5,645 research outputs found
Quantum XY criticality in a two-dimensional Bose gas near the Mott transition
We derive the equation of state of a two-dimensional Bose gas in an optical
lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of
the multicritical points where the quantum phase transition between the Mott
insulator and the superfluid phase occurs at fixed density and belongs to the
three-dimensional XY model universality class. Using a nonperturbative
renormalization-group approach, we compute the pressure as a
function of chemical potential and temperature. Our results compare favorably
with a calculation based on the quantum O(2) model -- we find the same
universal scaling function -- and allow us to determine the region of the phase
diagram in the vicinity of a quantum multicritical point where the equation of
state is universal. We also discuss the possible experimental observation of
quantum XY criticality in a ultracold gas in an optical lattice.Comment: v1) 6 pages, 4 figures. v2) Revised versio
Quantum criticality of a Bose gas in an optical lattice near the Mott transition
We derive the equation of state of bosons in an optical lattice in the
framework of the Bose-Hubbard model. Near the density-driven Mott transition,
the expression of the pressure P({\mu},T) versus chemical potential and
temperature is similar to that of a dilute Bose gas but with renormalized mass
m^* and scattering length a^*. m^* is the mass of the elementary excitations at
the quantum critical point governing the transition from the superfluid phase
to the Mott insulating phase, while a^* is related to their effective
interaction at low energy. We use a nonperturbative renormalization-group
approach to compute these parameters as a function of the ratio t/U between
hopping amplitude and on-site repulsion.Comment: v1) 4 pages, 6 figures. v2) Significant rewriting (new title) with
more emphasis on the quantum critical behavior near the Mott transitio
Quantum non-malleability and authentication
In encryption, non-malleability is a highly desirable property: it ensures
that adversaries cannot manipulate the plaintext by acting on the ciphertext.
Ambainis, Bouda and Winter gave a definition of non-malleability for the
encryption of quantum data. In this work, we show that this definition is too
weak, as it allows adversaries to "inject" plaintexts of their choice into the
ciphertext. We give a new definition of quantum non-malleability which resolves
this problem. Our definition is expressed in terms of entropic quantities,
considers stronger adversaries, and does not assume secrecy. Rather, we prove
that quantum non-malleability implies secrecy; this is in stark contrast to the
classical setting, where the two properties are completely independent. For
unitary schemes, our notion of non-malleability is equivalent to encryption
with a two-design (and hence also to the definition of Ambainis et al.). Our
techniques also yield new results regarding the closely-related task of quantum
authentication. We show that "total authentication" (a notion recently proposed
by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant
improvement over the eight-design construction of Garg et al. We also show
that, under a mild adaptation of the rejection procedure, both total
authentication and our notion of non-malleability yield quantum authentication
as defined by Dupuis, Nielsen and Salvail.Comment: 20+13 pages, one figure. v2: published version plus extra material.
v3: references added and update
Dynamics of sliding drops on superhydrophobic surfaces
We use a free energy lattice Boltzmann approach to investigate numerically
the dynamics of drops moving across superhydrophobic surfaces. The surfaces
comprise a regular array of posts small compared to the drop size. For drops
suspended on the posts the velocity increases as the number of posts decreases.
We show that this is because the velocity is primarily determined by the
contact angle which, in turn, depends on the area covered by posts. Collapsed
drops, which fill the interstices between the posts, behave in a very different
way. The posts now impede the drop behaviour and the velocity falls as their
density increases.Comment: 7 pages, 4 figures, accepted for publication in Europhys. Let
Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
We study the thermodynamics of the relativistic quantum O() model in two
space dimensions. In the vicinity of the zero-temperature quantum critical
point (QCP), the pressure can be written in the scaling form
P(T)=P(0)+N(T^3/c^2)\calF_N(\Delta/T) where is the velocity of the
excitations at the QCP and is a characteristic zero-temperature energy
scale. Using both a large- approach to leading order and the nonperturbative
renormalization group, we compute the universal scaling function \calF_N. For
small values of () we find that \calF_N(x) is nonmonotonous
in the quantum critical regime () with a maximum near . The
large- approach -- if properly interpreted -- is a good approximation both
in the renormalized classical () and quantum disordered
() regimes, but fails to describe the nonmonotonous behavior of
\calF_N in the quantum critical regime. We discuss the renormalization-group
flows in the various regimes near the QCP and make the connection with the
quantum nonlinear sigma model in the renormalized classical regime. We compute
the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2)
model and find that in the vicinity of the QCP the universal ratio
\Tkt/\rho_s(0) is very close to , implying that the stiffness
\rho_s(\Tkt^-) at the transition is only slightly reduced with respect to the
zero-temperature stiffness . Finally, we briefly discuss the
experimental determination of the universal function \calF_2 from the
pressure of a Bose gas in an optical lattice near the
superfluid--Mott-insulator transition.Comment: v1) 16 pages, 10 figures. v2) Revised versio
Rheology of cholesteric blue phases
Blue phases of cholesteric liquid crystals offer a spectacular example of
naturally occurring disclination line networks. Here we numerically solve the
hydrodynamic equations of motion to investigate the response of three types of
blue phases to an imposed Poiseuille flow. We show that shear forces bend and
twist and can unzip the disclination lines. Under gentle forcing the network
opposes the flow and the apparent viscosity is significantly higher than that
of an isotropic liquid. With increased forcing we find strong shear thinning
corresponding to the disruption of the defect network. As the viscosity starts
to drop, the imposed flow sets the network into motion. Disclinations break-up
and re-form with their neighbours in the flow direction. This gives rise to
oscillations in the time-dependent measurement of the average stress.Comment: 4 pages, 4 figure
Superconductivity of Quasi-One-Dimensional Electrons in Strong Magnetic Field
The superconductivity of quasi-one-dimensional electrons in the magnetic
field is studied. The system is described as the one-dimensional electrons with
no frustration due to the magnetic field. The interaction is assumed to be
attractive between electrons in the nearest chains, which corresponds to the
lines of nodes of the energy gap in the absence of the magnetic field. The
effective interaction depends on the magnetic field and the transverse
momentum. As the magnetic field becomes strong, the transition temperature of
the spin-triplet superconductivity oscillates, while that of the spin-singlet
increases monotonically.Comment: 15 pages, RevTeX, 3 PostScript figures in uuencoded compressed tar
file are appende
Infrared behavior of interacting bosons at zero temperature
We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser
Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010
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