16,085 research outputs found
Solution to the Equations of the Moment Expansions
We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach
Multiphoton entanglement through a Bell multiport beam splitter
Multiphoton entanglement is an important resource for linear optics quantum
computing. Here we show that a wide range of highly entangled multiphoton
states, including W-states, can be prepared by interfering single photons
inside a Bell multiport beam splitter and using postselection. A successful
state preparation is indicated by the collection of one photon per output port.
An advantage of the Bell multiport beam splitter is that it redirects the
photons without changing their inner degrees of freedom. The described setup
can therefore be used to generate polarisation, time-bin and frequency
multiphoton entanglement, even when using only a single photon source.Comment: 8 pages, 2 figures, carefully revised version, references adde
Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps
We study the stability of the fixed-point solution of an array of mutually
coupled logistic maps, focusing on the influence of the delay times,
, of the interaction between the th and th maps. Two of us
recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if
are random enough the array synchronizes in a spatially homogeneous
steady state. Here we study this behavior by comparing the dynamics of a map of
an array of delayed-coupled maps with the dynamics of a map with
self-feedback delayed loops. If is sufficiently large, the dynamics of a
map of the array is similar to the dynamics of a map with self-feedback loops
with the same delay times. Several delayed loops stabilize the fixed point,
when the delays are not the same; however, the distribution of delays plays a
key role: if the delays are all odd a periodic orbit (and not the fixed point)
is stabilized. We present a linear stability analysis and apply some
mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion,
figures, and references added
Classical and quantum fingerprinting with shared randomness and one-sided error
Within the simultaneous message passing model of communication complexity,
under a public-coin assumption, we derive the minimum achievable worst-case
error probability of a classical fingerprinting protocol with one-sided error.
We then present entanglement-assisted quantum fingerprinting protocols
attaining worst-case error probabilities that breach this bound.Comment: 10 pages, 1 figur
Quantum quench dynamics of the Bose-Hubbard model at finite temperatures
We study quench dynamics of the Bose-Hubbard model by exact diagonalization.
Initially the system is at thermal equilibrium and of a finite temperature. The
system is then quenched by changing the on-site interaction strength
suddenly. Both the single-quench and double-quench scenarios are considered. In
the former case, the time-averaged density matrix and the real-time evolution
are investigated. It is found that though the system thermalizes only in a very
narrow range of the quenched value of , it does equilibrate or relax well in
a much larger range. Most importantly, it is proven that this is guaranteed for
some typical observables in the thermodynamic limit. In order to test whether
it is possible to distinguish the unitarily evolving density matrix from the
time-averaged (thus time-independent), fully decoherenced density matrix, a
second quench is considered. It turns out that the answer is affirmative or
negative according to the intermediate value of is zero or not.Comment: preprint, 20 pages, 7 figure
Heat capacity of the quantum magnet TiOCl
Measurements of the heat capacity C(T,H) of the one-dimensional quantum
magnet TiOCl are presented for temperatures 2K < T < 300K and magnetic fields
up to 5T. Distinct anomalies at 91K and 67K signal two subsequent phase
transitions. The lower of these transitions clearly is of first order and seems
to be related to the spin degrees of freedom. The transition at 92K probably
involves the lattice and/or orbital moments. A detailed analysis of the data
reveals that the entropy change through both transitions is surprisingly small
(~ 0.1R), pointing to the existence strong fluctuations well into the
non-ordered high-temperature phase. No significant magnetic field dependence
was detected.Comment: 4 pages, 2 figure
Quantum equilibration in finite time
It has recently been shown that small quantum subsystems generically
equilibrate, in the sense that they spend most of the time close to a fixed
equilibrium state. This relies on just two assumptions: that the state is
spread over many different energies, and that the Hamiltonian has
non-degenerate energy gaps. Given the same assumptions, it has also been shown
that closed systems equilibrate with respect to realistic measurements. We
extend these results in two important ways. First, we prove equilibration over
a finite (rather than infinite) time-interval, allowing us to bound the
equilibration time. Second, we weaken the non degenerate energy gaps condition,
showing that equilibration occurs provided that no energy gap is hugely
degenerate.Comment: 7 page
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