8,475 research outputs found
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
Bethe Ansatz approach to quench dynamics in the Richardson model
By instantaneously changing a global parameter in an extended quantum system,
an initially equilibrated state will afterwards undergo a complex
non-equilibrium unitary evolution whose description is extremely challenging. A
non-perturbative method giving a controlled error in the long time limit
remained highly desirable to understand general features of the quench induced
quantum dynamics. In this paper we show how integrability (via the algebraic
Bethe ansatz) gives one numerical access, in a nearly exact manner, to the
dynamics resulting from a global interaction quench of an ensemble of fermions
with pairing interactions (Richardson's model). This possibility is deeply
linked to the specific structure of this particular integrable model which
gives simple expressions for the scalar product of eigenstates of two different
Hamiltonians. We show how, despite the fact that a sudden quench can create
excitations at any frequency, a drastic truncation of the Hilbert space can be
carried out therefore allowing access to large systems. The small truncation
error which results does not change with time and consequently the method
grants access to a controlled description of the long time behavior which is a
hard to reach limit with other numerical approaches.Comment: Proceedings of the CRM (Montreal) workshop on Integrable Quantum
Systems and Solvable Statistical Mechanics Model
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.
Dynamical correlation functions of the mesoscopic pairing model
We study the dynamical correlation functions of the Richardson pairing model
(also known as the reduced or discrete-state BCS model) in the canonical
ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact
expressions for the form factors of the most important observables. By summing
these form factors over a relevant set of states, we obtain very precise
estimates of the correlation functions, as confirmed by global sum-rules
(saturation above 99% in all cases considered). Unlike the case of many other
Bethe Ansatz solvable theories, simple two-particle states are sufficient to
achieve such saturations, even in the thermodynamic limit. We provide explicit
results at half-filling, and discuss their finite-size scaling behavior
Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
The Kondo-necklace model can describe magnetic low-energy limit of strongly
correlated heavy fermion materials. There exist multiple energy scales in this
model corresponding to each phase of the system. Here, we study quantum phase
transition between the Kondo-singlet phase and the antiferromagnetic long-range
ordered phase, and show the effect of anisotropies in terms of quantum
information properties and vanishing energy gap. We employ the "perturbative
continuous unitary transformations" approach to calculate the energy gap and
spin-spin correlations for the model in the thermodynamic limit of one, two,
and three spatial dimensions as well as for spin ladders. In particular, we
show that the method, although being perturbative, can predict the expected
quantum critical point, where the gap of low-energy spectrum vanishes, which is
in good agreement with results of other numerical and Green's function
analyses. In addition, we employ concurrence, a bipartite entanglement measure,
to study the criticality of the model. Absence of singularities in the
derivative of concurrence in two and three dimensions in the Kondo-necklace
model shows that this model features multipartite entanglement. We also discuss
crossover from the one-dimensional to the two-dimensional model via the ladder
structure.Comment: 12 pages, 6 figure
Dynamical density-density correlations in the one-dimensional Bose gas
The zero-temperature dynamical structure factor of the one-dimensional Bose
gas with delta-function interaction (Lieb-Liniger model) is computed using a
hybrid theoretical/numerical method based on the exact Bethe Ansatz solution,
which allows to interpolate continuously between the weakly-coupled
Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should
be experimentally accessible with Bragg spectroscopy.Comment: 4 pages, 3 figures, published versio
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
We study the time evolution of quantum one-dimensional gapless systems
evolving from initial states with a domain-wall. We generalize the
path-integral imaginary time approach that together with boundary conformal
field theory allows to derive the time and space dependence of general
correlation functions. The latter are explicitly obtained for the Ising
universality class, and the typical behavior of one- and two-point functions is
derived for the general case. Possible connections with the stochastic Loewner
evolution are discussed and explicit results for one-point time dependent
averages are obtained for generic \kappa for boundary conditions corresponding
to SLE. We use this set of results to predict the time evolution of the
entanglement entropy and obtain the universal constant shift due to the
presence of a domain wall in the initial state.Comment: 27 pages, 10 figure
Thermodynamic entropy of a many body energy eigenstate
It is argued that a typical many body energy eigenstate has a well defined
thermodynamic entropy and that individual eigenstates possess thermodynamic
characteristics analogous to those of generic isolated systems. We examine
large systems with eigenstate energies equivalent to finite temperatures. When
quasi-static evolution of a system is adiabatic (in the quantum mechanical
sense), two coupled subsystems can transfer heat from one subsystem to another
yet remain in an energy eigenstate. To explicitly construct the entropy from
the wave function, degrees of freedom are divided into two unequal parts. It is
argued that the entanglement entropy between these two subsystems is the
thermodynamic entropy per degree of freedom for the smaller subsystem. This is
done by tracing over the larger subsystem to obtain a density matrix, and
calculating the diagonal and off-diagonal contributions to the entanglement
entropy.Comment: 18 page
Zero dimensional area law in a gapless fermion system
The entanglement entropy of a gapless fermion subsystem coupled to a gapless
bulk by a "weak link" is considered. It is demonstrated numerically that each
independent weak link contributes an entropy proportional to lnL, where L is
linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio
Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
The critical thermodynamics of the two-dimensional N-vector cubic and MN
models is studied within the field-theoretical renormalization-group (RG)
approach. The beta functions and critical exponents are calculated in the
five-loop approximation and the RG series obtained are resummed using the
Borel-Leroy transformation combined with the generalized Pad\'e approximant and
conformal mapping techniques. For the cubic model, the RG flows for various N
are investigated. For N=2 it is found that the continuous line of fixed points
running from the XY fixed point to the Ising one is well reproduced by the
resummed RG series and an account for the five-loop terms makes the lines of
zeros of both beta functions closer to each another. For the cubic model with
N\geq 3, the five-loop contributions are shown to shift the cubic fixed point,
given by the four-loop approximation, towards the Ising fixed point. This
confirms the idea that the existence of the cubic fixed point in two dimensions
under N>2 is an artifact of the perturbative analysis. For the quenched dilute
O(M) models ( models with N=0) the results are compatible with a stable
pure fixed point for M\geq1. For the MN model with M,N\geq2 all the
non-perturbative results are reproduced. In addition a new stable fixed point
is found for moderate values of M and N.Comment: 26 pages, 3 figure
- …