Generalized constructive tree weights

The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on symmetric tree weights which define a measure on the set of spanning trees of any connected graph. In this paper we generalize this method by defining new tree weights. They depend on the choice of a partition of a set of vertices of the graph, and when the partition is non-trivial, they are no longer symmetric under permutation of vertices. Nevertheless we prove they have the required positivity property to lead to a convergent LVE; in fact, we formulate this positivity property precisely for the first time. Our generalized tree weights are inspired by the Brydges-Battle-Federbush work on cluster expansions and could be particularly suited to the computation of connected functions in QFT. Several concrete examples are explicitly given.Comment: 22 pages, 2 figure

Impossibility of distant indirect measurement of the quantum Zeno effect

We critically study the possibility of quantum Zeno effect for indirect measurements. If the detector is prepared to detect the emitted signal from the core system, and the detector does not reflect the signal back to the core system, then we can prove the decay probability of the system is not changed by the continuous measurement of the signal and the quantum Zeno effect never takes place. This argument also applies to the quantum Zeno effect for accelerated two-level systems, unstable particle decay, etc.Comment: 14 pages, 2 figure

Semiclassical limit of the entanglement in closed pure systems

We discuss the semiclassical limit of the entanglement for the class of closed pure systems. By means of analytical and numerical calculations we obtain two main results: (i) the short-time entanglement does not depend on Planck's constant and (ii) the long-time entanglement increases as more semiclassical regimes are attained. On one hand, this result is in contrast with the idea that the entanglement should be destroyed when the macroscopic limit is reached. On the other hand, it emphasizes the role played by decoherence in the process of emergence of the classical world. We also found that, for Gaussian initial states, the entanglement dynamics may be described by an entirely classical entropy in the semiclassical limit.Comment: 8 pages, 2 figures (accepted for publication in Phys. Rev. A

Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

Making Single-Source Precursors of Ternary Semiconductors

A synthesis route has been developed for the commercial manufacture of single- source precursors of chalcopyrite semiconductor absorber layers of thin-film solar photovoltaic cells. A closely related class of single-source precursors of these semiconductors, and their synthesis routes, were reported in "Improved Single-Source Precursors for Solar-Cell Absorbers" (LEW-17445-1), NASA Tech Briefs, Vol. 31, No. 6 (June 2007), page 56. The present synthesis route is better suited to commercialization because it is simpler and involves the use of commercially available agents, yet offers the flexibility needed for synthesis of a variety of precursors. A single-source precursor of the type of interest here is denoted by the general formula L2M'(mu-ER)2M(ER)2, where L signifies a Lewis base; M signifies Al, In, or Ga; M' signifies Ag or Cu; R signifies an alkyl, aryl, silyl, or perfluorocarbon group; E signifies O, S, Se, or Te; and mu signifies a bridging ligand. This compound can be synthesized in a "one-pot" procedure from ingredients that are readily available from almost any chemical supplier. In a demonstration, the following synthesis was performed: Under anaerobic conditions, InCl3 was reacted with sodium ethanethiolate in methanol in a 1:4 molar ratio to afford the ionic stable intermediate compound Na+[In(SEt)4]- (where Et signifies ethyl group). After approximately 15 minutes, a heterogeneous solution of CuCl and the Lewis base PPh3 (where Ph signifies phenyl) in a 1:2 ratio in a mixture of CH3CN and CH2Cl2 was added directly to the freshly prepared Na+[In(SEt)4]-. After 24 hours, the reaction was essentially complete. The methanolic solution was concentrated, then the product was extracted with CH2Cl2, then the product was washed with dry ether and pentane. The product in its final form was a creamy white solid. Spectroscopic and elemental analysis confirmed that the product was (PPh3)2Cu(mu-SEt)2In(mu-SEt)2, which is known to be a precursor of the ternary semiconductor CuInS2

Geometric phases and quantum phase transitions

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed so-called "criticality of geometric phase", in which geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of geometric quantities may open attractive avenues and fruitful dialog between different scientific communities.Comment: Invited review article for IJMPB; material covered till June 2007; 10 page

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed "values" of measurements. This leads us to question the relevance of SID for treating observed decoherence effects.Comment: 11 pages, 4 figures. Final published versio

Atom-molecule coexistence and collective dynamics near a Feshbach resonance of cold fermions

Degenerate Fermi gas interacting with molecules near Feshbach resonance is unstable with respect to formation of a mixed state in which atoms and molecules coexist as a coherent superposition. Theory of this state is developed using a mapping to the Dicke model, treating molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of molecular field in the mixed state.Comment: 5 pages, 2 figure

Programming the cerebellum

It is argued that large-scale neural network simulations of cerebellar cortex and nuclei, based on realistic compartmental models of me major cell populations, are necessary before the problem of motor learning in the cerebellum can be solved, [HOUK et al.; SIMPSON et al.