12,181 research outputs found
Entanglement renormalization
In the context of real-space renormalization group methods, we propose a
novel scheme for quantum systems defined on a D-dimensional lattice. It is
based on a coarse-graining transformation that attempts to reduce the amount of
entanglement of a block of lattice sites before truncating its Hilbert space.
Numerical simulations involving the ground state of a 1D system at criticality
show that the resulting coarse-grained site requires a Hilbert space dimension
that does not grow with successive rescaling transformations. As a result we
can address, in a quasi-exact way, tens of thousands of quantum spins with a
computational effort that scales logarithmically in the system's size. The
calculations unveil that ground state entanglement in extended quantum systems
is organized in layers corresponding to different length scales. At a quantum
critical point, each rellevant length scale makes an equivalent contribution to
the entanglement of a block with the rest of the system.Comment: 4 pages, 4 figures, updated versio
"Hidden” degassing from streams: estimation of the CO2 release from the thermal springs of Sperchios Basin, Greece
Areas located at plate boundaries are characterized by the presence of seismic, volcanic, and geothermal activity, as well as ore deposition. Such processes are enhanced by the circulation of hydrothermal fluids in the crust transporting volatiles from either the deep crust or the mantle to the surface. Intense geodynamic activity is also taking place in Greece giving rise to: (i) the highest seismicity in Europe, (ii) the presence of an active volcanic arc and numerous areas of anomalously high geothermal gradient, and (iii) a widespread occurrence of thermal springs. Elevated heat flow values are concentrated in Sperchios basin, an area characterised by a system of deeply rooted extensional faults and quaternary volcanic activity. This regime favoured the formation of hydrothermal systems, the surface expression of which are thermal springs with intense bubbling of CO2-rich gases. Flux measurements in the bubbling pools were made with the floating chamber method. The highest bubbling CO2 output is found in Thermopyles and Psoroneria (1 and 2 t/d, respectively). The outgoing channels of these springs have an elevated flow (>250 l/s) of gas-charged water (>15 mmol/l of CO2). Although no bubbling is noticed along the stream, the CO2 content decreases by an order of magnitude after few hundreds of metres, indicating an intense degassing from the water. Taking into account the water flow and the amount of CO2 lost to the atmosphere, the CO2 output of the outgoing channels is quantified in >10 t/d for Thermopyles and 9 t/d for Psoroneria. An estimation is also made at Ypati, Kamena Vourla, Koniavitis and Edipsos, where the mean values reach 1 t/d of CO2 for each spring. The obtained values are always higher respect to the estimated outputs from visible bubbling, suggesting that most of the degassing is “hidden”. Furthermore, the loss of CO2 from the water determines a shift in dissolved carbonate species as demonstrated by the pH increase along the channel that leads eventually to an oversaturation in carbonate minerals and therefore travertine deposition. To sum up, the total CO2 output of the study area is estimated at 30 t/d, with the major contribution deriving from the degassing along the outflow channels of the thermal springs. Such output is comparable to that of the single active volcanic systems along the South Aegean Volcanic Arc (Sousaki, Methana, Milos, Santorini, Kos and Nisyros) and highlights the importance of “hidden” degassing along CO2-oversaturated streams
An exact solution for the KPZ equation with flat initial conditions
We provide the first exact calculation of the height distribution at
arbitrary time of the continuum KPZ growth equation in one dimension with
flat initial conditions. We use the mapping onto a directed polymer (DP) with
one end fixed, one free, and the Bethe Ansatz for the replicated attractive
boson model. We obtain the generating function of the moments of the DP
partition sum as a Fredholm Pfaffian. Our formula, valid for all times,
exhibits convergence of the free energy (i.e. KPZ height) distribution to the
GOE Tracy Widom distribution at large time.Comment: 4 pages, no figur
Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations
Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.
Entanglement Entropy in Extended Quantum Systems
After a brief introduction to the concept of entanglement in quantum systems,
I apply these ideas to many-body systems and show that the von Neumann entropy
is an effective way of characterising the entanglement between the degrees of
freedom in different regions of space. Close to a quantum phase transition it
has universal features which serve as a diagnostic of such phenomena. In the
second part I consider the unitary time evolution of such systems following a
`quantum quench' in which a parameter in the hamiltonian is suddenly changed,
and argue that finite regions should effectively thermalise at late times,
after interesting transient effects.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200
Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise
We use the perturbative renormalization group to study classical stochastic
processes with memory. We focus on the generalized Langevin dynamics of the
\phi^4 Ginzburg-Landau model with additive noise, the correlations of which are
local in space but decay as a power-law with exponent \alpha in time. These
correlations are assumed to be due to the coupling to an equilibrium thermal
bath. We study both the equilibrium dynamics at the critical point and quenches
towards it, deriving the corresponding scaling forms and the associated
equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We
show that, while the first two retain their equilibrium values independently of
\alpha, the non-Markovian character of the dynamics affects the dynamic
exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial
dimensionality, N the number of components of the order parameter, and
\alpha_c(x,y) a function which we determine at second order in 4-D. We analyze
the dependence of the asymptotic fluctuation-dissipation ratio on various
parameters, including \alpha. We discuss the implications of our results for
several physical situations
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Time-dependence of correlation functions following a quantum quench
We show that the time-dependence of correlation functions in an extended
quantum system in d dimensions, which is prepared in the ground state of some
hamiltonian and then evolves without dissipation according to some other
hamiltonian, may be extracted using methods of boundary critical phenomena in
d+1 dimensions. For d=1 particularly powerful results are available using
conformal field theory. These are checked against those available from solvable
models. They may be explained in terms of a picture, valid more generally,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate classically through the system.Comment: 4+ pages, Corrected Typo
The Ubiquitous 'c': from the Stefan-Boltzmann Law to Quantum Information
I discuss various aspects of the role of the conformal anomaly number c in 2-
and 1+1-dimensional critical behaviour: its appearance as the analogue of
Stefan's constant, its fundamental role in conformal field theory, in the
classification of 2d universality classes, and as a measure of quantum
entanglement, among other topics.Comment: 8 pages, 2 figures. Boltzmann Medal Lecture, Statphys24, Cairns 2010.
v3: minor revision
Experimental study of vapor-cell magneto-optical traps for efficient trapping of radioactive atoms
We have studied magneto-optical traps (MOTs) for efficient on-line trapping
of radioactive atoms. After discussing a model of the trapping process in a
vapor cell and its efficiency, we present the results of detailed experimental
studies on Rb MOTs. Three spherical cells of different sizes were used. These
cells can be easily replaced, while keeping the rest of the apparatus
unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes
and power of the laser beams, detection system. By direct comparison, we find
that the trapping efficiency only weakly depends on the MOT cell size. It is
also found that the trapping efficiency of the MOT with the smallest cell,
whose diameter is equal to the diameter of the trapping beams, is about 40%
smaller than the efficiency of larger cells. Furthermore, we also demonstrate
the importance of two factors: a long coated tube at the entrance of the MOT
cell, used instead of a diaphragm; and the passivation with an alkali vapor of
the coating on the cell walls, in order to minimize the losses of trappable
atoms. These results guided us in the construction of an efficient
large-diameter cell, which has been successfully employed for on-line trapping
of Fr isotopes at INFN's national laboratories in Legnaro, Italy.Comment: 9 pages, 7 figures, submitted to Eur. Phys. J.
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