Nonvacuum pseudoparticles, quantum tunneling and metastability

It is shown that nonvacuum pseudoparticles can account for quantum tunneling and metastability. In particular the saddle-point nature of the pseudoparticles is demonstrated, and the evaluation of path-integrals in their neighbourhood. Finally the relation between instantons and bounces is used to derive a result conjectured by Bogomolny and Fateyev.Comment: Latex, 16 pages, no figure

Instanton Approach to Josephson Tunneling between Trapped Condensates

An instanton method is proposed to investigate the quantum tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. We point out some intrinsic pathologies in the earlier treatments of other authors and make an effort to go beyond these very simple zero order models. The tunneling amplitude may be calculated in the Thomas-Fermi approximation and beyond it; we find it depends on the number of the trapped atoms, through the chemical potential. Some suggestions are given for the observation of the Josephson oscillation and the MQST.Comment: 20 pages, Revtex4, 6 figures. Abbreviated version accepted by Eur. Phys. J

Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = \epsilon_0 - 2\triangle\epsilon cos (s+\xi)\pi$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+\xi)\pi$ in disagreement with the suppression of tunneling (i.e. $\triangle\epsilon = 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangle\epsilon)/(\pi)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.Comment: 13 pages, LaTex, no figure

Once again: Instanton method vs. WKB

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam${\acute e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.Comment: 10 pages, no figures. References list revised according to JHE

Instanton Induced Tunneling Amplitude at Excited States with the LSZ Method

Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory and may be of importance in the study of macroscopic quantum phenomena in magnetic systems.Comment: 8 pages, LaTex, no figure

Gross-Ooguri Phase Transition at Zero and Finite Temperature: Two Circular Wilson Loop Case

In the context of $AdS/CFT$ correspondence the two Wilson loop correlator is examined at both zero and finite temperatures. On the basis of an entirely analytical approach we have found for Nambu-Goto strings the functional relation $d S_c^{(Reg)} / dL = 2 \pi k$ between Euclidean action $S_c$ and loop separation $L$ with integration constant $k$, which corresponds to the analogous formula for point-particles. The physical implications of this relation are explored in particular for the Gross-Ooguri phase transition at finite temperature.Comment: 13pages, 6 postscript figures, published version in JHE