Homoclinic orbits and chaos in a multimode laser

We show experimentally that under certain conditions the chaotic intensity dynamics of an optically pumped NH3 bidirectional ring laser could be well described in terms of Shil'nikov homoclinic orbits and chaos. We found that the mechanism that resulted in this kind of dynamics of the laser is the competition between effects caused by the mode interaction between the forward and the backward modes of the laser and by the intrinsic single-mode dynamics of the interacting modes. (C) 1997 Optical Society of America.

A defense of backwards in time causation models in quantum mechanics

This paper offers a defense of backwards in time causation models in quantum mechanics. Particular attention is given to Cramer's transactional account, which is shown to have the threefold virtue of solving the Bell problem, explaining the complex conjugate aspect of the quantum mechanical formalism, and explaining various quantum mysteries such as Schrodinger's cat. The question is therefore asked, why has this model not received more attention from physicists and philosophers? One objection given by physicists in assessing Cramer's theory was that it is not testable. This paper seeks to answer this concern by utilizing an argument that backwards causation models entail a fork theory of causal direction. From the backwards causation model together with the fork theory one can deduce empirical predictions. Finally, the objection that this strategy is questionable because of its appeal to philosophy is deflected.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

Quantum criticality

We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrodinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrodinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrodinger car.