517 research outputs found
Coherent Control of Trapped Bosons
We investigate the quantum behavior of a mesoscopic two-boson system produced
by number-squeezing ultracold gases of alkali metal atoms. The quantum Poincare
maps of the wavefunctions are affected by chaos in those regions of the phase
space where the classical dynamics produces features that are comparable to
hbar. We also investigate the possibility for quantum control in the dynamics
of excitations in these systems. Controlled excitations are mediated by pulsed
signals that cause Stimulated Raman Adiabatic passage (STIRAP) from the ground
state to a state of higher energy. The dynamics of this transition is affected
by chaos caused by the pulses in certain regions of the phase space. A
transition to chaos can thus provide a method of controlling STIRAP.Comment: 17 figures, Appended a paragraph on section 1 and explained details
behind the hamiltonian on section
Shear band formation in granular media as a variational problem
Strain in sheared dense granular material is often localized in a narrow
region called shear band. Recent experiments in a modified Couette cell
provided localized shear flow in the bulk away from the confining walls. The
non-trivial shape of the shear band was measured as the function of the cell
geometry. First we present a geometric argument for narrow shear bands which
connects the function of their surface position with the shape in the bulk.
Assuming a simple dissipation mechanism we show that the principle of minimum
dissipation of energy provides a good description of the shape function.
Furthermore, we discuss the possibility and behavior of shear bands which are
detached from the free surface and are entirely covered in the bulk.Comment: 4 pages, 5 figures; minor changes, typos and journal-ref adde
Chaos assisted adiabatic passage
We study the exact dynamics underlying stimulated Raman adiabatic passage
(STIRAP) for a particle in a multi-level anharmonic system (the infinite
square-well) driven by two sequential laser pulses, each with constant carrier
frequency. In phase space regions where the laser pulses create chaos, the
particle can be transferred coherently into energy states different from those
predicted by traditional STIRAP. It appears that a transition to chaos can
provide a new tool to control the outcome of STIRAP
New algorithm for the computation of the partition function for the Ising model on a square lattice
A new and efficient algorithm is presented for the calculation of the
partition function in the Ising model. As an example, we use the
algorithm to obtain the thermal dependence of the magnetic spin susceptibility
of an Ising antiferromagnet for a square lattice with open boundary
conditions. The results agree qualitatively with the prediction of the Monte
Carlo simulations and with experimental data and they are better than the mean
field approach results. For the lattice, the algorithm reduces the
computation time by nine orders of magnitude.Comment: 7 pages, 3 figures, to appear in Int. J. Mod. Phys.
Entanglement and dynamics of spin-chains in periodically-pulsed magnetic fields: accelerator modes
We study the dynamics of a single excitation in a Heisenberg spin-chain
subjected to a sequence of periodic pulses from an external, parabolic,
magnetic field. We show that, for experimentally reasonable parameters, a pair
of counter-propagating coherent states are ejected from the centre of the
chain. We find an illuminating correspondence with the quantum time evolution
of the well-known paradigm of quantum chaos, the Quantum Kicked Rotor (QKR).
From this we can analyse the entanglement production and interpret the
ejected coherent states as a manifestation of so-called `accelerator modes' of
a classically chaotic system.Comment: 5 pages, 2 figures; minor corrections, tidied presentatio
Microcanonical Origin of the Maximum Entropy Principle for Open Systems
The canonical ensemble describes an open system in equilibrium with a heat
bath of fixed temperature. The probability distribution of such a system, the
Boltzmann distribution, is derived from the uniform probability distribution of
the closed universe consisting of the open system and the heat bath, by taking
the limit where the heat bath is much larger than the system of interest.
Alternatively, the Boltzmann distribution can be derived from the Maximum
Entropy Principle, where the Gibbs-Shannon entropy is maximized under the
constraint that the mean energy of the open system is fixed. To make the
connection between these two apparently distinct methods for deriving the
Boltzmann distribution, it is first shown that the uniform distribution for a
microcanonical distribution is obtained from the Maximum Entropy Principle
applied to a closed system. Then I show that the target function in the Maximum
Entropy Principle for the open system, is obtained by partial maximization of
Gibbs-Shannon entropy of the closed universe over the microstate probability
distributions of the heat bath. Thus, microcanonical origin of the Entropy
Maximization procedure for an open system, is established in a rigorous manner,
showing the equivalence between apparently two distinct approaches for deriving
the Boltzmann distribution. By extending the mathematical formalism to
dynamical paths, the result may also provide an alternative justification for
the principle of path entropy maximization as well.Comment: 12 pages, no figur
Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well
An infinite square well with a discontinuous step is one of the simplest
systems to exhibit non-Newtonian ray-splitting periodic orbits in the
semiclassical limit. This system is analyzed using both time-independent
perturbation theory (PT) and periodic-orbit theory and the approximate formulas
for the energy eigenvalues derived from these two approaches are compared. The
periodic orbits of the system can be divided into classes according to how many
times they reflect from the potential step. Different classes of orbits
contribute to different orders of PT. The dominant term in the second-order PT
correction is due to non-Newtonian orbits that reflect from the step exactly
once. In the limit in which PT converges the periodic-orbit theory results
agree with those of PT, but outside of this limit the periodic-orbit theory
gives much more accurate results for energies above the potential step.Comment: 22 pages, 2 figures, 2 tables, submitted to Physical Review
Isotropic AdS/CFT fireball
We study the AdS/CFT thermodynamics of the spatially isotropic counterpart of
the Bjorken similarity flow in d-dimensional Minkowski space with d>=3, and of
its generalisation to linearly expanding d-dimensional
Friedmann-Robertson-Walker cosmologies with arbitrary values of the spatial
curvature parameter k. The bulk solution is a nonstatic foliation of the
generalised Schwarzschild-AdS black hole with a horizon of constant curvature
k. The boundary matter is an expanding perfect fluid that satisfies the first
law of thermodynamics for all values of the temperature and the spatial
curvature, but it admits a description as a scale-invariant fluid in local
thermal equilibrium only when the inverse Hawking temperature is negligible
compared with the spatial curvature length scale. A Casimir-type term in the
holographic energy-momentum tensor is identified from the threshold of black
hole formation and is shown to take different forms for k>=0 and k<0.Comment: 20 pages. v3: typos corrected. Published versio
Global entangling properties of the coupled kicked tops
We study global entangling properties of the system of coupled kicked tops
testing various hypotheses and predictions concerning entanglement in quantum
chaotic systems. In order to analyze the averaged initial entanglement
production rate and the averaged asymptotic entanglement different ensembles of
initial product states are evolved. Two different ensembles with natural
probability distribution are considered: product states of independent
spin-coherent states and product states of arbitrary states. It appears that
the choice of either of these ensembles results in significantly different
averaged entanglement behavior. We investigate also a relation between the
averaged asymptotic entanglement and the mean entanglement of the eigenvectors
of an evolution operator. Lower bound on the averaged asymptotic entanglement
is derived, expressed in terms of the eigenvector entanglement.Comment: 11 pages, 7 figures, RevTe
- …