13,598 research outputs found
The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
In this Letter we show that an arbitrarily good approximation to the
propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may
be obtained with polynomial computational resources in n and the error
\epsilon, and exponential resources in |t|. Our proof makes use of the finitely
correlated state/matrix product state formalism exploited by numerical
renormalisation group algorithms like the density matrix renormalisation group.
There are two immediate consequences of this result. The first is that the
Vidal's time-dependent density matrix renormalisation group will require only
polynomial resources to simulate 1D quantum spin systems for logarithmic |t|.
The second consequence is that continuous-time 1D quantum circuits with
logarithmic |t| can be simulated efficiently on a classical computer, despite
the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen
Entanglement, quantum phase transitions, and density matrix renormalization
We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying
remark
Discrimination of low-frequency tones employs temporal fine structure
An auditory neuron can preserve the temporal fine structure of a
low-frequency tone by phase-locking its response to the stimulus. Apart from
sound localization, however, little is known about the role of this temporal
information for signal processing in the brain. Through psychoacoustic studies
we provide direct evidence that humans employ temporal fine structure to
discriminate between frequencies. To this end we construct tones that are based
on a single frequency but in which, through the concatenation of wavelets, the
phase changes randomly every few cycles. We then test the frequency
discrimination of these phase-changing tones, of control tones without phase
changes, and of short tones that consist of a single wavelets. For carrier
frequencies below a few kilohertz we find that phase changes systematically
worsen frequency discrimination. No such effect appears for higher carrier
frequencies at which temporal information is not available in the central
auditory system.Comment: 12 pages, 3 figure
Nonlocality with less Complementarity
In quantum mechanics, nonlocality (a violation of a Bell inequality) is
intimately linked to complementarity, by which we mean that consistently
assigning values to different observables at the same time is not possible.
Nonlocality can only occur when some of the relevant observables do not
commute, and this noncommutativity makes the observables complementary. Beyond
quantum mechanics, the concept of complementarity can be formalized in several
distinct ways. Here we describe some of these possible formalizations and ask
how they relate to nonlocality. We partially answer this question by describing
two toy theories which display nonlocality and obey the no-signaling principle,
although each of them does not display a certain kind of complementarity. The
first toy theory has the property that it maximally violates the CHSH
inequality, although the corresponding local observables are pairwise jointly
measurable. The second toy theory also maximally violates the CHSH inequality,
although its state space is classical and all measurements are mutually
nondisturbing: if a measurement sequence contains some measurement twice with
any number of other measurements in between, then these two measurements give
the same outcome with certainty.Comment: 6 pages, published versio
Dual contribution to amplification in the mammalian inner ear
The inner ear achieves a wide dynamic range of responsiveness by mechanically
amplifying weak sounds. The enormous mechanical gain reported for the mammalian
cochlea, which exceeds a factor of 4,000, poses a challenge for theory. Here we
show how such a large gain can result from an interaction between amplification
by low-gain hair bundles and a pressure wave: hair bundles can amplify both
their displacement per locally applied pressure and the pressure wave itself. A
recently proposed ratchet mechanism, in which hair-bundle forces do not feed
back on the pressure wave, delineates the two effects. Our analytical
calculations with a WKB approximation agree with numerical solutions.Comment: 4 pages, 4 figure
Observations by human subjects on radiation- induced light flashes in fast-neutron, X-ray, and positive-pion beams
Exposure of human subjects to fast neutron beam to determine cause of light flashes observed by astronauts on lunar mission
Information geometric approach to the renormalisation group
We propose a general formulation of the renormalisation group as a family of
quantum channels which connect the microscopic physical world to the observable
world at some scale. By endowing the set of quantum states with an
operationally motivated information geometry, we induce the space of
Hamiltonians with a corresponding metric geometry. The resulting structure
allows one to quantify information loss along RG flows in terms of the
distinguishability of thermal states. In particular, we introduce a family of
functions, expressible in terms of two-point correlation functions, which are
non increasing along the flow. Among those, we study the speed of the flow, and
its generalization to infinite lattices.Comment: Accepted in Phys. Rev.
The dynamics and excitation of torsional waves in geodynamo simulations
The predominant force balance in rapidly rotating planetary cores is between Coriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balance leads to a Taylor state where the spatially averaged azimuthal Lorentz force is compelled to vanish on cylinders aligned with the rotation axis. Any deviation from this state leads to a torsional oscillation, signatures of which have been observed in the Earth's secular variation and are thought to influence length of day variations via angular momentum conservation. In order to investigate the dynamics of torsional oscillations (TOs), we perform several 3-D dynamo simulations in a spherical shell. We find TOs, identified by their propagation at the correct Alfvén speed, in many of our simulations. We find that the frequency, location and direction of propagation of the waves are influenced by the choice of parameters. Torsional waves are observed within the tangent cylinder and also have the ability to pass through it. Several of our simulations display waves with core traveltimes of 4–6 yr. We calculate the driving terms for these waves and find that both the Reynolds force and ageostrophic convection acting through the Lorentz force are important in driving TOs
Bounds on Information Propagation in Disordered Quantum Spin Chains
We investigate the propagation of information through the disordered XY
model. We find, with a probability that increases with the size of the system,
that all correlations, both classical and quantum, are suppressed outside of an
effective lightcone whose radius grows at most polylogarithmically with |t|.Comment: 4 pages, pdflatex, 1 pdf figure. Corrected the bound for the
localised propagator and quantified the probability it bound occur
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