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