Accuracy of Trace Formulas

Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.Comment: 20 pages, uuencoded and gzipped, 1 LaTex text file and 9 PS files for figure

Cyclic Identities Involving Jacobi Elliptic Functions. II

Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at $p$ equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities discussed earlier are derivable as special cases. Master identities are also obtained which lead to cyclic identities with alternating signs. We discuss an extension of our results to pure imaginary and complex shifts as well as to the ratio of Jacobi theta functions.Comment: 38 pages. Modified and includes more new identities. A shorter version of this will appear in J. Math. Phys. (May 2003

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Involvement of Serine Threonine Protein Kinase, PknL, from Mycobacterium Tuberculosis H37Rv in Starvation Response of Mycobacteria

The adaptation to nutrient depletion in bacteria involves a highly organized series of intracellular events that enable them to adapt to starvation conditions. The regulatory effect of serine threonine protein kinase, PknL, from Mycobacterium tuberculosis strain H37Rv was investigated under nutrient deprived conditions that simulate circumstances leading to latency. Recombinant PknL was expressed in Mycobacterium smegmatis strain mc2155 in its wild type and mutant forms. In vitro growth kinetics experiments revealed that clone expressing active PknL had a significant growth advantage under nutrient limiting conditions. Experiments were conducted to ascertain the in silico predictions of the involvement of PknL in regulating glutamine metabolism in mycobacteria. Furthermore, a role for PknL in cell wall biogenesis/cell division was shown by scanning electron microscopy

Recurrence of fidelity in near integrable systems

Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.Comment: 13 pages, 6 figure

Entanglement transitions in random definite particle states

Entanglement within qubits are studied for the subspace of definite particle states or definite number of up spins. A transition from an algebraic decay of entanglement within two qubits with the total number $N$ of qubits, to an exponential one when the number of particles is increased from two to three is studied in detail. In particular the probability that the concurrence is non-zero is calculated using statistical methods and shown to agree with numerical simulations. Further entanglement within a block of $m$ qubits is studied using the log-negativity measure which indicates that a transition from algebraic to exponential decay occurs when the number of particles exceeds $m$. Several algebraic exponents for the decay of the log-negativity are analytically calculated. The transition is shown to be possibly connected with the changes in the density of states of the reduced density matrix, which has a divergence at the zero eigenvalue when the entanglement decays algebraically.Comment: Substantially added content (now 24 pages, 5 figures) with a discussion of the possible mechanism for the transition. One additional author in this version that is accepted for publication in Phys. Rev.