Some Properties of the Elliptic Ordinary Differential Equation

In this paper, some properties of the elliptic ordinary differential equation, which can be used to find travelling wave solutions of nonlinear evolution equations, are given. - PACS: 03.65.Ge

Exact Jacobian Elliptic Function Solutions To The Double Sine-Gordon Equation

In this paper, two transformations are introduced to solve the double sine-Gordon equation by using knowledge of the elliptic equation and Jacobian elliptic functions. It is shown that different transformations can be applied to obtain more kinds of solutions to the double sine-Gordon equation. PACS: 03.65.Ge

Exact Solutions to Double and Triple Sinh-Gordon Equations

In this paper, two transformations are introduced to solve double sinh-Gordon equation and triple sinh-Gordon equation, respectively. It is shown that different transformations are required in order to obtain more kinds of solutions to different types of sinh-Gordon equations. - PACS: 03.65.Ge

Combinability of Travelling Wave Solutions to Nonlinear Evolution Equation

First, applying the Jacobi elliptic sine function expansion, basic travelling wave solutions of some nonlinear evolution equations are obtained. Second, according to the formal invariance of nonlinear evolution equations, the sister travelling wave solutions, which have the same wave speed as the basic ones, are derived. Finally, we show that a suitable linear combination of these two solutions results in a combined travelling wave solution, whose wave speed is different from those of the basic and sister travelling wave solutions. The combination of travelling wave solutions to nonlinear evolution equations must satisfy certain conditions. - PACS: 03.65.Ge.

Multiparticle Quantum Superposition and Stimulated Entanglement by Parity Selective Amplification of Entangled States

A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modem endeavor on quantum information and in the basic physics of entanglement. - Pacs: 03.65.Bz, 03.67.-a, 42.50.Ar, 89.70.+C

Entangled State Reconstruction of an Electron in the Penning Trap

We apply a tomographic method we have recently proposed to the reconstruction of the full entangled quantum state for the cyclotron and spin degrees of freedom of a trapped electron. Our numerical simulations show that the entangled state is accurately reconstructed. -Pacs: 03.65.

The Mean King's Problem: Spin

We show how one can ascertain the values of four mutually complementary observables of a spin-1 degree of freedom. -Pacs: 03.65.Bz

Locality or Non-Locality in Quantum Mechanics: Hidden Variables without "Spooky Action-at-a-Distance"

The folklore notion of the "Non-Locality of Quantum Mechanics" is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the "third" kind. Causal implications of such theories are explored. -Pacs: 03.65.Bz

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 'Schrödinger 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 Schrödinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrödinger cat. -Pacs: 03.65.Bz