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 $S=\pm 1$ 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 $8\times 8$ 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 $8\times 8$ 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