1,182 research outputs found
Quantum quenches in the many-body localized phase
Many-body localized (MBL) systems are characterized by the absence of
transport and thermalization, and therefore cannot be described by conventional
statistical mechanics. In this paper, using analytic arguments and numerical
simulations, we study the behaviour of local observables in an isolated MBL
system following a quantum quench. For the case of a global quench, we find
that the local observables reach stationary, highly non-thermal values at long
times as a result of slow dephasing characteristic of the MBL phase. These
stationary values retain the local memory of the initial state due to the
existence of local integrals of motion in the MBL phase. The temporal
fluctuations around stationary values exhibit universal power-law decay in
time, with an exponent set by the localization length and the diagonal entropy
of the initial state. Such a power-law decay holds for any local observable and
is related to the logarithmic in time growth of entanglement in the MBL phase.
This behaviour distinguishes the MBL phase from both the Anderson insulator
(where no stationary state is reached), and from the ergodic phase (where
relaxation is expected to be exponential). For the case of a local quench, we
also find a power-law approach of local observables to their stationary values
when the system is prepared in a mixed state. Quench protocols considered in
this paper can be naturally implemented in systems of ultra cold atoms in
disordered optical lattices, and the behaviour of local observables provides a
direct experimental signature of many-body localization.Comment: 11 pages, 4 figure
Coarse Grained Computations for a Micellar System
We establish, through coarse-grained computation, a connection between
traditional, continuum numerical algorithms (initial value problems as well as
fixed point algorithms) and atomistic simulations of the Larson model of
micelle formation. The procedure hinges on the (expected) evolution of a few
slow, coarse-grained mesoscopic observables of the MC simulation, and on
(computational) time scale separation between these and the remaining "slaved",
fast variables. Short bursts of appropriately initialized atomistic simulation
are used to estimate the (coarse-grained, deterministic) local dynamics of the
evolution of the observables. These estimates are then in turn used to
accelerate the evolution to computational stationarity through traditional
continuum algorithms (forward Euler integration, Newton-Raphson fixed point
computation). This "equation-free" framework, bypassing the derivation of
explicit, closed equations for the observables (e.g. equations of state) may
provide a computational bridge between direct atomistic / stochastic simulation
and the analysis of its macroscopic, system-level consequences
Coarse-Grained Kinetic Computations for Rare Events: Application to Micelle Formation
We discuss a coarse-grained approach to the computation of rare events in the
context of grand canonical Monte Carlo (GCMC) simulations of self-assembly of
surfactant molecules into micelles. The basic assumption is that the {\it
computational} system dynamics can be decomposed into two parts -- fast (noise)
and slow (reaction coordinates) dynamics, so that the system can be described
by an effective, coarse grained Fokker-Planck (FP) equation. While such an
assumption may be valid in many circumstances, an explicit form of FP equation
is not always available. In our computations we bypass the analytic derivation
of such an effective FP equation. The effective free energy gradient and the
state-dependent magnitude of the random noise, which are necessary to formulate
the effective Fokker-Planck equation, are obtained from ensembles of short
bursts of microscopic simulations {\it with judiciously chosen initial
conditions}. The reaction coordinate in our micelle formation problem is taken
to be the size of a cluster of surfactant molecules. We test the validity of
the effective FP description in this system and reconstruct a coarse-grained
free energy surface in good agreement with full-scale GCMC simulations. We also
show that, for very small clusters, the cluster size seizes to be a good
reaction coordinate for a one-dimensional effective description. We discuss
possible ways to improve the current model and to take higher-dimensional
coarse-grained dynamics into account
Conformal Invariance and Shape-Dependent Conductance of Graphene Samples
For a sample of an arbitrary shape, the dependence of its conductance on the
longitudinal and Hall conductivity is identical to that of a rectangle. We use
analytic results for a conducting rectangle, combined with the semicircle model
for transport coefficients, to study properties of the monolayer and bilayer
graphene. A conductance plateau centered at the neutrality point, predicted for
square geometry, is in agreement with recent experiments. For rectangular
geometry, the conductance exhibits maxima at the densities of compressible
quantum Hall states for wide samples, and minima for narrow samples. The
positions and relative sizes of these features are different in the monolayer
and bilayer cases, indicating that the conductance can be used as a tool for
sample diagnostic.Comment: 9 pages, 6 figure
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Polygonization of carbon nanotubes
We use a multiscale procedure to derive a simple continuum model of
multiwalled carbon nanotubes that takes into account both strong covalent bonds
within graphene layers and weak bonds between atoms in different layers. The
model predicts polygonization of crossections of large multiwalled nanotubes as
a consequence of their curvature-induced turbostratic structure
Piperazine-based N4-type 16-membered macroheterocycles and their nickel(II) complexes
Square-planar diamagnetic nickel(II) complexes 5a and 5b containing 16-membered diamino-diimino ligands were prepared from the corresponding open-chain complexes 2a and 2b via condensation with o-phthalic dialdehyde in methanol. The solid-state structure of the starting complex 2b revealed the cisoid conformation of aryl groups compared to the transoid one found in the case of 2a. At the same time, the cisoid conformation is not retained in acetone solution: rather, the tert-Bu-substituted complex 2b was fully transformed into the trans form whereas its analogue 2aexhibits both cis and transforms in acetone solution. The cisoid conformation was also observed for the cyclic structures 5a and 5b by X-ray analysis and VT NMR experiments. The borohydride reduction of 5a with subsequent cyanide-assisted removal of nickel led to a new 16-membered tetraazamacrocycle 6. Its X-ray structure showed a cisoid conformation supported by two intramolecular hydrogen bonds that was also sustained in solution. VT NMR experiments revealed the degenerative interconvertion of a macrocycle with activation energy ca. 41.9±0.8 kJ/mol
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