Complex-classical mechanism of the tunnelling process in strongly coupled 1.5-dimensional barrier systems

Takahashi, Kin’ya; Ikeda, Kensuke S.

doi:10.1088/0305-4470/36/29/305

Cited by 35 publications

(72 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…dynamics is difficult [79][80][81][82][83][84][85][86][87][88] for the semiclassical methods, we avoid it by changing the form of the scalar potential. We checked that the model (3.1) is not chaotic, 11 i.e.…”

Section: Choosing the Potentialmentioning

confidence: 99%

Semiclassical description of soliton-antisoliton pair production in particle collisions

Demidov

Levkov

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

We develop a consistent semiclassical method to calculate the probability of topological soliton-antisoliton pair production in collisions of elementary particles. In our method one adds an auxiliary external field pulling the soliton and antisoliton in the opposite directions. This transforms the original scattering process into a Schwinger pair creation of the solitons induced by the particle collision. One describes the Schwinger process semiclassically and recovers the original scattering probability in the limit of vanishing external field. We illustrate the method in (1 + 1)-dimensional scalar field model where the suppression exponents of soliton-antisoliton production in the multiparticle and two-particle collisions are computed numerically.

show abstract

Section: Choosing the Potentialmentioning

confidence: 99%

Semiclassical description of soliton-antisoliton pair production in particle collisions

Demidov

Levkov

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…It is worth noting that formation of classically unstable "states" is a manifestation of general tunneling mechanism proposed recently in multidimensional quantum mechanics [16,20,22,12] and quantum field theory [18,23].…”

mentioning

confidence: 92%

Soliton-Antisoliton Pair Production in Particle Collisions

Demidov

Levkov

2011

Phys. Rev. Lett.

View full text Add to dashboard Cite

We propose general semiclassical method for computing the probability of soliton-antisoliton pair production in particle collisions. The method is illustrated by explicit numerical calculations in (1 + 1)-dimensional scalar field model. We find that the probability of the process is suppressed by an exponentially small factor which is almost constant at high energies.Ever since the discovery of topological solitons, a question remains [1, 2] of whether soliton-antisoliton (SA) pair can be produced at sizable probability in collision of two quantum particles. This process, which involves a transition from perturbative two-particle state to a nonperturbative state containing SA pair, eludes treatment by any of the standard methods. A general expectation [1,3] is that the probability of the process is exponentially suppressed in weak coupling regime,where E is the total energy, g ≪ 1 is the coupling constant. Indeed, crudely speaking, one can think of solitons as bound states of N S ∼ 1/g 2 particles [1]. Then the suppression (1) is due to multiparticle production [3]. In this Letter we propose general semiclassical method for computing the leading suppression exponent F (E) of the inclusive process "two particles → SA pair + particles." As a by-product, we calculate the exponent F N (E) of the same process with N initial particles. In our method the problem is deformed by introducing a small parameter δρ which turns the process of SA pair production into a well-known tunneling process. To the best of our knowledge, no method of this kind has ever been proposed before.For definiteness we consider (1 + 1)-dimensional scalar field theory with action [4]This model possesses topological solitons if the scalar potential V (φ) has a pair of degenerate minima φ − and φ + , see the inset in Fig. 1, solid line. Soliton and antisoliton solutions interpolate between the minima; their profiles are shown in Fig. 2a. An obstacle to the semiclassical description of SA pair production is related to the fact that soliton and antisoliton attract each other and annihilate classically into N SA ∼ 1/g 2 particles. Thus, there is no potential barrier separating SA pair from the particle sector and the process under study cannot be treated as potential tunneling.We get around this obstacle by introducing the potential barrier between SA pair and perturbative states. Namely, we add negative energy density (−δρ) to the vacuum φ + , see dashed line in the inset in Fig. 1. This turns φ − and φ + into false and true vacua, respectively; the process of SA pair production is now interpreted as false vacuum decay [5] induced by particle collisions. The latter is a well-studied tunneling process [6,7]. In the end of calculation we will take the limit δρ → 0.The height of the potential barrier between the false and true vacua is given by the energy E cb of the critical bubble [5] -unstable static solution "sitting" on top of the barrier. The pressure δρ inside this bubble is balanced by the soliton-antisoliton attraction. Let us estimate the criti...

show abstract

“…In other words, the singularities of the trajectory control its asymptotic nature in the complexified phase space. Thus, we would like to first discuss the crucial role of the singularities of the classical trajectory for the static barrier system, which was first investigated by Miller et al 7,23) Although an explicit result is not shown here, 9,12,15) in the limit of = 0, we can easily obtain a classical solution by integrating the classical equation of motion. From the solution, the positions of the singularities are easily estimated.…”

Section: Static Barriermentioning

confidence: 93%

“…Furthermore, if the movement of the singularities depending on the initial condition becomes significantly large, the topology of the integration path might suffer a serious deformation. 9,10,12) They, therefore, play an important role to understand tunneling phenomena in continuous-time systems. We would like to stress this problem in the present paper with taking the periodically perturbed barrier system as a concrete example.…”

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

Complex-Domain Semiclassical Theory and Periodically Perturbed Barrier Tunneling Problems

Takahashi

Ikeda

2003

J. Phys. Soc. Jpn.

View full text Add to dashboard Cite

In recent papers we demonstrated a new class of barrier tunneling phenomena which can be observed in periodically driven one dimensional barrier systems (i.e., 1.5D barrier tunneling systems). In such systems the tunneling component is in general accompanied by remarkable interference fringe patterns as the perturbation strength exceeds a certain characteristic value. Such a phenomenon is quite general and is not restricted to periodically driven 1D systems, and it may be also observed in intrinsic two dimensional autonomous systems. The complex-domain semiclassical theory developed by ourselves was applied to the problem, and we succeeded in reconstructing every detail of the fringed tunneling wavefunction only by using the complexified classical tunneling trajectories. This fact greatly motivates us to investigate the mechanism of the tunneling in terms of "classical mechanics." The later part of the present paper is devoted to asserting the generality of the "classical mechanism" of the fringed tunneling. We develop detailed semiclassical analyses in the complex domain and demonstrate that the key trajectories contributing to the fringed tunneling are quite different from the instanton-like trajectories, which works only in unperturbed or weakly-perturbed regimes. Indeed, such trajectories are traveling in the complex phase space being guided by the complexified stable and unstable manifolds which exhibit heteroclinic-like entanglement with the incoming wave manifolds.

show abstract

Complex-classical mechanism of the tunnelling process in strongly coupled 1.5-dimensional barrier systems

Cited by 35 publications

References 61 publications

Semiclassical description of soliton-antisoliton pair production in particle collisions

Semiclassical description of soliton-antisoliton pair production in particle collisions

Soliton-Antisoliton Pair Production in Particle Collisions

Complex-Domain Semiclassical Theory and Periodically Perturbed Barrier Tunneling Problems

Contact Info

Product

Resources

About