Model tests of cluster separability in relativistic quantum mechanics

A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster separability, whereby symmetries and conservation laws that hold for a system of particles also hold for isolated subsystems. Cluster separability can be restored by means of a recursive construction using unitary transformations, but implementation is difficult in practice, and the quantitative extent to which the Bakamjian-Thomas approach violates cluster separability has never been tested. This paper provides such a test by means of a model of a scalar probe in a three-particle system for which (1) it is simple enough that there is a straightforward solution that satisfies Poincar\'e invariance and cluster separability, and (2) one can also apply the Bakamjian-Thomas approach. The difference between these calculations provides a measure of the size of the corrections from the Sokolov construction that are needed to restore cluster properties. Our estimates suggest that, in models based on nucleon degrees of freedom, the corrections that restore cluster properties are too small to effect calculations of observables.Comment: 13 pages, 15 figure

A quantum volume hologram

We propose a new scheme for parallel spatially multimode quantum memory for light. The scheme is based on counter-propagating quantum signal wave and strong classical reference wave, like in a classical volume hologram, and therefore can be called a quantum volume hologram. The medium for the hologram consists of a spatially extended ensemble of atoms placed in a magnetic field. The write-in and read-out of this quantum hologram is as simple as that of its classical counterpart and consists of a single pass illumination. In addition we show that the present scheme for a quantum hologram is less sensitive to diffraction and therefore is capable of achieving higher density of storage of spatial modes as compared to previous proposals. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.Comment: 8 pages, 2 figure

Thermally activated breakdown in a simple polymer model

We consider the thermally activated fragmentation of a homopolymer chain. In our simple model the dynamics of the intact chain is a Rouse one until a bond breaks and bond breakdown is considered as a first passage problem over a barrier to an absorbing boundary. Using the framework of the Wilemski-Fixman approximation we calculate activation times of individual bonds for free and grafted chains. We show that these times crucially depend on the length of the chain and the location of the bond yielding a minimum at the free chain ends. Theoretical findings are qualitatively confirmed by Brownian dynamics simulations

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that the equivalence holds for models that satisfy cluster separability. The generalized Bakamjian Thomas construction is used in most applications, even though it only satisfies cluster properties for systems of less than four particles. Different forms of dynamics are related by unitary transformations that remove interactions from some infinitesimal generators and introduce them to other generators. These unitary transformation must be interaction dependent, because they can be applied to a non-interacting generator and produce an interacting generator. This suggests that these transformations can generate complex many-body forces when used in many-body problems. It turns out that this is not the case. In all cases of interest the result of applying the unitary scattering equivalence results in representations that have simple relations, even though the unitary transformations are dynamical. This applies to many-body models as well as models with particle production. In all cases no new many-body operators are generated by the unitary scattering equivalences relating the different forms of dynamics. This makes it clear that the various calculations used in applications that emphasize one form of the dynamics over another are equivalent. Furthermore, explicit representations of the equivalent dynamical models in any form of dynamics are easily constructed. Where differences do appear is when electromagnetic probes are treated in the one-photon exchange approximation. This approximation is different in each of Dirac's forms of dynamics.Comment: 6 pages, no figure